{
  "schema": "stable-curve-teaching-native-corpus/v1",
  "observed_utc": "2026-10-05T20:02:20.872334+00:00",
  "scope": "Full exact native proof chapters and direct native dependencies referenced in the required proof scopes; ordinary foundations retained and not newly certified.",
  "full_transitive_foundations_audited": false,
  "compiled": false,
  "files": [
    {
      "package_path": "native/COPYING",
      "sha256": "4b2c8fc390f802cd92f0622dc00a708a588bec54d0145d2ee135d6d7672bfe85",
      "bytes": 20404,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/COPYING",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/COPYING",
      "role": "original build support, licence or provenance",
      "terms": "Preserve original file notices; COPYING is the unmodified GFDL legal text, documentation preserves its actual source provenance.",
      "actual_read_scope": "Source/support identity and applicable notices; no extra mathematical closure asserted.",
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.910599+00:00"
    },
    {
      "package_path": "native/PROVENANCE.md",
      "sha256": "720213712ef43614e42a79feee1bb540a326a6aba81a179533593c33d4123122",
      "bytes": 17610,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/PROVENANCE.md",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/PROVENANCE.md",
      "role": "original build support, licence or provenance",
      "terms": "Preserve original file notices; COPYING is the unmodified GFDL legal text, documentation preserves its actual source provenance.",
      "actual_read_scope": "Source/support identity and applicable notices; no extra mathematical closure asserted.",
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:36.203606+00:00"
    },
    {
      "package_path": "native/README.md",
      "sha256": "eea487dda718bc94faef3d343515eebe465cb39d19b098aa08f36f0d01cb2400",
      "bytes": 16925,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/README.md",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/README.md",
      "role": "original build support, licence or provenance",
      "terms": "Preserve original file notices; COPYING is the unmodified GFDL legal text, documentation preserves its actual source provenance.",
      "actual_read_scope": "Source/support identity and applicable notices; no extra mathematical closure asserted.",
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:36.487837+00:00"
    },
    {
      "package_path": "native/algebra.tex",
      "sha256": "2789bc69c75351b0840206c4bc7ec6db0a7cc7765e1f7ecc1cfa671ea80d64cd",
      "bytes": 1808110,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/algebra.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/algebra.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "algebra-definition-analytically-unramified",
        "algebra-example-spec-kxy",
        "algebra-lemma-CM-over-regular-flat",
        "algebra-lemma-Noetherian-complete-local-Nagata",
        "algebra-lemma-analytically-unramified-easy",
        "algebra-lemma-apply-grothendieck",
        "algebra-lemma-complete-local-Noetherian-domain-finite-over-regular",
        "algebra-lemma-completion-Noetherian",
        "algebra-lemma-completion-faithfully-flat",
        "algebra-lemma-completion-finite-extension",
        "algebra-lemma-completion-flat",
        "algebra-lemma-criterion-normal",
        "algebra-lemma-derivative-zero-pth-power",
        "algebra-lemma-descend-properties-modules",
        "algebra-lemma-descent-Rk",
        "algebra-lemma-descent-Sk",
        "algebra-lemma-descent-normal",
        "algebra-lemma-descent-regular",
        "algebra-lemma-dim-affine-space",
        "algebra-lemma-dimension-base-fibre-total",
        "algebra-lemma-exact-sequence-NL",
        "algebra-lemma-finite-projective",
        "algebra-lemma-finite-projective-descends",
        "algebra-lemma-generically-finite",
        "algebra-lemma-hathat-finitely-generated",
        "algebra-lemma-integral-under-field",
        "algebra-lemma-local-nagata-domain-analytically-unramified",
        "algebra-lemma-nagata-in-reduced-finite-type-finite-integral-closure",
        "algebra-lemma-regular-domain",
        "algebra-lemma-regular-graded",
        "algebra-lemma-regular-mod-x",
        "algebra-lemma-regular-normal",
        "algebra-lemma-regular-ring-CM",
        "algebra-lemma-separable-smooth",
        "algebra-lemma-support-point",
        "algebra-proposition-dimension",
        "algebra-proposition-ubiquity-nagata",
        "algebra-section-blow-up",
        "algebra-section-completion-noetherian",
        "algebra-section-going-up"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4644,
          "label": "algebra-lemma-integral-under-field"
        },
        {
          "caller": "models.tex",
          "line": 5140,
          "label": "algebra-lemma-regular-ring-CM"
        },
        {
          "caller": "models.tex",
          "line": 5142,
          "label": "algebra-lemma-separable-smooth"
        },
        {
          "caller": "models.tex",
          "line": 5369,
          "label": "algebra-lemma-regular-ring-CM"
        },
        {
          "caller": "models.tex",
          "line": 5371,
          "label": "algebra-lemma-separable-smooth"
        },
        {
          "caller": "resolve.tex",
          "line": 321,
          "label": "algebra-lemma-exact-sequence-NL"
        },
        {
          "caller": "resolve.tex",
          "line": 494,
          "label": "algebra-lemma-regular-graded"
        },
        {
          "caller": "resolve.tex",
          "line": 520,
          "label": "algebra-lemma-regular-domain"
        },
        {
          "caller": "resolve.tex",
          "line": 533,
          "label": "algebra-lemma-dim-affine-space"
        },
        {
          "caller": "resolve.tex",
          "line": 535,
          "label": "algebra-lemma-regular-mod-x"
        },
        {
          "caller": "resolve.tex",
          "line": 869,
          "label": "algebra-lemma-support-point"
        },
        {
          "caller": "resolve.tex",
          "line": 2005,
          "label": "algebra-lemma-regular-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 2142,
          "label": "algebra-lemma-derivative-zero-pth-power"
        },
        {
          "caller": "resolve.tex",
          "line": 2765,
          "label": "algebra-lemma-hathat-finitely-generated"
        },
        {
          "caller": "resolve.tex",
          "line": 2797,
          "label": "algebra-lemma-completion-faithfully-flat"
        },
        {
          "caller": "resolve.tex",
          "line": 2799,
          "label": "algebra-lemma-descent-regular"
        },
        {
          "caller": "resolve.tex",
          "line": 2868,
          "label": "algebra-lemma-completion-flat"
        },
        {
          "caller": "resolve.tex",
          "line": 2901,
          "label": "algebra-definition-analytically-unramified"
        },
        {
          "caller": "resolve.tex",
          "line": 2911,
          "label": "algebra-lemma-analytically-unramified-easy"
        },
        {
          "caller": "resolve.tex",
          "line": 2929,
          "label": "algebra-lemma-completion-faithfully-flat"
        },
        {
          "caller": "resolve.tex",
          "line": 2932,
          "label": "algebra-section-going-up"
        },
        {
          "caller": "resolve.tex",
          "line": 2938,
          "label": "algebra-lemma-generically-finite"
        },
        {
          "caller": "resolve.tex",
          "line": 2959,
          "label": "algebra-lemma-Noetherian-complete-local-Nagata"
        },
        {
          "caller": "resolve.tex",
          "line": 2963,
          "label": "algebra-lemma-Noetherian-complete-local-Nagata"
        },
        {
          "caller": "resolve.tex",
          "line": 2964,
          "label": "algebra-lemma-nagata-in-reduced-finite-type-finite-integral-closure"
        },
        {
          "caller": "resolve.tex",
          "line": 2968,
          "label": "algebra-lemma-descend-properties-modules"
        },
        {
          "caller": "resolve.tex",
          "line": 2991,
          "label": "algebra-lemma-descent-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 2996,
          "label": "algebra-lemma-Noetherian-complete-local-Nagata"
        },
        {
          "caller": "resolve.tex",
          "line": 3014,
          "label": "algebra-lemma-descent-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 3077,
          "label": "algebra-lemma-local-nagata-domain-analytically-unramified"
        },
        {
          "caller": "resolve.tex",
          "line": 3146,
          "label": "algebra-lemma-derivative-zero-pth-power"
        },
        {
          "caller": "resolve.tex",
          "line": 3258,
          "label": "algebra-section-blow-up"
        },
        {
          "caller": "resolve.tex",
          "line": 3301,
          "label": "algebra-example-spec-kxy"
        },
        {
          "caller": "resolve.tex",
          "line": 3303,
          "label": "algebra-lemma-dim-affine-space"
        },
        {
          "caller": "resolve.tex",
          "line": 3555,
          "label": "algebra-lemma-descent-regular"
        },
        {
          "caller": "resolve.tex",
          "line": 3577,
          "label": "algebra-lemma-completion-flat"
        },
        {
          "caller": "resolve.tex",
          "line": 3579,
          "label": "algebra-lemma-criterion-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 3586,
          "label": "algebra-lemma-apply-grothendieck"
        },
        {
          "caller": "resolve.tex",
          "line": 3595,
          "label": "algebra-lemma-descent-Sk"
        },
        {
          "caller": "resolve.tex",
          "line": 3602,
          "label": "algebra-lemma-dimension-base-fibre-total"
        },
        {
          "caller": "resolve.tex",
          "line": 3606,
          "label": "algebra-lemma-descent-Rk"
        },
        {
          "caller": "resolve.tex",
          "line": 3639,
          "label": "algebra-lemma-completion-finite-extension"
        },
        {
          "caller": "resolve.tex",
          "line": 3680,
          "label": "algebra-lemma-descent-regular"
        },
        {
          "caller": "resolve.tex",
          "line": 3755,
          "label": "algebra-proposition-ubiquity-nagata"
        },
        {
          "caller": "resolve.tex",
          "line": 3843,
          "label": "algebra-proposition-ubiquity-nagata"
        },
        {
          "caller": "resolve.tex",
          "line": 3858,
          "label": "algebra-lemma-complete-local-Noetherian-domain-finite-over-regular"
        },
        {
          "caller": "resolve.tex",
          "line": 3973,
          "label": "algebra-lemma-CM-over-regular-flat"
        },
        {
          "caller": "resolve.tex",
          "line": 3976,
          "label": "algebra-lemma-criterion-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 3977,
          "label": "algebra-lemma-descent-regular"
        },
        {
          "caller": "resolve.tex",
          "line": 4452,
          "label": "algebra-lemma-completion-Noetherian"
        },
        {
          "caller": "resolve.tex",
          "line": 4455,
          "label": "algebra-proposition-dimension"
        },
        {
          "caller": "more-morphisms.tex",
          "line": 22450,
          "label": "algebra-lemma-finite-projective"
        },
        {
          "caller": "more-morphisms.tex",
          "line": 22454,
          "label": "algebra-section-completion-noetherian"
        },
        {
          "caller": "more-morphisms.tex",
          "line": 22455,
          "label": "algebra-lemma-finite-projective-descends"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.811691+00:00"
    },
    {
      "package_path": "native/algebraic.tex",
      "sha256": "08445616a6bb3555d25b8b589daf3faaf68e8ca5aa0bd7ce85e6332740d7dfcb",
      "bytes": 97496,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/algebraic.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/algebraic.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "algebraic-lemma-characterize-representable-by-space",
        "algebraic-lemma-criterion-map-representable-spaces-fibred-in-groupoids",
        "algebraic-lemma-representable-morphism-to-algebraic",
        "algebraic-section-morphisms-representable-by-algebraic-spaces",
        "algebraic-section-representable-morphism",
        "algebraic-section-representable-properties"
      ],
      "required_by": [
        {
          "caller": "quot.tex",
