{
  "schema": "AN01-current-HA-LCA-actual-reading/v1",
  "provider_commit": "724d1a8dd6e33982a18e71a7735cc02ccb10b812",
  "purpose": "Actual proof reading for preserved broader quotient/lattice route in U056. The one-dimensional proof is already complete independently.",
  "selected_roots": [
    "HA-LCA-11/theorem.1.1",
    "HA-LCA-11/corollary.2.1",
    "HA-LCA-11/corollary.2.2",
    "HA-LCA-11/proposition.1.2"
  ],
  "selected_proof_count": 192,
  "completed_document_selections": {
    "prerequisites/src/banach-spectrum.md": {
      "checked_at": "2026-10-05T08:38:18.554113+00:00",
      "source_sha256": "ef20db2c562c9fb68f31cfc0b9c6e9cec0abce7fe0d31f41b109c2d932a2d598",
      "proof_ids": [
        "HA-LCA-PRE-BANACH/corollary.2.3",
        "HA-LCA-PRE-BANACH/lemma.1.1",
        "HA-LCA-PRE-BANACH/lemma.1.2",
        "HA-LCA-PRE-BANACH/lemma.1.3",
        "HA-LCA-PRE-BANACH/lemma.1.4",
        "HA-LCA-PRE-BANACH/lemma.2.1",
        "HA-LCA-PRE-BANACH/lemma.3.1",
        "HA-LCA-PRE-BANACH/lemma.3.2",
        "HA-LCA-PRE-BANACH/lemma.4.1",
        "HA-LCA-PRE-BANACH/theorem.2.2",
        "HA-LCA-PRE-BANACH/theorem.3.3",
        "HA-LCA-PRE-BANACH/theorem.3.4",
        "HA-LCA-PRE-BANACH/theorem.4.2"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "prerequisites/src/dual-balls-and-compact-convexity.md": {
      "checked_at": "2026-10-05T08:38:18.554621+00:00",
      "source_sha256": "14d1c69babbdca3e54ba0f13b1b85a3dcb5d837aa17c57f74241874e3660b6ea",
      "proof_ids": [
        "HA-LCA-PRE-DUAL-CONVEX/corollary.1.3",
        "HA-LCA-PRE-DUAL-CONVEX/corollary.3.3",
        "HA-LCA-PRE-DUAL-CONVEX/lemma.1.1",
        "HA-LCA-PRE-DUAL-CONVEX/lemma.2.2",
        "HA-LCA-PRE-DUAL-CONVEX/lemma.3.1",
        "HA-LCA-PRE-DUAL-CONVEX/theorem.1.2",
        "HA-LCA-PRE-DUAL-CONVEX/theorem.2.1",
        "HA-LCA-PRE-DUAL-CONVEX/theorem.3.2"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "prerequisites/src/finite-radon-products.md": {
      "checked_at": "2026-10-05T08:38:18.555139+00:00",
      "source_sha256": "c241e2b01e0750b5b94ab045c430a336be0e4870df99c9df948a06252a8a28ba",
      "proof_ids": [
        "HA-LCA-PRE-PRODUCT/corollary.2.3",
        "HA-LCA-PRE-PRODUCT/lemma.1.1",
        "HA-LCA-PRE-PRODUCT/lemma.1.2",
        "HA-LCA-PRE-PRODUCT/proposition.3.1",
        "HA-LCA-PRE-PRODUCT/proposition.3.2",
        "HA-LCA-PRE-PRODUCT/theorem.2.1",
        "HA-LCA-PRE-PRODUCT/theorem.2.2",
        "HA-LCA-PRE-PRODUCT/theorem.3.3"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "prerequisites/src/finite-radon-representation.md": {
      "checked_at": "2026-10-05T08:38:18.555139+00:00",
      "source_sha256": "36722b08bed4c318b43fcd6b387602b3629135d535aad45bbd12943a2fe56082",
      "proof_ids": [
        "HA-LCA-PRE-RADON/corollary.4.5",
        "HA-LCA-PRE-RADON/lemma.1.1",
