{ "schema": "selected-prerequisite-readings/v1", "course": "representations-of-compact-groups", "readings": [ { "course": "harmonic-analysis-on-locally-compact-groups", "lesson": "haar-measure-on-locally-compact-groups", "source_sha256": "6c3ba44cc4d8c0c1fb12ec478481c44bf623f4252d8366d208939e5bd79f979d", "editable_source": "reader/courses/harmonic-analysis-on-locally-compact-groups/src/haar-measure-on-locally-compact-groups.md", "reader": "reader/courses/harmonic-analysis-on-locally-compact-groups/haar-measure-on-locally-compact-groups.html", "proof_scope": [ "Section2 complete Riesz/Radon representation, regularity and new bounded complex C0 functional theorem: lines45–146", "Sections3–6 complete density, product, full Radon Tonelli/Fubini and L2 tensor-product statements/proofs: lines147–272", "Section7 full topological group and uniform continuity proofs: lines273–304", "Theorem8.3/Lemma8.4 entire existence construction; Proposition9.1/Theorem9.2 positivity/uniqueness; Theorem10.1 modular function; Theorem11.1 inversion: lines305–443", "Theorem14.2 statement and complete proof, especially translation continuity part6: lines554–627" ], "authorship_notice": "*Originally written by Claude Opus 5.5 (Anthropic), September 2026, with a separate historical AI spot-check of that text. Repaired and self-checked by GPT-6.1 Sol (OpenAI), Ultra reasoning effort, October 2026. The current edition has no separately recorded independent AI or human review. Original programme content is dedicated under CC0.*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "foundations-of-von-neumann-algebras", "lesson": "hilbert-spaces-and-compact-operators", "source_sha256": "24e37107d506fcc8b4400cc70f8a8934815b3dbe24d73a9150a12c3fddc32fbe", "editable_source": "reader/courses/foundations-of-von-neumann-algebras/src/hilbert-spaces-and-compact-operators.md", "reader": "reader/courses/foundations-of-von-neumann-algebras/hilbert-spaces-and-compact-operators.html", "proof_scope": [ "Sections1–4 complete Cauchy–Schwarz, projection, Riesz–Frechet, bounded forms/adjoints and arbitrary orthonormal bases: lines1–120", "Sections5–6 complete compact approximation and compact self-adjoint spectral theorem: lines121–178" ], "authorship_notice": "*Written by Claude Opus 5.5 (Anthropic), October 2026. Self-checked by the writing AI. Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "foundations-of-von-neumann-algebras", "lesson": "the-spectral-theorem-for-bounded-self-adjoint-operators", "source_sha256": "d85fe0965b436b79f5260526e3e7b05fbe56d6811320a5fc7f3bcd1b696a82e5", "editable_source": "reader/courses/foundations-of-von-neumann-algebras/src/the-spectral-theorem-for-bounded-self-adjoint-operators.md", "reader": "reader/courses/foundations-of-von-neumann-algebras/the-spectral-theorem-for-bounded-self-adjoint-operators.html", "proof_scope": [ "Conventions/isometric continuous calculus; sections1–4 complete, including Borel calculus, commutation and projection-valued theorem: lines1–249" ], "authorship_notice": "*Written by Claude Opus 5.5 (Anthropic), October 2026. Self-checked by the writing AI. Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "function-algebras-and-approximation", "lesson": "the-stone-weierstrass-theorem-for-functions-vanishing-at-infinity", "source_sha256": "e96dff833d3ea82967912dfa90a653d90ad06b934da315773a1482f7caeda204", "editable_source": "reader/courses/function-algebras-and-approximation/src/the-stone-weierstrass-theorem-for-functions-vanishing-at-infinity.md", "reader": "reader/courses/function-algebras-and-approximation/the-stone-weierstrass-theorem-for-functions-vanishing-at-infinity.html", "proof_scope": [ "Theorem 5.1 and Corollary 5.2 with complete proofs: lines152–177", "Sections6–10 complete polynomial/interpolation/lattice/real and complex density proofs: lines205–355" ], "authorship_notice": "*Written by Claude Opus 5.5 (Anthropic), September 2026. Spot-checked by Claude Opus 5.5 in a separate session. Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "DG-FND", "lesson": "local-tools-for-bundles-and-transport", "source_sha256": "c75114b2329f48febd2fabb6f045f5890c93a6357ea522804f22814ebc9e0e93", "editable_source": "reader/courses/DG-FND/src/local-tools-for-bundles-and-transport.md", "reader": "reader/courses/DG-FND/local-tools-for-bundles-and-transport.html", "proof_scope": [ "Sections1–2 complete contraction, inverse-function and flow proofs, invariant-equation lemma and exponential construction: lines9–95" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI), Ultra effort, October 2026. Draft; self-checked by the writing AI, GPT-6.1 Sol, at Ultra effort. Original text dedicated to the public domain under CC0 1.0.*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "DG-FND", "lesson": "invariant-connections-on-homogeneous-bundles", "source_sha256": "24fa182cc32a18bffc8aaab12e0b4b22a991335f92d7a4d794ae5858d0653031", "editable_source": "reader/courses/DG-FND/src/invariant-connections-on-homogeneous-bundles.md", "reader": "reader/courses/DG-FND/invariant-connections-on-homogeneous-bundles.html", "proof_scope": [ "Theorem 1.1 full closed-subgroup proof and surrounding conventions: lines1–59" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI), Ultra effort, October 2026. Draft; self-checked by the writing AI, GPT-6.1 Sol, at Ultra effort. Original text dedicated to the public domain under CC0 1.0.*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "foundations-of-von-neumann-algebras", "lesson": "hahn-banach-baire-and-the-basic-theorems-on-banach-spaces", "source_sha256": "0ddb8296704ac067318d411b8f4097aa119b244f6436e96ce6623a9932d116ed", "editable_source": "reader/courses/foundations-of-von-neumann-algebras/src/hahn-banach-baire-and-the-basic-theorems-on-banach-spaces.md", "reader": "reader/courses/foundations-of-von-neumann-algebras/hahn-banach-baire-and-the-basic-theorems-on-banach-spaces.html", "proof_scope": [ "Sections1–2 complete Zorn and real/complex seminorm Hahn–Banach proofs: lines30–99" ], "authorship_notice": "*Written by Claude Opus 5.5 (Anthropic), October 2026. Self-checked by the writing AI. Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "DG-FND", "lesson": "flat-connections-and-infinitesimal-holonomy", "source_sha256": "6f8bcb5d4dc2e86ac4407b1516dbdca8864d66c5f3d07d973c9f341ea1620367", "editable_source": "reader/courses/DG-FND/src/flat-connections-and-infinitesimal-holonomy.md", "reader": "reader/courses/DG-FND/flat-connections-and-infinitesimal-holonomy.html", "proof_scope": [ "Lemma2.1 complete path/homotopy universal-cover proof: lines43–66", "Lemma3.2 complete immersed subgroup and uniqueness proof: lines166–173" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI), Ultra effort, October 2026. Draft; self-checked by the writing AI, GPT-6.1 Sol, at Ultra effort. Original text dedicated to the public domain under CC0 1.0.*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "DG-FND", "lesson": "curvature-and-holonomy-groups", "source_sha256": "7d5cd25f235ee35685b94deb3919be7c69a7fe6aef0679f1a5b8a5fe36e9fec6", "editable_source": "reader/courses/DG-FND/src/curvature-and-holonomy-groups.md", "reader": "reader/courses/DG-FND/curvature-and-holonomy-groups.html", "proof_scope": [ "Lemma4.1 complete smoothly generated subgroup maximal-rank/chart/countability proof: lines139–162", "Lemma5.2 countability of fundamental group proof: lines179–184" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI), Ultra effort, October 2026. Draft; self-checked by the writing AI, GPT-6.1 Sol, at Ultra effort. Original text dedicated to the public domain under CC0 1.0.*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "DG-FND", "lesson": "riemannian-connections-and-convex-neighbourhoods", "source_sha256": "58c35cc6e38afdf81b8ee0b5430543be6169c73f2c5062579a63f863068837f9", "editable_source": "reader/courses/DG-FND/src/riemannian-connections-and-convex-neighbourhoods.md", "reader": "reader/courses/DG-FND/riemannian-connections-and-convex-neighbourhoods.html", "proof_scope": [ "Sections1–2 complete distance/topology and Levi–Civita/Koszul proofs: lines1–208", "Theorem3.1 Gauss lemma and Theorem3.2 complete normal-ball minimizing proof: lines265–409", "Theorem4.1 complete strong convexity proof: lines463–501" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI), Ultra effort, October 2026. Draft; self-checked by the writing AI, GPT-6.1 Sol, at Ultra effort. Original text dedicated to the public domain under CC0 1.0.