          "line": 2803,
          "label": "algebraic-lemma-representable-morphism-to-algebraic"
        },
        {
          "caller": "quot.tex",
          "line": 3247,
          "label": "algebraic-section-representable-morphism"
        },
        {
          "caller": "quot.tex",
          "line": 3248,
          "label": "algebraic-section-morphisms-representable-by-algebraic-spaces"
        },
        {
          "caller": "quot.tex",
          "line": 3249,
          "label": "algebraic-section-representable-properties"
        },
        {
          "caller": "quot.tex",
          "line": 3257,
          "label": "algebraic-lemma-criterion-map-representable-spaces-fibred-in-groupoids"
        },
        {
          "caller": "quot.tex",
          "line": 3341,
          "label": "algebraic-lemma-representable-morphism-to-algebraic"
        },
        {
          "caller": "quot.tex",
          "line": 3346,
          "label": "algebraic-lemma-characterize-representable-by-space"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.953066+00:00"
    },
    {
      "package_path": "native/bibliography.tex",
      "sha256": "417f904daa77cc42e74d99f4f5647f5cb79c14cc15631a43770a97f432aa1243",
      "bytes": 165,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/bibliography.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/bibliography.tex",
      "role": "original build support, licence or provenance",
      "terms": "Preserve original file notices; COPYING is the unmodified GFDL legal text, documentation preserves its actual source provenance.",
      "actual_read_scope": "Source/support identity and applicable notices; no extra mathematical closure asserted.",
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.910359+00:00"
    },
    {
      "package_path": "native/bootstrap.tex",
      "sha256": "fd2b99bb99e4ab6ea55491ca819e4964097dc504403b5b306c455614d5ff9f27",
      "bytes": 96614,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/bootstrap.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/bootstrap.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "bootstrap-theorem-final-bootstrap"
      ],
      "required_by": [
        {
          "caller": "quot.tex",
          "line": 3331,
          "label": "bootstrap-theorem-final-bootstrap"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.966912+00:00"
    },
    {
      "package_path": "native/chow.tex",
      "sha256": "0522bd9a5934c5a65d9fccd651c77c1e012d9937aec49737d0b7fea6190dc001",
      "bytes": 688563,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/chow.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/chow.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "chow-definition-cycle-associated-to-closed-subscheme"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4385,
          "label": "chow-definition-cycle-associated-to-closed-subscheme"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.883193+00:00"
    },
    {
      "package_path": "native/coherent.tex",
      "sha256": "d219cba93ea84084a35be94b3454e316c54037af0bfbf795a1824543d9440bbc",
      "bytes": 357482,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/coherent.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/coherent.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "coherent-lemma-chow-Noetherian",
        "coherent-lemma-coherent-support-dimension-0",
        "coherent-lemma-cohomology-projective-space-over-ring",
        "coherent-lemma-flat-base-change-cohomology",
        "coherent-lemma-formal-functions-stalk",
        "coherent-lemma-higher-direct-images-zero-above-dimension-fibre",
        "coherent-lemma-kill-by-twisting",
        "coherent-lemma-power-ideal-kills-sheaf",
        "coherent-lemma-proper-over-affine-cohomology-finite",
        "coherent-lemma-recover-tail-graded-module",
        "coherent-lemma-relative-affine-cohomology",
        "coherent-lemma-vanishing-nr-affines",
        "coherent-lemma-vanshing-gives-ample",
        "coherent-proposition-proper-pushforward-coherent",
        "coherent-theorem-formal-functions"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 5790,
          "label": "coherent-lemma-power-ideal-kills-sheaf"
        },
        {
          "caller": "models.tex",
          "line": 5813,
          "label": "coherent-theorem-formal-functions"
        },
        {
          "caller": "curves.tex",
          "line": 3769,
          "label": "coherent-lemma-flat-base-change-cohomology"
        },
        {
          "caller": "resolve.tex",
          "line": 595,
          "label": "coherent-lemma-vanishing-nr-affines"
        },
        {
          "caller": "resolve.tex",
          "line": 604,
          "label": "coherent-lemma-kill-by-twisting"
        },
        {
          "caller": "resolve.tex",
          "line": 622,
          "label": "coherent-lemma-cohomology-projective-space-over-ring"
        },
        {
          "caller": "resolve.tex",
          "line": 624,
          "label": "coherent-lemma-relative-affine-cohomology"
        },
        {
          "caller": "resolve.tex",
          "line": 653,
          "label": "coherent-lemma-recover-tail-graded-module"
        },
        {
          "caller": "resolve.tex",
          "line": 695,
          "label": "coherent-lemma-cohomology-projective-space-over-ring"
        },
        {
          "caller": "resolve.tex",
          "line": 1712,
          "label": "coherent-lemma-higher-direct-images-zero-above-dimension-fibre"
        },
        {
          "caller": "resolve.tex",
          "line": 1721,
          "label": "coherent-lemma-coherent-support-dimension-0"
        },
        {
          "caller": "resolve.tex",
          "line": 2259,
          "label": "coherent-lemma-higher-direct-images-zero-above-dimension-fibre"
        },
        {
          "caller": "resolve.tex",
          "line": 2456,
          "label": "coherent-lemma-kill-by-twisting"
        },
        {
          "caller": "resolve.tex",
          "line": 2866,
          "label": "coherent-lemma-flat-base-change-cohomology"
        },
        {
          "caller": "resolve.tex",
          "line": 3541,
          "label": "coherent-lemma-proper-over-affine-cohomology-finite"
        },
        {
          "caller": "resolve.tex",
          "line": 3628,
          "label": "coherent-lemma-proper-over-affine-cohomology-finite"
        },
        {
          "caller": "resolve.tex",
          "line": 3649,
          "label": "coherent-lemma-flat-base-change-cohomology"
        },
        {
          "caller": "resolve.tex",
          "line": 3659,
          "label": "coherent-lemma-flat-base-change-cohomology"
        },
        {
          "caller": "resolve.tex",
          "line": 4500,
          "label": "coherent-lemma-formal-functions-stalk"
        },
        {
          "caller": "resolve.tex",
          "line": 4511,
          "label": "coherent-lemma-power-ideal-kills-sheaf"
        },
        {
          "caller": "resolve.tex",
          "line": 4604,
          "label": "coherent-lemma-flat-base-change-cohomology"
        },
        {
          "caller": "resolve.tex",
          "line": 4688,
          "label": "coherent-lemma-vanshing-gives-ample"
        },
        {
          "caller": "resolve.tex",
          "line": 4841,
          "label": "coherent-lemma-chow-Noetherian"
        },
        {
          "caller": "more-morphisms.tex",
          "line": 22447,
          "label": "coherent-proposition-proper-pushforward-coherent"
        },
        {
          "caller": "more-morphisms.tex",
          "line": 22457,
          "label": "coherent-lemma-formal-functions-stalk"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.372671+00:00"
    },
    {
      "package_path": "native/cohomology.tex",
      "sha256": "591f19389ef437ddfe05b00214064dda31aa225d44b019a779f9f98f6ec0b4de",
      "bytes": 539704,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/cohomology.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/cohomology.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "cohomology-lemma-Leray",
        "cohomology-lemma-h1-extensions",
        "cohomology-lemma-projection-formula",
        "cohomology-lemma-quasi-separated-cohomology-colimit",
        "cohomology-proposition-vanishing-Noetherian"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 5170,
          "label": "cohomology-proposition-vanishing-Noetherian"
        },
        {
          "caller": "curves.tex",
          "line": 3780,
          "label": "cohomology-proposition-vanishing-Noetherian"
        },
        {
          "caller": "resolve.tex",
          "line": 643,
          "label": "cohomology-lemma-quasi-separated-cohomology-colimit"
        },
        {
          "caller": "resolve.tex",
          "line": 1488,
          "label": "cohomology-lemma-h1-extensions"
        },
        {
          "caller": "resolve.tex",
          "line": 1726,
          "label": "cohomology-lemma-Leray"
        },
        {
          "caller": "resolve.tex",
          "line": 2266,
          "label": "cohomology-lemma-quasi-separated-cohomology-colimit"
        },
        {
          "caller": "more-morphisms.tex",
          "line": 22435,
          "label": "cohomology-lemma-projection-formula"
        },
        {
          "caller": "more-morphisms.tex",
          "line": 22480,
          "label": "cohomology-proposition-vanishing-Noetherian"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.739907+00:00"
    },
    {
      "package_path": "native/constructions.tex",
      "sha256": "cfebd4fe907082611f346447285454e473fc35f68ed3f10494c412547cf80fad",
      "bytes": 209942,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/constructions.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/constructions.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "constructions-lemma-base-change-map-proj",
        "constructions-lemma-globally-generated-omega-twist-1",
        "constructions-lemma-proj-quasi-compact",
        "constructions-lemma-proj-separated",
        "constructions-lemma-projective-space",
        "constructions-lemma-surjective-graded-rings-generated-degree-1-map-proj"
      ],
      "required_by": [
        {
          "caller": "resolve.tex",
          "line": 482,
          "label": "constructions-lemma-surjective-graded-rings-generated-degree-1-map-proj"
        },
        {
          "caller": "resolve.tex",
          "line": 497,
          "label": "constructions-lemma-base-change-map-proj"
        },
        {
          "caller": "resolve.tex",
          "line": 590,
          "label": "constructions-lemma-proj-quasi-compact"
        },
        {
          "caller": "resolve.tex",
          "line": 592,
          "label": "constructions-lemma-proj-separated"
        },
        {
          "caller": "resolve.tex",
          "line": 2298,
          "label": "constructions-lemma-globally-generated-omega-twist-1"
        },
        {
          "caller": "resolve.tex",
          "line": 4714,
          "label": "constructions-lemma-projective-space"
        },
        {
          "caller": "resolve.tex",
          "line": 4729,
          "label": "constructions-lemma-projective-space"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:33.178030+00:00"
    },
    {
      "package_path": "native/curves.tex",
      "sha256": "8881792e2c8e0977e778827b852b010af11f054f98866c61beb5dffe70515ebe",
      "bytes": 271533,
      "source_id": "AGGS-NATIVE-STACKS-565B-CURVES-TEX",
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/curves.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/curves.tex",
      "role": "native proof body",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": [
        "smooth Picard torsion visibility and reduced-normalization/gluing torsion proof, lines3398-3621",
        "arbitrary-field torsion bound, lines3748-3802"
      ],
      "proof_locators": [
        "curves-lemma-torsion-picard-becomes-visible/0CDU",
        "normalization/gluing torsion and multicross equality in Section53"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4668,
          "label": "curves-definition-genus"
        },
        {
          "caller": "models.tex",
          "line": 5223,
          "label": "curves-section-genus-geometric-genus"
        },
        {
          "caller": "models.tex",
          "line": 5250,
          "label": "curves-lemma-genus-base-change"
        },
        {
          "caller": "models.tex",
          "line": 5253,
          "label": "curves-lemma-genus-normalization"
        },
        {
          "caller": "models.tex",
          "line": 5298,