        "HA-LCA-PRE-RADON/lemma.1.2",
        "HA-LCA-PRE-RADON/lemma.1.3",
        "HA-LCA-PRE-RADON/lemma.1.4",
        "HA-LCA-PRE-RADON/lemma.1.5",
        "HA-LCA-PRE-RADON/lemma.1.6",
        "HA-LCA-PRE-RADON/lemma.2.1",
        "HA-LCA-PRE-RADON/lemma.2.2",
        "HA-LCA-PRE-RADON/lemma.4.1",
        "HA-LCA-PRE-RADON/lemma.4.2",
        "HA-LCA-PRE-RADON/proposition.4.4",
        "HA-LCA-PRE-RADON/theorem.3.1",
        "HA-LCA-PRE-RADON/theorem.4.3"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "prerequisites/src/haar-measure.md": {
      "checked_at": "2026-10-05T08:38:18.555656+00:00",
      "source_sha256": "b0993ca756deab4bb8f3af07eff6b2eacb2f243e5e9a9a1c34a07752f6f6e91f",
      "proof_ids": [
        "HA-LCA-PRE-HAAR/corollary.6.3",
        "HA-LCA-PRE-HAAR/lemma.1.1",
        "HA-LCA-PRE-HAAR/lemma.2.1",
        "HA-LCA-PRE-HAAR/lemma.5.2",
        "HA-LCA-PRE-HAAR/lemma.6.1",
        "HA-LCA-PRE-HAAR/theorem.2.2",
        "HA-LCA-PRE-HAAR/theorem.3.1",
        "HA-LCA-PRE-HAAR/theorem.4.1",
        "HA-LCA-PRE-HAAR/theorem.5.1",
        "HA-LCA-PRE-HAAR/theorem.6.2"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "prerequisites/src/hilbert-spaces-and-unitary-representations.md": {
      "checked_at": "2026-10-05T08:38:18.556178+00:00",
      "source_sha256": "cc1b8a90c8f8a6436864722be988570922c96e85ec970b595a29e1e1d11bf703",
      "proof_ids": [
        "HA-LCA-PRE-HILBERT/corollary.2.2",
        "HA-LCA-PRE-HILBERT/lemma.1.1",
        "HA-LCA-PRE-HILBERT/lemma.4.1",
        "HA-LCA-PRE-HILBERT/proposition.2.4",
        "HA-LCA-PRE-HILBERT/proposition.3.1",
        "HA-LCA-PRE-HILBERT/proposition.3.3",
        "HA-LCA-PRE-HILBERT/proposition.6.2",
        "HA-LCA-PRE-HILBERT/proposition.7.1",
        "HA-LCA-PRE-HILBERT/proposition.7.3",
        "HA-LCA-PRE-HILBERT/theorem.1.2",
        "HA-LCA-PRE-HILBERT/theorem.2.1",
        "HA-LCA-PRE-HILBERT/theorem.2.3",
        "HA-LCA-PRE-HILBERT/theorem.3.2",
        "HA-LCA-PRE-HILBERT/theorem.4.2",
        "HA-LCA-PRE-HILBERT/theorem.4.3",
        "HA-LCA-PRE-HILBERT/theorem.5.1",
        "HA-LCA-PRE-HILBERT/theorem.6.1",
        "HA-LCA-PRE-HILBERT/theorem.7.2"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "prerequisites/src/integration-and-l1.md": {
      "checked_at": "2026-10-05T08:38:18.556178+00:00",
      "source_sha256": "cd5ed704758a55778630c7a5b0d503c6024f69ced182b2ee6cb1b49a62e339c0",
      "proof_ids": [
        "HA-LCA-PRE-INTEGRAL/corollary.1.3",
        "HA-LCA-PRE-INTEGRAL/corollary.4.3",
        "HA-LCA-PRE-INTEGRAL/lemma.1.1",
        "HA-LCA-PRE-INTEGRAL/lemma.2.1",
        "HA-LCA-PRE-INTEGRAL/lemma.2.3",
        "HA-LCA-PRE-INTEGRAL/lemma.2.5",
        "HA-LCA-PRE-INTEGRAL/lemma.4.1",
        "HA-LCA-PRE-INTEGRAL/theorem.1.2",
        "HA-LCA-PRE-INTEGRAL/theorem.2.2",
        "HA-LCA-PRE-INTEGRAL/theorem.2.4",
        "HA-LCA-PRE-INTEGRAL/theorem.3.1",
        "HA-LCA-PRE-INTEGRAL/theorem.4.2",
        "HA-LCA-PRE-INTEGRAL/theorem.4.4"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "prerequisites/src/nonabelian-haar-integration.md": {
      "checked_at": "2026-10-05T08:38:18.556717+00:00",
      "source_sha256": "d9cc75409ca3f44876bee54596d690bb6de65302b6a317615ca71f9aa1733c68",
      "proof_ids": [
        "HA-LCA-PRE-NONABELIAN-HAAR/corollary.6.2",
        "HA-LCA-PRE-NONABELIAN-HAAR/lemma.1.1",
        "HA-LCA-PRE-NONABELIAN-HAAR/lemma.3.2",
        "HA-LCA-PRE-NONABELIAN-HAAR/lemma.5.1",
        "HA-LCA-PRE-NONABELIAN-HAAR/proposition.5.2",
        "HA-LCA-PRE-NONABELIAN-HAAR/proposition.7.1",
        "HA-LCA-PRE-NONABELIAN-HAAR/theorem.2.1",
        "HA-LCA-PRE-NONABELIAN-HAAR/theorem.2.2",
        "HA-LCA-PRE-NONABELIAN-HAAR/theorem.3.1",
        "HA-LCA-PRE-NONABELIAN-HAAR/theorem.3.3",
        "HA-LCA-PRE-NONABELIAN-HAAR/theorem.4.1",
        "HA-LCA-PRE-NONABELIAN-HAAR/theorem.6.1",
        "HA-LCA-PRE-NONABELIAN-HAAR/theorem.7.2"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "prerequisites/src/uniform-approximation.md": {
      "checked_at": "2026-10-05T08:38:18.557234+00:00",
      "source_sha256": "300884a9ff1e9afde332c49627163ec8d58a828bba89e5476d8b19c15adf833d",
      "proof_ids": [
        "HA-LCA-PRE-APPROX/corollary.2.2",
        "HA-LCA-PRE-APPROX/lemma.1.1",
        "HA-LCA-PRE-APPROX/lemma.1.2",
        "HA-LCA-PRE-APPROX/lemma.3.1",
        "HA-LCA-PRE-APPROX/theorem.2.1",
        "HA-LCA-PRE-APPROX/theorem.3.2"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/the-poisson-summation-formula.md": {
      "checked_at": "2026-10-05T08:38:18.557755+00:00",
      "source_sha256": "5bd7f675716289c5512ef2ff4d2daff2d9bb6882a0953f28bffb551b51daa582",
      "proof_ids": [
        "HA-LCA-11/corollary.2.1",
        "HA-LCA-11/corollary.2.2",
        "HA-LCA-11/lemma.1.0",
        "HA-LCA-11/lemma.2.0",
        "HA-LCA-11/proposition.1.2",
        "HA-LCA-11/theorem.1.1"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "prerequisites/src/real-variable-calculations.md": {
      "checked_at": "2026-10-05T08:43:31.690890+00:00",
      "source_sha256": "966bfe9626f8698b5e50b4b3f11448534db3ab8e24a78c7492a51288ad73086c",
      "proof_ids": [
        "HA-LCA-PRE-REAL/lemma.1.1",
        "HA-LCA-PRE-REAL/lemma.1.2",
        "HA-LCA-PRE-REAL/lemma.1.3",
        "HA-LCA-PRE-REAL/lemma.1.4",
        "HA-LCA-PRE-REAL/theorem.2.1"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/bochners-theorem.md": {
      "checked_at": "2026-10-05T08:43:31.691891+00:00",
      "source_sha256": "475168293f87bbfa059dfe17c993de9826e9a177b444b9ac6fe37887e7487250",
      "proof_ids": [
        "HA-LCA-06/lemma.1.2",
        "HA-LCA-06/lemma.2.0",