          "label": "curves-lemma-bound-geometric-genus"
        },
        {
          "caller": "models.tex",
          "line": 5311,
          "label": "curves-lemma-bound-geometric-genus-curve"
        },
        {
          "caller": "models.tex",
          "line": 5349,
          "label": "curves-lemma-genus-normalization"
        },
        {
          "caller": "models.tex",
          "line": 5383,
          "label": "curves-lemma-genus-normalization"
        },
        {
          "caller": "models.tex",
          "line": 6251,
          "label": "curves-lemma-genus-zero"
        },
        {
          "caller": "models.tex",
          "line": 6255,
          "label": "curves-lemma-smooth-plane-curve-point-over-separable"
        },
        {
          "caller": "models.tex",
          "line": 6270,
          "label": "curves-proposition-projective-line"
        },
        {
          "caller": "models.tex",
          "line": 6313,
          "label": "curves-lemma-torsion-picard-becomes-visible"
        },
        {
          "caller": "models.tex",
          "line": 6398,
          "label": "curves-lemma-bound-torsion-simple"
        },
        {
          "caller": "models.tex",
          "line": 6403,
          "label": "curves-lemma-bound-geometric-genus"
        },
        {
          "caller": "models.tex",
          "line": 6404,
          "label": "curves-lemma-bound-geometric-genus-curve"
        },
        {
          "caller": "models.tex",
          "line": 6425,
          "label": "curves-lemma-genus-normalization"
        },
        {
          "caller": "models.tex",
          "line": 6438,
          "label": "curves-proposition-projective-line"
        },
        {
          "caller": "models.tex",
          "line": 6451,
          "label": "curves-proposition-torsion-picard-reduced-proper"
        },
        {
          "caller": "models.tex",
          "line": 6457,
          "label": "curves-lemma-multicross-gorenstein-is-nodal"
        },
        {
          "caller": "models.tex",
          "line": 6466,
          "label": "curves-lemma-torsion-picard-smooth-projective"
        },
        {
          "caller": "models.tex",
          "line": 6494,
          "label": "curves-lemma-rhe"
        },
        {
          "caller": "models.tex",
          "line": 6530,
          "label": "curves-lemma-torsion-picard-becomes-visible"
        },
        {
          "caller": "models.tex",
          "line": 6571,
          "label": "curves-lemma-bound-torsion-simple"
        },
        {
          "caller": "models.tex",
          "line": 6607,
          "label": "curves-proposition-torsion-picard-reduced-proper"
        },
        {
          "caller": "models.tex",
          "line": 6613,
          "label": "curves-lemma-multicross-gorenstein-is-nodal"
        },
        {
          "caller": "models.tex",
          "line": 6680,
          "label": "curves-lemma-torsion-picard-becomes-visible"
        },
        {
          "caller": "resolve.tex",
          "line": 2449,
          "label": "curves-lemma-vanishing-twist"
        },
        {
          "caller": "resolve.tex",
          "line": 2461,
          "label": "curves-lemma-tensor-omega-with-globally-generated-invertible"
        },
        {
          "caller": "resolve.tex",
          "line": 3209,
          "label": "curves-section-Riemann-Roch"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.292118+00:00"
    },
    {
      "package_path": "native/decent-spaces.tex",
      "sha256": "761d71fa0c53320fe2ec7f1063c667a5a0172a4d789ab4a3ba8e4ca1ecb4c69f",
      "bytes": 223472,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/decent-spaces.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/decent-spaces.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "decent-spaces-lemma-bounded-fibres",
        "decent-spaces-lemma-quasi-compact-reasonable-stratification"
      ],
      "required_by": [
        {
          "caller": "spaces-cohomology.tex",
          "line": 3293,
          "label": "decent-spaces-lemma-bounded-fibres"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3297,
          "label": "decent-spaces-lemma-quasi-compact-reasonable-stratification"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.695599+00:00"
    },
    {
      "package_path": "native/derham.tex",
      "sha256": "0aa0f22d9765ccbb167d3c63d47143acd35b241972b6b71fc772d8f0b327cdf3",
      "bytes": 237942,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/derham.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/derham.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "derham-example-Garel",
        "derham-proposition-Garel",
        "derham-section-trace"
      ],
      "required_by": [
        {
          "caller": "resolve.tex",
          "line": 158,
          "label": "derham-section-trace"
        },
        {
          "caller": "resolve.tex",
          "line": 353,
          "label": "derham-proposition-Garel"
        },
        {
          "caller": "resolve.tex",
          "line": 361,
          "label": "derham-example-Garel"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:33.497674+00:00"
    },
    {
      "package_path": "native/descent.tex",
      "sha256": "ef34f287456e31eb5a359279d24dc089b70191223de396a0f1f50c52fc83577c",
      "bytes": 395223,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/descent.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/descent.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "descent-lemma-descending-fppf-property-immersion",
        "descent-lemma-reduced-local-smooth"
      ],
      "required_by": [
        {
          "caller": "quot.tex",
          "line": 3384,
          "label": "descent-lemma-descending-fppf-property-immersion"
        },
        {
          "caller": "resolve.tex",
          "line": 2916,
          "label": "descent-lemma-reduced-local-smooth"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.280149+00:00"
    },
    {
      "package_path": "native/divisors.tex",
      "sha256": "4c022ef77f817b5a8f8f1a2368cda9c711a65e68209b58aaf14e2703418ded4f",
      "bytes": 379689,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/divisors.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/divisors.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "divisors-definition-admissible-blowup",
        "divisors-definition-blow-up",
        "divisors-definition-divisor-invertible-sheaf",
        "divisors-lemma-Pic-projective-space-UFD",
        "divisors-lemma-S1-no-embedded",
        "divisors-lemma-blow-up-and-irreducible-components",
        "divisors-lemma-blow-up-integral-scheme",
        "divisors-lemma-blow-up-pullback-effective-Cartier",
        "divisors-lemma-blowing-up-affine",
        "divisors-lemma-blowing-up-gives-effective-Cartier-divisor",
        "divisors-lemma-blowing-up-projective",
        "divisors-lemma-blowup-fitting-ideal",
        "divisors-lemma-characterize-affine-blowup",
        "divisors-lemma-characterize-effective-Cartier-divisor",
        "divisors-lemma-codim-1-part",
        "divisors-lemma-conormal-effective-Cartier-divisor",
        "divisors-lemma-conormal-sheaf-section-projective-bundle",
        "divisors-lemma-describe-reflexive-hull",
        "divisors-lemma-effective-Cartier-divisor-is-a-sum",
        "divisors-lemma-extend-invertible-module",
        "divisors-lemma-extend-rational-map-after-modification",
        "divisors-lemma-flat-base-change-blowing-up",
        "divisors-lemma-integral-effective-Cartier-divisor-dvr",
        "divisors-lemma-invertible-sheaf-sum-effective-Cartier-divisors",
        "divisors-lemma-normal-c1-injective",
        "divisors-lemma-normal-effective-Cartier-divisor-S1",
        "divisors-lemma-open-subscheme-UFD",
        "divisors-lemma-pullback-effective-Cartier-defined",
        "divisors-lemma-reflexive-over-regular-dim-2",
        "divisors-lemma-restriction-injective-open-contains-weakly-ass",
        "divisors-lemma-section-smooth-regular-immersion",
        "divisors-lemma-ses-add-divisor",
        "divisors-lemma-sum-effective-Cartier-divisors",
        "divisors-lemma-universal-property-blowing-up",
        "divisors-lemma-wedge-product-ses"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4355,
          "label": "divisors-lemma-characterize-effective-Cartier-divisor"
        },
        {
          "caller": "models.tex",
          "line": 4363,
          "label": "divisors-lemma-effective-Cartier-divisor-is-a-sum"
        },
        {
          "caller": "models.tex",
          "line": 4372,
          "label": "divisors-lemma-integral-effective-Cartier-divisor-dvr"
        },
        {
          "caller": "models.tex",
          "line": 4446,
          "label": "divisors-lemma-extend-invertible-module"
        },
        {
          "caller": "models.tex",
          "line": 4452,
          "label": "divisors-definition-divisor-invertible-sheaf"
        },
        {
          "caller": "models.tex",
          "line": 4453,
          "label": "divisors-lemma-normal-c1-injective"
        },
        {
          "caller": "models.tex",
          "line": 4637,
          "label": "divisors-lemma-ses-add-divisor"
        },
        {
          "caller": "models.tex",
          "line": 4698,
          "label": "divisors-lemma-ses-add-divisor"
        },
        {
          "caller": "resolve.tex",
          "line": 395,
          "label": "divisors-lemma-describe-reflexive-hull"
        },
        {
          "caller": "resolve.tex",
          "line": 471,
          "label": "divisors-lemma-blowing-up-affine"
        },
        {
          "caller": "resolve.tex",
          "line": 485,
          "label": "divisors-lemma-blowing-up-gives-effective-Cartier-divisor"
        },
        {
          "caller": "resolve.tex",
          "line": 506,
          "label": "divisors-lemma-conormal-effective-Cartier-divisor"
        },
        {
          "caller": "resolve.tex",
          "line": 518,
          "label": "divisors-lemma-blow-up-integral-scheme"
        },
        {
          "caller": "resolve.tex",
          "line": 548,
          "label": "divisors-lemma-Pic-projective-space-UFD"
        },
        {
          "caller": "resolve.tex",
          "line": 556,
          "label": "divisors-lemma-open-subscheme-UFD"
        },
        {
          "caller": "resolve.tex",
          "line": 562,
          "label": "divisors-definition-divisor-invertible-sheaf"
        },
        {
          "caller": "resolve.tex",
          "line": 563,
          "label": "divisors-lemma-normal-c1-injective"
        },
        {
          "caller": "resolve.tex",
          "line": 589,
          "label": "divisors-lemma-blowing-up-affine"
        },
        {
          "caller": "resolve.tex",
          "line": 599,
          "label": "divisors-definition-blow-up"
        },
        {
          "caller": "resolve.tex",
          "line": 602,
          "label": "divisors-lemma-blowing-up-gives-effective-Cartier-divisor"
        },
        {
          "caller": "resolve.tex",
          "line": 744,
          "label": "divisors-lemma-codim-1-part"
        },
        {
          "caller": "resolve.tex",
          "line": 842,
          "label": "divisors-lemma-blowing-up-projective"
        },
        {
          "caller": "resolve.tex",
          "line": 880,
          "label": "divisors-lemma-flat-base-change-blowing-up"
        },
        {
          "caller": "resolve.tex",
          "line": 923,
          "label": "divisors-lemma-blow-up-pullback-effective-Cartier"
        },
        {
          "caller": "resolve.tex",
          "line": 925,
          "label": "divisors-lemma-sum-effective-Cartier-divisors"
        },
        {
          "caller": "resolve.tex",
          "line": 960,
          "label": "divisors-lemma-universal-property-blowing-up"
        },
        {
          "caller": "resolve.tex",
          "line": 984,
          "label": "divisors-lemma-extend-rational-map-after-modification"
        },
        {
          "caller": "resolve.tex",
          "line": 1017,
          "label": "divisors-lemma-blow-up-and-irreducible-components"
        },
        {
          "caller": "resolve.tex",
          "line": 1037,
          "label": "divisors-lemma-blowing-up-projective"
        },
        {
          "caller": "resolve.tex",
          "line": 1188,
          "label": "divisors-lemma-extend-rational-map-after-modification"
        },
        {
          "caller": "resolve.tex",
          "line": 1451,
          "label": "divisors-lemma-invertible-sheaf-sum-effective-Cartier-divisors"
        },
        {
          "caller": "resolve.tex",