        "HA-LCA-06/proposition.1.1",
        "HA-LCA-06/proposition.4.1",
        "HA-LCA-06/theorem.1.3",
        "HA-LCA-06/theorem.2.1"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/characters-and-the-dual-group.md": {
      "checked_at": "2026-10-05T08:43:31.692890+00:00",
      "source_sha256": "b1c3000a40213e58931562d8edbbfa4566aa7b4b45bdf21227d1d7ee8f77fd95",
      "proof_ids": [
        "HA-LCA-02/corollary.3.2",
        "HA-LCA-02/lemma.1.2",
        "HA-LCA-02/lemma.1.3",
        "HA-LCA-02/lemma.3.3",
        "HA-LCA-02/proposition.1.1",
        "HA-LCA-02/proposition.1.4",
        "HA-LCA-02/proposition.4.1",
        "HA-LCA-02/proposition.5.1",
        "HA-LCA-02/theorem.2.1",
        "HA-LCA-02/theorem.3.1",
        "HA-LCA-02/theorem.5.2"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/fourier-analysis-on-finite-abelian-groups.md": {
      "checked_at": "2026-10-05T08:43:31.692890+00:00",
      "source_sha256": "e143c7d8feb489c4a7bb3c45020f7d32c4903863f1153ca346758e88f303a2ec",
      "proof_ids": [
        "HA-LCA-01/lemma.0.0",
        "HA-LCA-01/lemma.0.1",
        "HA-LCA-01/theorem.1.1"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/functions-of-positive-type.md": {
      "checked_at": "2026-10-05T08:43:31.692890+00:00",
      "source_sha256": "b62bb6b90538a7baabd9a3f66e01906dde1d40094a07588d9cc29a6198928c2a",
      "proof_ids": [
        "HA-LCA-04/corollary.3.2",
        "HA-LCA-04/example.6.1",
        "HA-LCA-04/example.6.3",
        "HA-LCA-04/exercise.7.1",
        "HA-LCA-04/lemma.1.2",
        "HA-LCA-04/lemma.2.0",
        "HA-LCA-04/lemma.2.1",
        "HA-LCA-04/lemma.3.3",
        "HA-LCA-04/lemma.4.2",
        "HA-LCA-04/proposition.1.1",
        "HA-LCA-04/proposition.2.2",
        "HA-LCA-04/theorem.3.1",
        "HA-LCA-04/theorem.4.1",
        "HA-LCA-04/theorem.4.3"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/raikovs-theorem-and-the-gelfand-raikov-theorem.md": {
      "checked_at": "2026-10-05T08:43:31.692890+00:00",
      "source_sha256": "c4ccf366511b842a7b1e67f6a1ef4e44a510d0de1e8d6a669511d633fadb0753",
      "proof_ids": [
        "HA-LCA-05/corollary.4.2",
        "HA-LCA-05/lemma.1.1",
        "HA-LCA-05/lemma.1.2",
        "HA-LCA-05/lemma.1.3",
        "HA-LCA-05/lemma.3.0",
        "HA-LCA-05/proposition.3.1",
        "HA-LCA-05/theorem.2.1",
        "HA-LCA-05/theorem.4.1"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/the-dual-group-as-the-gelfand-spectrum-of-l1.md": {
      "checked_at": "2026-10-05T08:43:31.694417+00:00",
      "source_sha256": "b0b08cb7f524ab82e3b8bbfb738ab5bac85f442b5d0252819960a0175987a90b",
      "proof_ids": [
        "HA-LCA-03/corollary.2.2",
        "HA-LCA-03/lemma.1.1",
        "HA-LCA-03/lemma.1.2",
        "HA-LCA-03/lemma.4.1",
        "HA-LCA-03/lemma.5.1",
        "HA-LCA-03/theorem.2.1",
        "HA-LCA-03/theorem.3.1",
        "HA-LCA-03/theorem.3.2"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/subgroups-quotients-and-annihilators.md": {
      "checked_at": "2026-10-05T08:44:17.464603+00:00",
      "source_sha256": "26c9704658dd289d50f3184b5b5ba333538f2b028bbbbf4aea04f1c4824acb60",
      "proof_ids": [
        "HA-LCA-10/example.6.2",
        "HA-LCA-10/lemma.1.1",
        "HA-LCA-10/lemma.3.1",
        "HA-LCA-10/lemma.3.2",
        "HA-LCA-10/lemma.5.0",
        "HA-LCA-10/lemma.6.0",
        "HA-LCA-10/proposition.1.2",
        "HA-LCA-10/theorem.2.1",
        "HA-LCA-10/theorem.4.1"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/the-fourier-inversion-theorem-and-the-dual-haar-measure.md": {
      "checked_at": "2026-10-05T08:44:17.464603+00:00",
      "source_sha256": "69b747ad7396e65bb21174a1005d3f58a3893f201ea529ee5bc1c0636c1c938a",
      "proof_ids": [
        "HA-LCA-07/lemma.1.0",
        "HA-LCA-07/lemma.1.1",
        "HA-LCA-07/lemma.1.2",
        "HA-LCA-07/lemma.3.0",
        "HA-LCA-07/proposition.3.1",
        "HA-LCA-07/proposition.3.2",
        "HA-LCA-07/proposition.3.3",
        "HA-LCA-07/theorem.2.1"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/the-plancherel-theorem.md": {
      "checked_at": "2026-10-05T08:44:17.464603+00:00",
      "source_sha256": "bfb076ca1da813ff3d4bd0aa103266114be28cc52815abc3d1326eb34954a210",
      "proof_ids": [
        "HA-LCA-08/corollary.3.2",
        "HA-LCA-08/proposition.2.1",
        "HA-LCA-08/theorem.1.1",
        "HA-LCA-08/theorem.3.1"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    },
    "src/the-pontryagin-duality-theorem.md": {
      "checked_at": "2026-10-05T08:44:17.464603+00:00",
      "source_sha256": "512aa0190639e6dd873b9f5fd0c36bb2eee2332072455eee0861635e0034880b",
      "proof_ids": [
        "HA-LCA-09/lemma.1.2",
        "HA-LCA-09/lemma.1.3",
        "HA-LCA-09/lemma.6.0",
        "HA-LCA-09/proposition.3.1",
        "HA-LCA-09/proposition.5.1",
        "HA-LCA-09/theorem.2.1",
        "HA-LCA-09/theorem.4.1"
      ],
      "scope": "Complete selected proof blocks and introductory definitions actually read; hypotheses and proof steps compared. Dependencies are separately tracked.",
      "defects_found": []
    }
  },
  "partial_documents": {},
  "independent_review_claimed": false,
  "full_provider_review_complete": false,
  "selected_proofs_read": 192,
  "remaining_document_selections": [],
  "updated_at": "2026-10-05T08:44:17.464603+00:00",
  "selected_dependency_closure_checked": true,
  "selected_dependency_graph_acyclic": true,
  "selected_proof_reading_complete": true,
  "checked_at": "2026-10-05T08:47:27.269660+00:00",
  "topological_proof_order": [
    "HA-LCA-01/lemma.0.0",
    "HA-LCA-PRE-BANACH/lemma.1.1",