          "line": 1452,
          "label": "divisors-lemma-conormal-effective-Cartier-divisor"
        },
        {
          "caller": "resolve.tex",
          "line": 1461,
          "label": "divisors-lemma-normal-effective-Cartier-divisor-S1"
        },
        {
          "caller": "resolve.tex",
          "line": 1464,
          "label": "divisors-lemma-S1-no-embedded"
        },
        {
          "caller": "resolve.tex",
          "line": 1465,
          "label": "divisors-lemma-restriction-injective-open-contains-weakly-ass"
        },
        {
          "caller": "resolve.tex",
          "line": 1494,
          "label": "divisors-lemma-conormal-sheaf-section-projective-bundle"
        },
        {
          "caller": "resolve.tex",
          "line": 1528,
          "label": "divisors-lemma-section-smooth-regular-immersion"
        },
        {
          "caller": "resolve.tex",
          "line": 2110,
          "label": "divisors-lemma-reflexive-over-regular-dim-2"
        },
        {
          "caller": "resolve.tex",
          "line": 2124,
          "label": "divisors-lemma-wedge-product-ses"
        },
        {
          "caller": "resolve.tex",
          "line": 2336,
          "label": "divisors-lemma-blowing-up-projective"
        },
        {
          "caller": "resolve.tex",
          "line": 2339,
          "label": "divisors-lemma-pullback-effective-Cartier-defined"
        },
        {
          "caller": "resolve.tex",
          "line": 2385,
          "label": "divisors-lemma-normal-effective-Cartier-divisor-S1"
        },
        {
          "caller": "resolve.tex",
          "line": 2491,
          "label": "divisors-lemma-blowup-fitting-ideal"
        },
        {
          "caller": "resolve.tex",
          "line": 2669,
          "label": "divisors-lemma-characterize-affine-blowup"
        },
        {
          "caller": "resolve.tex",
          "line": 2824,
          "label": "divisors-definition-admissible-blowup"
        },
        {
          "caller": "resolve.tex",
          "line": 2832,
          "label": "divisors-lemma-flat-base-change-blowing-up"
        },
        {
          "caller": "resolve.tex",
          "line": 4335,
          "label": "divisors-lemma-blowing-up-projective"
        },
        {
          "caller": "resolve.tex",
          "line": 4539,
          "label": "divisors-lemma-universal-property-blowing-up"
        },
        {
          "caller": "resolve.tex",
          "line": 4576,
          "label": "divisors-lemma-Pic-projective-space-UFD"
        },
        {
          "caller": "resolve.tex",
          "line": 4654,
          "label": "divisors-lemma-Pic-projective-space-UFD"
        },
        {
          "caller": "resolve.tex",
          "line": 4851,
          "label": "divisors-lemma-blowing-up-projective"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.804788+00:00"
    },
    {
      "package_path": "native/duality.tex",
      "sha256": "2a0b9b65c79ec3fb149937b8b65cdb0a0021360637b46bdce9334ae1989f8287",
      "bytes": 360284,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/duality.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/duality.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "duality-example-iso-on-RSheafHom-noetherian",
        "duality-example-proper-over-local",
        "duality-lemma-duality-bootstrap",
        "duality-lemma-dualizing-module",
        "duality-lemma-dualizing-module-CM-scheme",
        "duality-lemma-gorenstein-base-change",
        "duality-lemma-gorenstein-morphism",
        "duality-lemma-regular-gorenstein",
        "duality-lemma-sheaf-with-exact-support-effective-Cartier",
        "duality-lemma-shriek-dualizing",
        "duality-lemma-twisted-inverse-image-closed",
        "duality-section-duality",
        "duality-section-dualizing-module",
        "duality-section-glue",
        "duality-section-trace"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4401,
          "label": "duality-lemma-gorenstein-morphism"
        },
        {
          "caller": "models.tex",
          "line": 4403,
          "label": "duality-lemma-regular-gorenstein"
        },
        {
          "caller": "models.tex",
          "line": 6455,
          "label": "duality-lemma-gorenstein-base-change"
        },
        {
          "caller": "models.tex",
          "line": 6611,
          "label": "duality-lemma-gorenstein-base-change"
        },
        {
          "caller": "resolve.tex",
          "line": 1600,
          "label": "duality-lemma-dualizing-module-CM-scheme"
        },
        {
          "caller": "resolve.tex",
          "line": 1603,
          "label": "duality-section-dualizing-module"
        },
        {
          "caller": "resolve.tex",
          "line": 1608,
          "label": "duality-example-proper-over-local"
        },
        {
          "caller": "resolve.tex",
          "line": 1612,
          "label": "duality-section-glue"
        },
        {
          "caller": "resolve.tex",
          "line": 1640,
          "label": "duality-lemma-dualizing-module-CM-scheme"
        },
        {
          "caller": "resolve.tex",
          "line": 1642,
          "label": "duality-example-proper-over-local"
        },
        {
          "caller": "resolve.tex",
          "line": 1665,
          "label": "duality-example-iso-on-RSheafHom-noetherian"
        },
        {
          "caller": "resolve.tex",
          "line": 1669,
          "label": "duality-lemma-shriek-dualizing"
        },
        {
          "caller": "resolve.tex",
          "line": 2034,
          "label": "duality-section-trace"
        },
        {
          "caller": "resolve.tex",
          "line": 2040,
          "label": "duality-lemma-duality-bootstrap"
        },
        {
          "caller": "resolve.tex",
          "line": 2041,
          "label": "duality-section-duality"
        },
        {
          "caller": "resolve.tex",
          "line": 2042,
          "label": "duality-example-iso-on-RSheafHom-noetherian"
        },
        {
          "caller": "resolve.tex",
          "line": 2104,
          "label": "duality-section-duality"
        },
        {
          "caller": "resolve.tex",
          "line": 2443,
          "label": "duality-lemma-sheaf-with-exact-support-effective-Cartier"
        },
        {
          "caller": "resolve.tex",
          "line": 2444,
          "label": "duality-lemma-twisted-inverse-image-closed"
        },
        {
          "caller": "resolve.tex",
          "line": 2523,
          "label": "duality-lemma-dualizing-module"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.940982+00:00"
    },
    {
      "package_path": "native/dualizing.tex",
      "sha256": "b1262987c3041fd1b15fbae46a0cc66dc9ba2c28917ed32330e4904981b131c2",
      "bytes": 210693,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/dualizing.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/dualizing.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "dualizing-lemma-gorenstein-divide-by-nonzerodivisor",
        "dualizing-lemma-regular-gorenstein",
        "dualizing-lemma-special-case-local-duality",
        "dualizing-lemma-ubiquity-dualizing",
        "dualizing-proposition-matlis",
        "dualizing-section-dualizing-local"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4407,
          "label": "dualizing-lemma-gorenstein-divide-by-nonzerodivisor"
        },
        {
          "caller": "resolve.tex",
          "line": 1635,
          "label": "dualizing-section-dualizing-local"
        },
        {
          "caller": "resolve.tex",
          "line": 2063,
          "label": "dualizing-lemma-special-case-local-duality"
        },
        {
          "caller": "resolve.tex",
          "line": 2065,
          "label": "dualizing-proposition-matlis"
        },
        {
          "caller": "resolve.tex",
          "line": 2089,
          "label": "dualizing-lemma-regular-gorenstein"
        },
        {
          "caller": "resolve.tex",
          "line": 2506,
          "label": "dualizing-lemma-regular-gorenstein"
        },
        {
          "caller": "resolve.tex",
          "line": 3759,
          "label": "dualizing-lemma-ubiquity-dualizing"
        },
        {
          "caller": "resolve.tex",
          "line": 3847,
          "label": "dualizing-lemma-ubiquity-dualizing"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.945698+00:00"
    },
    {
      "package_path": "native/examples-stacks.tex",
      "sha256": "54dbc9d017b82b7c93a6ccd72a0295e5a2c1a3e535187083e4100101cd577976",
      "bytes": 65671,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/examples-stacks.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/examples-stacks.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "examples-stacks-section-picard-stack"
      ],
      "required_by": [
        {
          "caller": "quot.tex",
          "line": 2729,
          "label": "examples-stacks-section-picard-stack"
        },
        {
          "caller": "quot.tex",
          "line": 2746,
          "label": "examples-stacks-section-picard-stack"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.868786+00:00"
    },
    {
      "package_path": "native/examples.tex",
      "sha256": "67a1c8c75378391e6282040f4cdbd873a5f9b00e3261b49588116a6a7305c5f5",
      "bytes": 277677,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/examples.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/examples.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "examples-section-bad"
      ],
      "required_by": [
        {
          "caller": "resolve.tex",
          "line": 3071,
          "label": "examples-section-bad"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.840666+00:00"
    },
    {
      "package_path": "native/fdl.tex",
      "sha256": "41f30f5c60d0d61012e3ba7d80ad27be062b7132d84ade3102e460e619e9a9f6",
      "bytes": 21760,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/fdl.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/fdl.tex",
      "role": "original build support, licence or provenance",
      "terms": "Preserve original file notices; COPYING is the unmodified GFDL legal text, documentation preserves its actual source provenance.",
      "actual_read_scope": "Source/support identity and applicable notices; no extra mathematical closure asserted.",
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:36.129233+00:00"
    },
    {
      "package_path": "native/fields.tex",
      "sha256": "0b263dfe4e10eaae84a317703ca5de47ced45aad67518726b06caf340dd4d0fa",
      "bytes": 144567,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/fields.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/fields.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "fields-lemma-separable-trace-pairing"
      ],
      "required_by": [
        {
          "caller": "resolve.tex",
          "line": 1934,
          "label": "fields-lemma-separable-trace-pairing"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.273599+00:00"
    },
    {
      "package_path": "native/flat.tex",
      "sha256": "b4d84512290a62109009ed1a6e9ce4b58d09a566589cae90fecf88efb630a804",
      "bytes": 563759,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/flat.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/flat.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "flat-lemma-dominate-modification-by-blowup",
        "flat-lemma-finite-after-blowing-up"
      ],
      "required_by": [
        {
          "caller": "resolve.tex",
          "line": 944,
          "label": "flat-lemma-dominate-modification-by-blowup"
        },
        {
          "caller": "resolve.tex",
          "line": 1402,
          "label": "flat-lemma-dominate-modification-by-blowup"
        },
        {
          "caller": "resolve.tex",
          "line": 1942,
          "label": "flat-lemma-finite-after-blowing-up"
        },
        {
          "caller": "regular-surface-models.md",
          "label": "flat-lemma-dominate-modification-by-blowup"
        },
        {
          "caller": "regular-surface-models.md",
          "label": "flat-lemma-finite-after-blowing-up"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:33.309611+00:00"
    },
    {
      "package_path": "native/groupoids.tex",
      "sha256": "906061343b5f46807a99fb3843ba9ef60b6fbe3d9daddc1aa964aeafaa9a59b7",
      "bytes": 205809,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/groupoids.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/groupoids.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "groupoids-definition-abelian-variety",
        "groupoids-proposition-review-abelian-varieties"
      ],
      "required_by": [
        {
          "caller": "curves.tex",
          "line": 3433,
          "label": "groupoids-definition-abelian-variety"
        },
        {
          "caller": "curves.tex",
          "line": 3435,
          "label": "groupoids-proposition-review-abelian-varieties"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:33.242640+00:00"
    },
    {
      "package_path": "native/introduction.tex",
      "sha256": "43abd6493bf48325878d6573966e97025770d4b4e12db1dda31da7fd181d4acf",
      "bytes": 6560,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/introduction.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/introduction.tex",
      "role": "original build support, licence or provenance",
      "terms": "Preserve original file notices; COPYING is the unmodified GFDL legal text, documentation preserves its actual source provenance.",
      "actual_read_scope": "Source/support identity and applicable notices; no extra mathematical closure asserted.",
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:36.327947+00:00"
    },
    {
      "package_path": "native/limits.tex",
      "sha256": "dccddc3622ebad21dd6219ea50b157fcf20c574e82b9e920b7f4d1ed127e0aa4",
      "bytes": 222594,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/limits.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/limits.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "limits-lemma-modifications",
        "limits-lemma-modifications-properties"
      ],
      "required_by": [
        {
          "caller": "resolve.tex",
          "line": 1236,
          "label": "limits-lemma-modifications"
        },
        {
          "caller": "resolve.tex",
          "line": 1263,
          "label": "limits-lemma-modifications-properties"
        },
        {
          "caller": "resolve.tex",
          "line": 1854,
          "label": "limits-lemma-modifications"
        },
        {
          "caller": "resolve.tex",
          "line": 1858,
          "label": "limits-lemma-modifications-properties"
        },
        {
          "caller": "resolve.tex",
          "line": 1896,
          "label": "limits-lemma-modifications"
        },
        {
          "caller": "resolve.tex",
          "line": 1900,
          "label": "limits-lemma-modifications-properties"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:33.451165+00:00"
    },
    {
      "package_path": "native/models.tex",
      "sha256": "5cfa014ca4381c99333043af35ed443f10e083fa601f854f78770b71c9a5f98b",
      "bytes": 205089,
      "source_id": "AGGS-NATIVE-STACKS-565B-MODELS-TEX",
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/models.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/models.tex",
      "role": "native proof body",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": [
        "Section17 genus>=2 proof, lines6292-6624",
        "numerical matrix proof, lines293-411",
        "heart/neighbour/bound-wm proof, lines3884-4121",
        "minimal-model and Gorenstein input, lines4215-4409",
        "strict genus and equality proof, lines5158-5393",
        "torsion sequence and specialization proof, lines5652-5831"
      ],
      "proof_locators": [
        "models-theorem-semistable-reduction/0CDN",
        "models-lemma-bound-wm/0C9W",
        "models-lemma-equality-genus-reduction-bigger-than/0CEE: only algebraically closed residue-field case used",
        "models-lemma-sequence-torsion/0CAD",
        "models-lemma-torsion-embeds/0CAE"
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.274419+00:00"
    },
    {
      "package_path": "native/moduli-curves.tex",
      "sha256": "d4dba83e25d3aea239197824bca0706b650917000540ef4d324a87feaeaf41fe",
      "bytes": 128255,
      "source_id": "AGAS-NATIVE-STACKS-565B-MODULI-CURVES",
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/moduli-curves.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/moduli-curves.tex",
      "role": "native source comparator",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": [
        "relevant stable-model, finite-type and properness proof bodies compared in initial source audit"
      ],
      "proof_locators": [
        "Native comparison only: current owned AG-AS supplies stabilization, uniqueness and tricanonical frame construction"
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.449618+00:00"
    },
    {
      "package_path": "native/more-algebra.tex",
      "sha256": "0490028f82effcf08c0d790d0c8145eeb8d55db66bfb8cf7ba29ccd27fc3fabe",
      "bytes": 1518081,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/more-algebra.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/more-algebra.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "more-algebra-definition-extension-discrete-valuation-rings",
        "more-algebra-lemma-application-formal-glueing",
        "more-algebra-lemma-completion-dimension",
        "more-algebra-lemma-completion-dvr",
        "more-algebra-lemma-completion-regular",
        "more-algebra-lemma-dedekind-torsion-free-flat",
        "more-algebra-lemma-divides-radical",
        "more-algebra-lemma-finite-type-over-excellent",
        "more-algebra-lemma-isomorphic-completions",
        "more-algebra-lemma-normal-goes-up",
        "more-algebra-lemma-power-series-ring-subfields",
        "more-algebra-lemma-regular-local-UFD",
        "more-algebra-proposition-ubiquity-J-2",
        "more-algebra-proposition-ubiquity-excellent",
        "more-algebra-remark-finite-separable-extension",
        "more-algebra-remark-formal-glueing-algebras"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4145,
          "label": "more-algebra-definition-extension-discrete-valuation-rings"
        },
        {
          "caller": "models.tex",
          "line": 4174,
          "label": "more-algebra-lemma-dedekind-torsion-free-flat"
        },
        {
          "caller": "models.tex",
          "line": 4190,
          "label": "more-algebra-lemma-completion-dvr"
        },
        {
          "caller": "models.tex",
          "line": 4209,
          "label": "more-algebra-proposition-ubiquity-excellent"
        },
        {
          "caller": "models.tex",
          "line": 4217,
          "label": "more-algebra-lemma-normal-goes-up"
        },
        {
          "caller": "models.tex",
          "line": 4234,
          "label": "more-algebra-proposition-ubiquity-J-2"
        },
        {
          "caller": "models.tex",
          "line": 4348,
          "label": "more-algebra-lemma-dedekind-torsion-free-flat"
        },
        {
          "caller": "models.tex",
          "line": 5815,
          "label": "more-algebra-lemma-isomorphic-completions"
        },
        {
          "caller": "models.tex",
          "line": 6258,
          "label": "more-algebra-remark-finite-separable-extension"
        },
        {
          "caller": "models.tex",
          "line": 6316,
          "label": "more-algebra-remark-finite-separable-extension"
        },
        {
          "caller": "models.tex",
          "line": 6533,
          "label": "more-algebra-remark-finite-separable-extension"
        },
        {
          "caller": "resolve.tex",
          "line": 553,
          "label": "more-algebra-lemma-regular-local-UFD"
        },
        {
          "caller": "resolve.tex",
          "line": 1761,
          "label": "more-algebra-lemma-divides-radical"
        },
        {
          "caller": "resolve.tex",
          "line": 2144,
          "label": "more-algebra-lemma-power-series-ring-subfields"
        },
        {
          "caller": "resolve.tex",
          "line": 2803,
          "label": "more-algebra-lemma-completion-regular"
        },
        {
          "caller": "resolve.tex",
          "line": 2879,
          "label": "more-algebra-proposition-ubiquity-excellent"
        },
        {
          "caller": "resolve.tex",
          "line": 2882,
          "label": "more-algebra-lemma-finite-type-over-excellent"
        },
        {
          "caller": "resolve.tex",
          "line": 2886,
          "label": "more-algebra-lemma-normal-goes-up"
        },
        {
          "caller": "resolve.tex",
          "line": 3005,
          "label": "more-algebra-lemma-application-formal-glueing"
        },
        {
          "caller": "resolve.tex",
          "line": 3006,
          "label": "more-algebra-remark-formal-glueing-algebras"
        },
        {
          "caller": "resolve.tex",
          "line": 3757,
          "label": "more-algebra-proposition-ubiquity-excellent"
        },
        {
          "caller": "resolve.tex",
          "line": 3763,
          "label": "more-algebra-lemma-normal-goes-up"
        },
        {
          "caller": "resolve.tex",
          "line": 3842,
          "label": "more-algebra-proposition-ubiquity-J-2"
        },
        {
          "caller": "resolve.tex",
          "line": 3845,
          "label": "more-algebra-proposition-ubiquity-excellent"
        },
        {
          "caller": "resolve.tex",
          "line": 3851,
          "label": "more-algebra-lemma-normal-goes-up"
        },
        {
          "caller": "resolve.tex",
          "line": 4524,
          "label": "more-algebra-lemma-completion-regular"
        },
        {
          "caller": "resolve.tex",
          "line": 4525,
          "label": "more-algebra-lemma-completion-dimension"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.477601+00:00"
    },
    {
      "package_path": "native/more-morphisms.tex",
      "sha256": "6f36e5ff2c2b5c66fc2aa762421f0024c08c409ab86d1d814f70a065f416475a",
      "bytes": 976082,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/more-morphisms.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/more-morphisms.tex",
      "role": "native proof body",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": [
        "Full fibre-trivial Picard descent proof, lines22421–22487, read after required independent correction"
      ],
      "proof_locators": [
        "more-morphisms-lemma-bijection-on-Pic/0E24"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4288,
          "label": "more-morphisms-lemma-projective"
        },
        {
          "caller": "models.tex",
          "line": 4429,
          "label": "more-morphisms-lemma-geometrically-connected-fibres-towards-normal"
        },
        {
          "caller": "models.tex",
          "line": 5794,
          "label": "more-morphisms-lemma-torsion-pic-thickening"
        },
        {
          "caller": "quot.tex",
          "line": 3381,
          "label": "more-morphisms-lemma-separated-locally-quasi-finite-morphisms-fppf-descend"
        },
        {
          "caller": "resolve.tex",
          "line": 1098,
          "label": "more-morphisms-lemma-geometrically-connected-fibres-towards-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 1383,
          "label": "more-morphisms-lemma-geometrically-connected-fibres-towards-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 1388,
          "label": "more-morphisms-lemma-proper-finite-fibre-finite-in-neighbourhood"
        },
        {
          "caller": "resolve.tex",
          "line": 1708,
          "label": "more-morphisms-lemma-geometrically-connected-fibres-towards-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 1845,
          "label": "more-morphisms-lemma-category-projective"
        },
        {
          "caller": "resolve.tex",
          "line": 4477,
          "label": "more-morphisms-theorem-stein-factorization-Noetherian"
        },
        {
          "caller": "resolve.tex",
          "line": 4491,
          "label": "more-morphisms-lemma-characterize-finite"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 1996,
          "label": "more-morphisms-lemma-dominate-fppf-finite"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2001,
          "label": "more-morphisms-lemma-extend-finite-surjective-morphisms"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.607394+00:00"
    },
    {
      "package_path": "native/morphisms.tex",
      "sha256": "51cfcb7402d0e84aad95bdb6dd8840552f6f635fc20709521fd4ab895df05242",
      "bytes": 593209,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/morphisms.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/morphisms.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "morphisms-definition-alteration",
        "morphisms-definition-birational",
        "morphisms-definition-modification",
        "morphisms-definition-normalization",
        "morphisms-definition-quasi-projective",
        "morphisms-definition-scheme-theoretic-image",
        "morphisms-example-scheme-theoretic-image",