    "HA-LCA-PRE-BANACH/lemma.1.2",
    "HA-LCA-PRE-BANACH/lemma.1.3",
    "HA-LCA-01/lemma.0.1",
    "HA-LCA-01/theorem.1.1",
    "HA-LCA-PRE-RADON/lemma.1.1",
    "HA-LCA-02/lemma.1.3",
    "HA-LCA-02/proposition.1.1",
    "HA-LCA-02/lemma.1.2",
    "HA-LCA-PRE-BANACH/lemma.4.1",
    "HA-LCA-02/theorem.2.1",
    "HA-LCA-02/theorem.3.1",
    "HA-LCA-02/proposition.1.4",
    "HA-LCA-02/corollary.3.2",
    "HA-LCA-PRE-RADON/lemma.1.2",
    "HA-LCA-PRE-RADON/lemma.1.3",
    "HA-LCA-PRE-RADON/lemma.1.6",
    "HA-LCA-PRE-RADON/lemma.2.1",
    "HA-LCA-PRE-RADON/lemma.2.2",
    "HA-LCA-PRE-RADON/lemma.4.1",
    "HA-LCA-PRE-PRODUCT/lemma.1.1",
    "HA-LCA-PRE-HAAR/lemma.1.1",
    "HA-LCA-PRE-HAAR/lemma.2.1",
    "HA-LCA-PRE-HAAR/theorem.2.2",
    "HA-LCA-PRE-RADON/lemma.1.5",
    "HA-LCA-PRE-RADON/lemma.1.4",
    "HA-LCA-PRE-RADON/theorem.3.1",
    "HA-LCA-PRE-RADON/proposition.4.4",
    "HA-LCA-PRE-PRODUCT/lemma.1.2",
    "HA-LCA-PRE-RADON/lemma.4.2",
    "HA-LCA-PRE-RADON/theorem.4.3",
    "HA-LCA-PRE-PRODUCT/theorem.2.1",
    "HA-LCA-PRE-RADON/corollary.4.5",
    "HA-LCA-PRE-PRODUCT/theorem.2.2",
    "HA-LCA-PRE-PRODUCT/corollary.2.3",
    "HA-LCA-PRE-INTEGRAL/lemma.1.1",
    "HA-LCA-PRE-INTEGRAL/theorem.1.2",
    "HA-LCA-PRE-INTEGRAL/corollary.1.3",
    "HA-LCA-PRE-INTEGRAL/lemma.2.1",
    "HA-LCA-PRE-HAAR/theorem.3.1",
    "HA-LCA-PRE-INTEGRAL/lemma.2.5",
    "HA-LCA-PRE-HAAR/theorem.4.1",
    "HA-LCA-PRE-HAAR/theorem.5.1",
    "HA-LCA-PRE-INTEGRAL/lemma.4.1",
    "HA-LCA-02/lemma.3.3",
    "HA-LCA-02/proposition.4.1",
    "HA-LCA-02/proposition.5.1",
    "HA-LCA-02/theorem.5.2",
    "HA-LCA-PRE-INTEGRAL/theorem.2.2",
    "HA-LCA-PRE-INTEGRAL/lemma.2.3",
    "HA-LCA-PRE-INTEGRAL/theorem.2.4",
    "HA-LCA-PRE-INTEGRAL/theorem.3.1",
    "HA-LCA-PRE-HAAR/lemma.5.2",
    "HA-LCA-PRE-HAAR/lemma.6.1",
    "HA-LCA-PRE-INTEGRAL/theorem.4.2",
    "HA-LCA-PRE-INTEGRAL/corollary.4.3",
    "HA-LCA-PRE-INTEGRAL/theorem.4.4",
    "HA-LCA-PRE-HAAR/theorem.6.2",
    "HA-LCA-03/lemma.1.1",
    "HA-LCA-PRE-HAAR/corollary.6.3",
    "HA-LCA-03/lemma.1.2",
    "HA-LCA-PRE-BANACH/lemma.1.4",
    "HA-LCA-PRE-BANACH/lemma.2.1",
    "HA-LCA-PRE-BANACH/theorem.2.2",
    "HA-LCA-PRE-BANACH/lemma.3.1",
    "HA-LCA-PRE-BANACH/corollary.2.3",
    "HA-LCA-PRE-BANACH/lemma.3.2",
    "HA-LCA-PRE-BANACH/theorem.3.3",
    "HA-LCA-PRE-BANACH/theorem.3.4",
    "HA-LCA-03/theorem.2.1",
    "HA-LCA-PRE-BANACH/theorem.4.2",
    "HA-LCA-03/corollary.2.2",
    "HA-LCA-03/lemma.4.1",
    "HA-LCA-PRE-PRODUCT/proposition.3.1",
    "HA-LCA-PRE-REAL/lemma.1.1",
    "HA-LCA-03/lemma.5.1",
    "HA-LCA-03/theorem.3.1",
    "HA-LCA-PRE-APPROX/lemma.3.1",
    "HA-LCA-PRE-APPROX/lemma.1.1",
    "HA-LCA-PRE-APPROX/lemma.1.2",
    "HA-LCA-PRE-APPROX/theorem.2.1",
    "HA-LCA-PRE-APPROX/corollary.2.2",