        "morphisms-lemma-H-quasi-projective-open-H-projective",
        "morphisms-lemma-algebraic-residue-field-extension-closed-point-fibre",
        "morphisms-lemma-base-change-differentials",
        "morphisms-lemma-base-change-proper",
        "morphisms-lemma-characterize-proper",
        "morphisms-lemma-characterize-relatively-ample",
        "morphisms-lemma-composition-projective",
        "morphisms-lemma-composition-proper",
        "morphisms-lemma-composition-quasi-projective",
        "morphisms-lemma-conormal-functorial",
        "morphisms-lemma-conormal-functorial-flat",
        "morphisms-lemma-differentials-relative-immersion",
        "morphisms-lemma-dimension-fibre-after-base-change",
        "morphisms-lemma-dimension-formula",
        "morphisms-lemma-extend-across",
        "morphisms-lemma-finite-birational-over-normal",
        "morphisms-lemma-finite-proper",
        "morphisms-lemma-finite-type-nagata",
        "morphisms-lemma-finite-type-over-affine-ample-very-ample",
        "morphisms-lemma-locally-projective-proper",
        "morphisms-lemma-nagata-normalization",
        "morphisms-lemma-normalization-normal",
        "morphisms-lemma-projective-is-quasi-projective-proper",
        "morphisms-lemma-projective-permanence",
        "morphisms-lemma-projective-quasi-projective",
        "morphisms-lemma-proper-local-on-the-base",
        "morphisms-lemma-pullback-ample-tensor-relatively-ample",
        "morphisms-lemma-quasi-affine-finite-type-over-S",
        "morphisms-lemma-quasi-compact-immersion",
        "morphisms-lemma-quasi-compact-scheme-theoretic-image",
        "morphisms-lemma-quasi-projective-open-projective",
        "morphisms-lemma-scheme-theoretic-union",
        "morphisms-lemma-ubiquity-nagata",
        "morphisms-proposition-generic-flatness",
        "morphisms-section-dimension-formula",
        "morphisms-section-generically-finite",
        "morphisms-section-nagata",
        "morphisms-section-normalization",
        "morphisms-section-projective"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4166,
          "label": "morphisms-lemma-quasi-compact-scheme-theoretic-image"
        },
        {
          "caller": "models.tex",
          "line": 4167,
          "label": "morphisms-example-scheme-theoretic-image"
        },
        {
          "caller": "models.tex",
          "line": 5132,
          "label": "morphisms-lemma-characterize-proper"
        },
        {
          "caller": "models.tex",
          "line": 5277,
          "label": "morphisms-lemma-scheme-theoretic-union"
        },
        {
          "caller": "curves.tex",
          "line": 3611,
          "label": "morphisms-lemma-dimension-fibre-after-base-change"
        },
        {
          "caller": "resolve.tex",
          "line": 810,
          "label": "morphisms-lemma-differentials-relative-immersion"
        },
        {
          "caller": "resolve.tex",
          "line": 812,
          "label": "morphisms-lemma-base-change-differentials"
        },
        {
          "caller": "resolve.tex",
          "line": 980,
          "label": "morphisms-lemma-extend-across"
        },
        {
          "caller": "resolve.tex",
          "line": 1018,
          "label": "morphisms-definition-normalization"
        },
        {
          "caller": "resolve.tex",
          "line": 1039,
          "label": "morphisms-lemma-finite-type-nagata"
        },
        {
          "caller": "resolve.tex",
          "line": 1041,
          "label": "morphisms-lemma-nagata-normalization"
        },
        {
          "caller": "resolve.tex",
          "line": 1043,
          "label": "morphisms-lemma-finite-proper"
        },
        {
          "caller": "resolve.tex",
          "line": 1044,
          "label": "morphisms-lemma-composition-proper"
        },
        {
          "caller": "resolve.tex",
          "line": 1047,
          "label": "morphisms-lemma-normalization-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 1057,
          "label": "morphisms-definition-birational"
        },
        {
          "caller": "resolve.tex",
          "line": 1081,
          "label": "morphisms-section-nagata"
        },
        {
          "caller": "resolve.tex",
          "line": 1082,
          "label": "morphisms-section-dimension-formula"
        },
        {
          "caller": "resolve.tex",
          "line": 1083,
          "label": "morphisms-section-normalization"
        },
        {
          "caller": "resolve.tex",
          "line": 1364,
          "label": "morphisms-definition-modification"
        },
        {
          "caller": "resolve.tex",
          "line": 1390,
          "label": "morphisms-lemma-finite-birational-over-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 1502,
          "label": "morphisms-definition-scheme-theoretic-image"
        },
        {
          "caller": "resolve.tex",
          "line": 1513,
          "label": "morphisms-lemma-finite-proper"
        },
        {
          "caller": "resolve.tex",
          "line": 1515,
          "label": "morphisms-lemma-finite-birational-over-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 1521,
          "label": "morphisms-lemma-nagata-normalization"
        },
        {
          "caller": "resolve.tex",
          "line": 1522,
          "label": "morphisms-lemma-ubiquity-nagata"
        },
        {
          "caller": "resolve.tex",
          "line": 1533,
          "label": "morphisms-lemma-conormal-functorial-flat"
        },
        {
          "caller": "resolve.tex",
          "line": 1835,
          "label": "morphisms-lemma-dimension-formula"
        },
        {
          "caller": "resolve.tex",
          "line": 1838,
          "label": "morphisms-lemma-algebraic-residue-field-extension-closed-point-fibre"
        },
        {
          "caller": "resolve.tex",
          "line": 1842,
          "label": "morphisms-lemma-nagata-normalization"
        },
        {
          "caller": "resolve.tex",
          "line": 2331,
          "label": "morphisms-lemma-nagata-normalization"
        },
        {
          "caller": "resolve.tex",
          "line": 2805,
          "label": "morphisms-lemma-base-change-proper"
        },
        {
          "caller": "resolve.tex",
          "line": 2940,
          "label": "morphisms-section-generically-finite"
        },
        {
          "caller": "resolve.tex",
          "line": 2998,
          "label": "morphisms-lemma-nagata-normalization"
        },
        {
          "caller": "resolve.tex",
          "line": 3551,
          "label": "morphisms-definition-alteration"
        },
        {
          "caller": "resolve.tex",
          "line": 3553,
          "label": "morphisms-proposition-generic-flatness"
        },
        {
          "caller": "resolve.tex",
          "line": 3968,
          "label": "morphisms-lemma-normalization-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 4336,
          "label": "morphisms-lemma-locally-projective-proper"
        },
        {
          "caller": "resolve.tex",
          "line": 4546,
          "label": "morphisms-lemma-conormal-functorial"
        },
        {
          "caller": "resolve.tex",
          "line": 4693,
          "label": "morphisms-lemma-finite-type-over-affine-ample-very-ample"
        },
        {
          "caller": "resolve.tex",
          "line": 4723,
          "label": "morphisms-lemma-finite-proper"
        },
        {
          "caller": "resolve.tex",
          "line": 4724,
          "label": "morphisms-lemma-composition-proper"
        },
        {
          "caller": "resolve.tex",
          "line": 4727,
          "label": "morphisms-lemma-pullback-ample-tensor-relatively-ample"
        },
        {
          "caller": "resolve.tex",
          "line": 4789,
          "label": "morphisms-lemma-projective-is-quasi-projective-proper"
        },
        {
          "caller": "resolve.tex",
          "line": 4790,
          "label": "morphisms-definition-quasi-projective"
        },
        {
          "caller": "resolve.tex",
          "line": 4806,
          "label": "morphisms-lemma-proper-local-on-the-base"
        },
        {
          "caller": "resolve.tex",
          "line": 4815,
          "label": "morphisms-lemma-characterize-relatively-ample"
        },
        {
          "caller": "resolve.tex",
          "line": 4821,
          "label": "morphisms-lemma-quasi-projective-open-projective"
        },
        {
          "caller": "resolve.tex",
          "line": 4852,
          "label": "morphisms-lemma-composition-projective"
        },
        {
          "caller": "resolve.tex",
          "line": 4854,
          "label": "morphisms-lemma-projective-permanence"
        },
        {
          "caller": "resolve.tex",
          "line": 4856,
          "label": "morphisms-lemma-composition-quasi-projective"
        },
        {
          "caller": "resolve.tex",
          "line": 4858,
          "label": "morphisms-lemma-projective-quasi-projective"
        },
        {
          "caller": "resolve.tex",
          "line": 4875,
          "label": "morphisms-lemma-projective-is-quasi-projective-proper"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3316,
          "label": "morphisms-lemma-quasi-affine-finite-type-over-S"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3317,
          "label": "morphisms-lemma-H-quasi-projective-open-H-projective"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3328,
          "label": "morphisms-lemma-quasi-compact-immersion"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3331,
          "label": "morphisms-section-projective"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3392,
          "label": "morphisms-lemma-locally-projective-proper"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.741020+00:00"
    },
    {
      "package_path": "native/perfect.tex",
      "sha256": "83bd632e693848d32b54acc48ea7d89b0ed024c4b84499486687e31e92bfdcf0",
      "bytes": 417503,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/perfect.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/perfect.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "perfect-lemma-chi-locally-constant-geometric"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4672,
          "label": "perfect-lemma-chi-locally-constant-geometric"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.596464+00:00"
    },
    {
      "package_path": "native/pic.tex",
      "sha256": "e6651e5453a362eb65096efa90a116188af3396425a2d3857e1648658823cc60",
      "bytes": 65446,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/pic.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/pic.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "pic-lemma-picard-pieces",
        "pic-lemma-torsion-descends"
      ],
      "required_by": [
        {
          "caller": "curves.tex",
          "line": 3430,
          "label": "pic-lemma-picard-pieces"
        },
        {
          "caller": "curves.tex",
          "line": 3467,
          "label": "pic-lemma-torsion-descends"
        },
        {
          "caller": "curves.tex",
          "line": 3472,
          "label": "pic-lemma-torsion-descends"
        },
        {
          "caller": "curves.tex",
          "line": 3784,
          "label": "pic-lemma-torsion-descends"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.567526+00:00"
    },
    {
      "package_path": "native/preamble.tex",
      "sha256": "4af3f52ed0f1e932def5c8725068968407ce9e4b0cd4f4c4b803607b5bcbbe0d",
      "bytes": 8596,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/preamble.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/preamble.tex",
      "role": "original build support, licence or provenance",
      "terms": "Preserve original file notices; COPYING is the unmodified GFDL legal text, documentation preserves its actual source provenance.",
      "actual_read_scope": "Source/support identity and applicable notices; no extra mathematical closure asserted.",
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.927394+00:00"
    },
    {
      "package_path": "native/properties.tex",
      "sha256": "2f8be43be8da39df575581181f8a28aaa077266464947157e70838462e8291fa",
      "bytes": 213401,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/properties.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/properties.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "properties-definition-nagata",
        "properties-lemma-ample-on-closed",
        "properties-lemma-ample-power-ample",
        "properties-lemma-ample-quasi-coherent",
        "properties-lemma-characterize-regular",
        "properties-lemma-normal-dimension-2-Cohen-Macaulay",
        "properties-lemma-normal-integral-sections",
        "properties-lemma-regular-normal"
      ],
      "required_by": [
        {
          "caller": "resolve.tex",
          "line": 523,
          "label": "properties-lemma-characterize-regular"
        },
        {
          "caller": "resolve.tex",
          "line": 1025,
          "label": "properties-definition-nagata"
        },
        {
          "caller": "resolve.tex",
          "line": 1599,
          "label": "properties-lemma-normal-dimension-2-Cohen-Macaulay"
        },
        {
          "caller": "resolve.tex",
          "line": 1638,
          "label": "properties-lemma-normal-dimension-2-Cohen-Macaulay"
        },
        {
          "caller": "resolve.tex",
          "line": 2349,
          "label": "properties-lemma-ample-quasi-coherent"
        },
        {
          "caller": "resolve.tex",
          "line": 2808,
          "label": "properties-lemma-characterize-regular"
        },
        {
          "caller": "resolve.tex",
          "line": 3543,
          "label": "properties-lemma-regular-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 3545,
          "label": "properties-lemma-normal-integral-sections"
        },
        {
          "caller": "resolve.tex",
          "line": 3630,
          "label": "properties-lemma-regular-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 3632,
          "label": "properties-lemma-normal-integral-sections"
        },
        {
          "caller": "resolve.tex",
          "line": 3662,
          "label": "properties-lemma-regular-normal"
        },
        {
          "caller": "resolve.tex",
          "line": 3668,
          "label": "properties-lemma-normal-integral-sections"
        },
        {
          "caller": "resolve.tex",
          "line": 4684,
          "label": "properties-lemma-ample-on-closed"
        },
        {
          "caller": "resolve.tex",
          "line": 4734,
          "label": "properties-lemma-ample-power-ample"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:33.274735+00:00"
    },
    {
      "package_path": "native/quot.tex",
      "sha256": "4949679b9a1b178ce7df1f3295cc3dedc5e8e141b9e1838db9766a5237690395",
      "bytes": 237556,
      "source_id": "AGGS-NATIVE-STACKS-565B-QUOT-TEX",
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/quot.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/quot.tex",
      "role": "native proof body",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": [
        "Picard-stack construction, lines2725-2818",
        "rigidification and representability proof, lines3241-3404",
        "flat coherent-stack proof reduction, lines1448-1510: current owned AG-AS supplies the full coherent theorem"
      ],
      "proof_locators": [
        "quot-proposition-pic-functor/0D2C",
        "quot-proposition-pic: comparison; no unexamined replacement for owned AG-AS7.2-7.3"
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.233125+00:00"
    },
    {
      "package_path": "native/resolve.tex",
      "sha256": "4cc743f7c82f9c3845bb8c91447cb7adc27bdc3305fc2036eeddf41469320554",
      "bytes": 202393,
      "source_id": "AGGS-NATIVE-STACKS-565B-RESOLVE-TEX",
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/resolve.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/resolve.tex",
      "role": "native proof body",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": [
        "Full continuous proof bodies lines153-4016: differential trace, quadratic transformation, domination, local modification gluing, vanishing, boundedness, rational singularities, arcs, completion, rational double points, completed-local resolution and full Lipman theorem",
        "Full exceptional-curve and contraction proof bodies lines4292-4883, including contract-ample and projectivity comparison",
        "The forward implication(4)->(3) and the projective model bridge are the scope used; exact extraction and omitted routine-details completion are in STABLE-CURVE-ALTERATION-SURFACE-PROVIDER.md"
      ],
      "proof_locators": [
        "resolve-theorem-resolve/0BGP",
        "resolve-lemma-resolve-complete/0BGN",
        "resolve-lemma-rational-to-gorenstein/0BBV",
        "resolve-lemma-resolve-rational-double-points/0BGE",
        "resolve-lemma-contraction/0C2L",
        "resolve-lemma-contract-ample/0C2M"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4201,
          "label": "resolve-lemma-normalization-completion"
        },
        {
          "caller": "models.tex",
          "line": 4212,
          "label": "resolve-lemma-iso-completions"
        },
        {
          "caller": "models.tex",
          "line": 4230,
          "label": "resolve-theorem-resolve"
        },
        {
          "caller": "models.tex",
          "line": 4240,
          "label": "resolve-definition-resolution"
        },
        {
          "caller": "models.tex",
          "line": 4253,
          "label": "resolve-section-minus-one"
        },
        {
          "caller": "models.tex",
          "line": 4285,
          "label": "resolve-lemma-regular-dim-2-projective"
        },
        {
          "caller": "models.tex",
          "line": 4291,
          "label": "resolve-section-minus-one"
        },
        {
          "caller": "models.tex",
          "line": 4292,
          "label": "resolve-lemma-contract-ample"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.258670+00:00"
    },
    {
      "package_path": "native/schemes.tex",
      "sha256": "028a8204a03e736e9f22ff0d7c6444a17d04bfd5cdbbd31f4cdf322bec55f233",
      "bytes": 189721,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/schemes.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/schemes.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "schemes-lemma-morphism-into-affine",
        "schemes-proposition-characterize-universally-closed",
        "schemes-section-points"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 5136,
          "label": "schemes-section-points"
        },
        {
          "caller": "resolve.tex",
          "line": 4762,
          "label": "schemes-lemma-morphism-into-affine"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3394,
          "label": "schemes-proposition-characterize-universally-closed"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.549573+00:00"
    },
    {
      "package_path": "native/sites-cohomology.tex",
      "sha256": "0d9e067d20f6a708bb228ec7b0f6da7881901c6c49cb38887553c17cd3a7b023",
      "bytes": 534532,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/sites-cohomology.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/sites-cohomology.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "sites-cohomology-example-hom-complex-into-sheaf"
      ],
      "required_by": [
        {
          "caller": "resolve.tex",
          "line": 1566,
          "label": "sites-cohomology-example-hom-complex-into-sheaf"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.318298+00:00"
    },
    {
      "package_path": "native/spaces-cohomology.tex",
      "sha256": "81438f655ceab1a2e07cfeec645a9a7c2447db983d6bcefaed6575859b75d196",
      "bytes": 174442,
      "source_id": "AGGS-DIM1-NATIVE-STACKS-R39-SPACES-COHOMOLOGY",
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/spaces-cohomology.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/spaces-cohomology.tex",
      "role": "native proof body",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": [
        "complete weak Chow proof, lines3273-3401"
      ],
      "proof_locators": [
        "spaces-cohomology-lemma-weak-chow/089J; generic-etale/projective extraction is written in S.6"
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.370767+00:00"
    },
    {
      "package_path": "native/spaces-limits.tex",
      "sha256": "63df4873f4d309a436ee8551a480a37805344fc377f1963376219f98d07bc228",
      "bytes": 209790,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/spaces-limits.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/spaces-limits.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "spaces-limits-lemma-refined-valuative-criterion-proper",
        "spaces-limits-proposition-there-is-a-scheme-finite-over"
      ],
      "required_by": [
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2010,
          "label": "spaces-limits-proposition-there-is-a-scheme-finite-over"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2061,
          "label": "spaces-limits-proposition-there-is-a-scheme-finite-over"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2796,
          "label": "spaces-limits-lemma-refined-valuative-criterion-proper"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.726956+00:00"
    },
    {
      "package_path": "native/spaces-more-morphisms.tex",
      "sha256": "d739b3b42ce8590331c4dcf81c45d17a5f2430e46d03c004fef64034816c5081",
      "bytes": 516999,
      "source_id": "AGAS-NATIVE-STACKS-565B-SPACES-MORE-MORPHISMS",
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/spaces-more-morphisms.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/spaces-more-morphisms.tex",
      "role": "native source comparator",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": [
        "Picard/global-functions and source-comparison portions read in initial source audit; no new theorem closure assigned to this file"
      ],
      "proof_locators": [
        "Ordinary source comparator, not a substitute stable-moduli proof"
      ],
      "required_by": [
        {
          "caller": "quot.tex",
          "line": 2772,
          "label": "spaces-more-morphisms-lemma-finite-free-open"
        },
        {
          "caller": "quot.tex",
          "line": 3399,
          "label": "spaces-more-morphisms-lemma-diagonal-picard-flat-proper"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2195,
          "label": "spaces-more-morphisms-lemma-get-section-after-blowup"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.496570+00:00"
    },
    {
      "package_path": "native/spaces-morphisms.tex",
      "sha256": "048bc16d80e71dbaa9c5cf11b109b69b481d920b278cbcb379c3bc9b8bbfc252",
      "bytes": 398512,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/spaces-morphisms.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/spaces-morphisms.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "spaces-morphisms-lemma-base-change-flat",
        "spaces-morphisms-lemma-base-change-proper",
        "spaces-morphisms-lemma-diagonal-unramified-morphism",
        "spaces-morphisms-lemma-equality-of-morphisms",
        "spaces-morphisms-lemma-etale-unramified",
        "spaces-morphisms-lemma-lift-valuation-ring-through-flat-morphism",
        "spaces-morphisms-lemma-push-down-solution",
        "spaces-morphisms-lemma-refined-valuative-criterion-universally-closed"
      ],
      "required_by": [
        {
          "caller": "quot.tex",
          "line": 2754,
          "label": "spaces-morphisms-lemma-base-change-flat"
        },
        {
          "caller": "quot.tex",
          "line": 2755,
          "label": "spaces-morphisms-lemma-base-change-proper"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2226,
          "label": "spaces-morphisms-lemma-equality-of-morphisms"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2777,
          "label": "spaces-morphisms-lemma-push-down-solution"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3307,
          "label": "spaces-morphisms-lemma-etale-unramified"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3308,
          "label": "spaces-morphisms-lemma-diagonal-unramified-morphism"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3340,
          "label": "spaces-morphisms-lemma-equality-of-morphisms"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3360,
          "label": "spaces-morphisms-lemma-refined-valuative-criterion-universally-closed"
        },
        {
          "caller": "spaces-cohomology.tex",
          "line": 3380,
          "label": "spaces-morphisms-lemma-lift-valuation-ring-through-flat-morphism"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:32.854743+00:00"
    },
    {
      "package_path": "native/stacks-more-morphisms.tex",
      "sha256": "38c2be1dc32b9fca7e819aabf1ad3c5067c6eab475f82bd61e5b8b3e12f7bbbc",
      "bytes": 198225,
      "source_id": "AGAS-NATIVE-STACKS-565B-STACKS-MORE-MORPHISMS",
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/stacks-more-morphisms.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/stacks-more-morphisms.tex",
      "role": "native proof body",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": [