    "HA-LCA-PRE-APPROX/theorem.3.2",
    "HA-LCA-03/theorem.3.2",
    "HA-LCA-PRE-HILBERT/lemma.1.1",
    "HA-LCA-PRE-HILBERT/theorem.1.2",
    "HA-LCA-04/lemma.2.0",
    "HA-LCA-PRE-NONABELIAN-HAAR/lemma.1.1",
    "HA-LCA-PRE-NONABELIAN-HAAR/theorem.2.1",
    "HA-LCA-PRE-NONABELIAN-HAAR/theorem.2.2",
    "HA-LCA-PRE-NONABELIAN-HAAR/theorem.3.1",
    "HA-LCA-PRE-NONABELIAN-HAAR/lemma.3.2",
    "HA-LCA-PRE-NONABELIAN-HAAR/theorem.3.3",
    "HA-LCA-PRE-NONABELIAN-HAAR/theorem.4.1",
    "HA-LCA-PRE-HILBERT/theorem.6.1",
    "HA-LCA-PRE-HILBERT/proposition.6.2",
    "HA-LCA-PRE-NONABELIAN-HAAR/lemma.5.1",
    "HA-LCA-PRE-NONABELIAN-HAAR/proposition.5.2",
    "HA-LCA-PRE-NONABELIAN-HAAR/theorem.6.1",
    "HA-LCA-PRE-NONABELIAN-HAAR/corollary.6.2",
    "HA-LCA-PRE-HILBERT/theorem.2.1",
    "HA-LCA-PRE-HILBERT/corollary.2.2",
    "HA-LCA-PRE-HILBERT/theorem.2.3",
    "HA-LCA-PRE-HILBERT/proposition.2.4",
    "HA-LCA-PRE-NONABELIAN-HAAR/theorem.7.2",
    "HA-LCA-PRE-HILBERT/proposition.3.1",
    "HA-LCA-PRE-DUAL-CONVEX/lemma.1.1",
    "HA-LCA-PRE-DUAL-CONVEX/theorem.1.2",
    "HA-LCA-04/lemma.1.2",
    "HA-LCA-04/lemma.2.1",
    "HA-LCA-PRE-HILBERT/theorem.3.2",
    "HA-LCA-PRE-NONABELIAN-HAAR/proposition.7.1",
    "HA-LCA-04/proposition.2.2",
    "HA-LCA-PRE-DUAL-CONVEX/corollary.1.3",
    "HA-LCA-04/theorem.3.1",
    "HA-LCA-04/corollary.3.2",
    "HA-LCA-PRE-REAL/lemma.1.2",
    "HA-LCA-PRE-REAL/lemma.1.3",
    "HA-LCA-PRE-REAL/lemma.1.4",
    "HA-LCA-PRE-REAL/theorem.2.1",
    "HA-LCA-04/example.6.1",
    "HA-LCA-PRE-HILBERT/lemma.4.1",
    "HA-LCA-PRE-HILBERT/theorem.4.2",
    "HA-LCA-PRE-HILBERT/theorem.4.3",
    "HA-LCA-04/example.6.3",
    "HA-LCA-PRE-HILBERT/proposition.7.1",
    "HA-LCA-PRE-HILBERT/proposition.7.3",
    "HA-LCA-04/exercise.7.1",
    "HA-LCA-04/lemma.3.3",
    "HA-LCA-PRE-DUAL-CONVEX/lemma.3.1",
    "HA-LCA-PRE-DUAL-CONVEX/lemma.2.2",
    "HA-LCA-PRE-DUAL-CONVEX/theorem.3.2",
    "HA-LCA-PRE-HILBERT/theorem.5.1",
    "HA-LCA-PRE-DUAL-CONVEX/theorem.2.1",
    "HA-LCA-PRE-DUAL-CONVEX/corollary.3.3",
    "HA-LCA-04/lemma.4.2",
    "HA-LCA-PRE-HILBERT/proposition.3.3",
    "HA-LCA-PRE-HILBERT/theorem.7.2",
    "HA-LCA-04/proposition.1.1",
    "HA-LCA-04/theorem.4.1",
    "HA-LCA-04/theorem.4.3",
    "HA-LCA-05/lemma.3.0",
    "HA-LCA-05/proposition.3.1",
    "HA-LCA-05/lemma.1.1",
    "HA-LCA-05/lemma.1.2",
    "HA-LCA-05/lemma.1.3",
    "HA-LCA-05/theorem.2.1",
    "HA-LCA-05/theorem.4.1",
    "HA-LCA-05/corollary.4.2",
    "HA-LCA-06/lemma.1.2",
    "HA-LCA-06/lemma.2.0",
    "HA-LCA-06/proposition.1.1",
    "HA-LCA-06/theorem.1.3",
    "HA-LCA-06/theorem.2.1",
    "HA-LCA-PRE-PRODUCT/proposition.3.2",
    "HA-LCA-PRE-PRODUCT/theorem.3.3",
    "HA-LCA-06/proposition.4.1",
    "HA-LCA-07/lemma.1.0",
    "HA-LCA-07/lemma.1.1",
    "HA-LCA-07/lemma.1.2",
    "HA-LCA-07/theorem.2.1",