        "general stack Chow proof and finite-cover factorisation, lines1977-2240",
        "complete refined properness/separatedness proofs, lines2691-2871"
      ],
      "proof_locators": [
        "stacks-more-morphisms-lemma-refined-valuative-criterion-proper/0CQM",
        "stacks-more-morphisms-lemma-refined-valuative-criterion-separated/0E95",
        "stacks-more-morphisms-theorem-chow-finite-type/0CQ5"
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.200251+00:00"
    },
    {
      "package_path": "native/stacks-morphisms.tex",
      "sha256": "1f81f01c6748709778c0f877f1cb687152b344aa1c455449d2a341bbfe6a8b90",
      "bytes": 404259,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/stacks-morphisms.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/stacks-morphisms.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "stacks-morphisms-definition-fill-in-diagram",
        "stacks-morphisms-lemma-cat-dotted-arrows",
        "stacks-morphisms-lemma-cat-dotted-arrows-base-change",
        "stacks-morphisms-lemma-cat-dotted-arrows-independent",
        "stacks-morphisms-lemma-criterion-proper",
        "stacks-morphisms-lemma-fppf-open",
        "stacks-morphisms-lemma-gerbe-fppf",
        "stacks-morphisms-lemma-gerbe-isom-fppf",
        "stacks-morphisms-lemma-helper-diagonal",
        "stacks-morphisms-lemma-image-proper-is-proper",
        "stacks-morphisms-lemma-properties-diagonal",
        "stacks-morphisms-lemma-section-immersion",
        "stacks-morphisms-lemma-separated-implies-isom"
      ],
      "required_by": [
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2069,
          "label": "stacks-morphisms-lemma-gerbe-fppf"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2136,
          "label": "stacks-morphisms-lemma-gerbe-isom-fppf"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2191,
          "label": "stacks-morphisms-lemma-separated-implies-isom"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2235,
          "label": "stacks-morphisms-lemma-section-immersion"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2718,
          "label": "stacks-morphisms-definition-fill-in-diagram"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2730,
          "label": "stacks-morphisms-lemma-fppf-open"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2734,
          "label": "stacks-morphisms-lemma-cat-dotted-arrows-base-change"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2747,
          "label": "stacks-morphisms-lemma-cat-dotted-arrows-independent"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2784,
          "label": "stacks-morphisms-lemma-criterion-proper"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2798,
          "label": "stacks-morphisms-lemma-image-proper-is-proper"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2831,
          "label": "stacks-morphisms-lemma-properties-diagonal"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2844,
          "label": "stacks-morphisms-lemma-helper-diagonal"
        },
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2865,
          "label": "stacks-morphisms-lemma-cat-dotted-arrows"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.634075+00:00"
    },
    {
      "package_path": "native/stacks-project.cls",
      "sha256": "dbace0cb163b1b24f2816d89c547a3d487d51d59ede0303fad079e8ae3f93254",
      "bytes": 60186,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/stacks-project.cls",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/stacks-project.cls",
      "role": "original build support, licence or provenance",
      "terms": "Preserve original file notices; COPYING is the unmodified GFDL legal text, documentation preserves its actual source provenance.",
      "actual_read_scope": "Source/support identity and applicable notices; no extra mathematical closure asserted.",
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.917260+00:00"
    },
    {
      "package_path": "native/stacks-properties.tex",
      "sha256": "59d6b6df8f528ed5d3a68d9b9d74622e9b643f3622cc4d381bb46cc27a990016",
      "bytes": 120421,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/stacks-properties.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/stacks-properties.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "stacks-properties-lemma-points-cartesian"
      ],
      "required_by": [
        {
          "caller": "stacks-more-morphisms.tex",
          "line": 2725,
          "label": "stacks-properties-lemma-points-cartesian"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.698594+00:00"
    },
    {
      "package_path": "native/topology.tex",
      "sha256": "38d2e107901be84fa1ead3587db2fbfc50589914d49db0ed5937c14d9b934f34",
      "bytes": 245067,
      "revision": "91cc89df5804b8c1949d8267602fc076649ee49b",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/91cc89df5804b8c1949d8267602fc076649ee49b/topology.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/91cc89df5804b8c1949d8267602fc076649ee49b/topology.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "topology-lemma-closed-morphism-quotient-topology"
      ],
      "required_by": [
        {
          "caller": "resolve.tex",
          "line": 4339,
          "label": "topology-lemma-closed-morphism-quotient-topology"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:35.745139+00:00"
    },
    {
      "package_path": "native/varieties.tex",
      "sha256": "bb075fde0a9a393f3a15a5006ed9b755efc06050e746fd6113629bec0d92511a",
      "bytes": 463806,
      "revision": "565b10e987aba5969b21145a0833f42d69f96790",
      "source_url": "https://raw.githubusercontent.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/565b10e987aba5969b21145a0833f42d69f96790/varieties.tex",
      "pinned_browse_url": "https://github.com/KokunoYumeto/unofficial-stacks-project-ai-drafts/blob/565b10e987aba5969b21145a0833f42d69f96790/varieties.tex",
      "role": "native dependency",
      "terms": "Original native Stacks/AI Integrated Stacks source: GFDL 1.2 or later under the preserved grant; not AI-original CC0.",
      "actual_read_scope": "Bundled direct ordinary-foundation/dependency chapter; full independent audit not claimed.",
      "proof_locators": [
        "varieties-definition-algebraic-scheme",
        "varieties-definition-degree-invertible-sheaf",
        "varieties-lemma-ample-curve",
        "varieties-lemma-ampleness-in-terms-of-degrees-components",
        "varieties-lemma-change-fields-pic",
        "varieties-lemma-check-invertible-sheaf-trivial",
        "varieties-lemma-degree-effective-Cartier-divisor",
        "varieties-lemma-degree-tensor-product",
        "varieties-lemma-dimension-fibre-in-higher-codimension",
        "varieties-lemma-dimension-locally-algebraic",
        "varieties-lemma-divisible",
        "varieties-lemma-euler-characteristic-additive",
        "varieties-lemma-finite-in-codim-1",
        "varieties-lemma-image-irreducible",
        "varieties-lemma-modification-normal-iso-over-codimension-1",
        "varieties-lemma-prepare-delta-invariant",
        "varieties-lemma-proper-geometrically-reduced-global-sections",
        "varieties-lemma-regular-functions-proper-variety",
        "varieties-lemma-smooth-separable-closed-points-dense",
        "varieties-lemma-variety-with-smooth-rational-point",
        "varieties-section-divisors-curves"
      ],
      "required_by": [
        {
          "caller": "models.tex",
          "line": 4120,
          "label": "varieties-definition-algebraic-scheme"
        },
        {
          "caller": "models.tex",
          "line": 4242,
          "label": "varieties-lemma-modification-normal-iso-over-codimension-1"
        },
        {
          "caller": "models.tex",
          "line": 4478,
          "label": "varieties-section-divisors-curves"
        },
        {
          "caller": "models.tex",
          "line": 4498,
          "label": "varieties-lemma-degree-tensor-product"
        },
        {
          "caller": "models.tex",
          "line": 4514,
          "label": "varieties-lemma-degree-effective-Cartier-divisor"
        },
        {
          "caller": "models.tex",
          "line": 4616,
          "label": "varieties-lemma-proper-geometrically-reduced-global-sections"
        },
        {
          "caller": "models.tex",
          "line": 4641,
          "label": "varieties-lemma-check-invertible-sheaf-trivial"
        },
        {
          "caller": "models.tex",
          "line": 4700,
          "label": "varieties-lemma-euler-characteristic-additive"
        },
        {
          "caller": "models.tex",
          "line": 4706,
          "label": "varieties-lemma-degree-tensor-product"
        },
        {
          "caller": "models.tex",
          "line": 5148,
          "label": "varieties-lemma-regular-functions-proper-variety"
        },
        {
          "caller": "models.tex",
          "line": 5248,
          "label": "varieties-lemma-variety-with-smooth-rational-point"
        },
        {
          "caller": "models.tex",
          "line": 5313,
          "label": "varieties-lemma-divisible"
        },
        {
          "caller": "models.tex",
          "line": 5373,
          "label": "varieties-lemma-variety-with-smooth-rational-point"
        },
        {
          "caller": "models.tex",
          "line": 5712,
          "label": "varieties-lemma-divisible"
        },
        {
          "caller": "models.tex",
          "line": 6419,
          "label": "varieties-lemma-variety-with-smooth-rational-point"
        },
        {
          "caller": "models.tex",
          "line": 6445,
          "label": "varieties-lemma-change-fields-pic"
        },
        {
          "caller": "models.tex",
          "line": 6598,
          "label": "varieties-lemma-change-fields-pic"
        },
        {
          "caller": "curves.tex",
          "line": 3493,
          "label": "varieties-lemma-smooth-separable-closed-points-dense"
        },
        {
          "caller": "curves.tex",
          "line": 3514,
          "label": "varieties-lemma-prepare-delta-invariant"
        },
        {
          "caller": "curves.tex",
          "line": 3609,
          "label": "varieties-lemma-image-irreducible"
        },
        {
          "caller": "curves.tex",
          "line": 3768,
          "label": "varieties-lemma-change-fields-pic"
        },
        {
          "caller": "resolve.tex",
          "line": 1092,
          "label": "varieties-lemma-modification-normal-iso-over-codimension-1"
        },
        {
          "caller": "resolve.tex",
          "line": 1139,
          "label": "varieties-lemma-dimension-locally-algebraic"
        },
        {
          "caller": "resolve.tex",
          "line": 1377,
          "label": "varieties-lemma-modification-normal-iso-over-codimension-1"
        },
        {
          "caller": "resolve.tex",
          "line": 1381,
          "label": "varieties-lemma-dimension-fibre-in-higher-codimension"
        },
        {
          "caller": "resolve.tex",
          "line": 1454,
          "label": "varieties-lemma-degree-tensor-product"
        },
        {
          "caller": "resolve.tex",
          "line": 1471,
          "label": "varieties-lemma-check-invertible-sheaf-trivial"
        },
        {
          "caller": "resolve.tex",
          "line": 1771,
          "label": "varieties-lemma-finite-in-codim-1"
        },
        {
          "caller": "resolve.tex",
          "line": 2396,
          "label": "varieties-definition-degree-invertible-sheaf"
        },
        {
          "caller": "resolve.tex",
          "line": 2850,
          "label": "varieties-lemma-modification-normal-iso-over-codimension-1"
        },
        {
          "caller": "resolve.tex",
          "line": 3218,
          "label": "varieties-lemma-ampleness-in-terms-of-degrees-components"
        },
        {
          "caller": "resolve.tex",
          "line": 3793,
          "label": "varieties-lemma-modification-normal-iso-over-codimension-1"
        },
        {
          "caller": "resolve.tex",
          "line": 3971,
          "label": "varieties-lemma-finite-in-codim-1"
        },
        {
          "caller": "resolve.tex",
          "line": 4556,
          "label": "varieties-lemma-modification-normal-iso-over-codimension-1"
        },
        {
          "caller": "resolve.tex",
          "line": 4683,
          "label": "varieties-lemma-ample-curve"
        }
      ],
      "byte_verification": "pinned remote bytes equal existing local source; no remote source saved",
      "verified_utc": "2026-10-05T19:49:31.579019+00:00"
    }
  ]
}