    "HA-LCA-07/lemma.3.0",
    "HA-LCA-07/proposition.3.1",
    "HA-LCA-07/proposition.3.2",
    "HA-LCA-07/proposition.3.3",
    "HA-LCA-08/theorem.1.1",
    "HA-LCA-08/proposition.2.1",
    "HA-LCA-08/theorem.3.1",
    "HA-LCA-08/corollary.3.2",
    "HA-LCA-09/lemma.1.2",
    "HA-LCA-09/lemma.1.3",
    "HA-LCA-09/lemma.6.0",
    "HA-LCA-09/theorem.2.1",
    "HA-LCA-09/proposition.3.1",
    "HA-LCA-09/proposition.5.1",
    "HA-LCA-09/theorem.4.1",
    "HA-LCA-10/lemma.6.0",
    "HA-LCA-10/lemma.3.1",
    "HA-LCA-10/lemma.3.2",
    "HA-LCA-10/theorem.4.1",
    "HA-LCA-10/example.6.2",
    "HA-LCA-10/lemma.1.1",
    "HA-LCA-10/lemma.5.0",
    "HA-LCA-10/proposition.1.2",
    "HA-LCA-10/theorem.2.1",
    "HA-LCA-11/lemma.1.0",
    "HA-LCA-11/theorem.1.1",
    "HA-LCA-11/corollary.2.1",
    "HA-LCA-11/lemma.2.0",
    "HA-LCA-11/corollary.2.2",
    "HA-LCA-11/proposition.1.2"
  ],
  "extra_actual_reading": [
    "HA-LCA-10/proposition.5.1: dual Weil normalization, including its admissible C0 representative and positive test determining the constant.",
    "HA-LCA-10/proposition.6.1: discrete subgroup basis and closed Euclidean subgroup decomposition.",
    "HA-LCA-10/example.4.0: Borel null representative with nonzero coset integrals on a non-sigma-compact group.",
    "HA-LCA-11/examples.2.3-2.4: continuity counterexample and square/hexagonal lattice normalization."
  ],
  "mathematical_comparison": {
    "measures": "Complete locally determined Haar domains; quotient and dual measures are linked by Weil integration and inversion, not chosen independently.",
    "representatives": "P1 acts on L1 classes. Actual slicing uses a Borel representative zero outside an open sigma-compact subgroup; arbitrary completed representatives are admitted only in the sigma-compact case. An everywhere continuous absolute average agrees everywhere.",
    "normalization": "HA uses exp(-2*pi*i*x.xi); AN-01 uses exp(-i*x.s), so the transforms are related by s=2*pi*xi. The lattice factor is reciprocal covolume.",
    "dependencies": "Actual proofs read through finite Radon representation/products, Haar domains, integration, Hilbert/Banach tools, positive type, Bochner, inversion, Plancherel, duality, quotient and lattice statements. No graph traversal is presented as mathematical reading.",
    "preserved": "AN-01 U056 one-dimensional Schwartz/Fejer proof and all twelve solutions remain independent and unchanged."
  },
  "limits": "192 selected proof blocks in 21 documents were actually read and compared. Additional sections in the preserved full provider edition retain their original author-check status; this record does not independently review the entire HA-LCA course. Its external-source access records are provenance from that edition, not a claim of new external-source reading here."
}