*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "DG-FND", "lesson": "completeness-and-the-hopf-rinow-theorem", "source_sha256": "3e38489f6809ed011f5bc3c652f75e27877ebcc4413c7e6cb5dc47f61bbfb3c5", "editable_source": "reader/courses/DG-FND/src/completeness-and-the-hopf-rinow-theorem.md", "reader": "reader/courses/DG-FND/completeness-and-the-hopf-rinow-theorem.html", "proof_scope": [ "Sections1–3 entire radius-extension proof, completeness equivalences Theorem3.1 and compact Corollary3.2: lines1–360" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI), Ultra effort, October 2026. Draft; self-checked by the writing AI, GPT-6.1 Sol, at Ultra effort. Original text is CC0 1.0; the attributed Clifton half-cylinder subsection retains CC BY 4.0.*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "RT-LIE", "lesson": "RT-LIE-08", "source_sha256": "857737779e83230da3e5e9169e0799306ec139c092c4aa6df296d66dd2939300", "editable_source": "reader/courses/RT-LIE/src/RT-LIE-08.md", "reader": "reader/courses/RT-LIE/RT-LIE-08.html", "proof_scope": [ "Sections1–5 complete base, walls, simple-root permutation, exchange, word length, chamber simple transitivity and longest element proofs: lines1–204" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI) in Codex, Ultra setting, October 2026. Self-checked by the writing AI. Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "RT-LIE", "lesson": "RT-LIE-13", "source_sha256": "021ac3965e1b08741cda139f911501313ca0ded65fe419846bc379576091f856", "editable_source": "reader/courses/RT-LIE/src/RT-LIE-13.md", "reader": "reader/courses/RT-LIE/RT-LIE-13.html", "proof_scope": [ "Theorem2.1 complete ordered-word PBW proof with all ambiguity cases: lines42–105", "Section4 full subalgebra and triangular multiplication proofs: lines147–188" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI) in Codex, Ultra setting, October 2026. Self-checked by the writing AI. Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "RT-LIE", "lesson": "RT-LIE-16", "source_sha256": "0228e1c7023b143d5cd467878aa23bc6650596799303598ab2a90ed7a17c7394", "editable_source": "reader/courses/RT-LIE/src/RT-LIE-16.md", "reader": "reader/courses/RT-LIE/RT-LIE-16.html", "proof_scope": [ "Sections4–5 complete Kostant and Freudenthal proofs: lines167–244; semisimple/inverse-Killing scope compared to own arbitrary reductive/invariant-metric proof" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI) in Codex, Ultra setting, October 2026. Self-checked by the writing AI. Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "HA-LCA", "lesson": "HA-LCA-02", "source_sha256": "8f385917fc9b73f0fc0032136c669a1d83f0470a2f51780391b2dffb6bc5529e", "editable_source": "reader/courses/HA-LCA/src/HA-LCA-02.md", "reader": "reader/courses/HA-LCA/HA-LCA-02.html", "proof_scope": [ "Theorem3.1 full real-line local-lift and topology proof; Corollary3.2 full circle/integers proof: lines80–137" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI) in Codex, Ultra setting, October 2026. Self-checked by GPT-6.1 Sol (OpenAI). Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "HA-LCA", "lesson": "HA-LCA-08", "source_sha256": "bfb076ca1da813ff3d4bd0aa103266114be28cc52815abc3d1326eb34954a210", "editable_source": "reader/courses/HA-LCA/src/HA-LCA-08.md", "reader": "reader/courses/HA-LCA/HA-LCA-08.html", "proof_scope": [ "Theorem1.1 full arbitrary-LCA Plancherel isometry/surjectivity and exact Fourier convention: lines1–88" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI) in Codex, Ultra setting, October 2026. Self-checked by GPT-6.1 Sol (OpenAI). Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "HA-LCA", "lesson": "HA-LCA-10", "source_sha256": "26c9704658dd289d50f3184b5b5ba333538f2b028bbbbf4aea04f1c4824acb60", "editable_source": "reader/courses/HA-LCA/src/HA-LCA-10.md", "reader": "reader/courses/HA-LCA/HA-LCA-10.html", "proof_scope": [ "Theorem4.1 complete Radon/L1 Weil integration proof, no sigma compactness, null-representative handling: lines151–223" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI) in Codex, Ultra setting, October 2026. Self-checked by GPT-6.1 Sol (OpenAI). Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "HA-LCA", "lesson": "HA-LCA-12", "source_sha256": "a6f5c55b037bbc34615d6516b336be76e34f2114268c096a2abedcee05b1e9af", "editable_source": "reader/courses/HA-LCA/src/HA-LCA-12.md", "reader": "reader/courses/HA-LCA/HA-LCA-12.html", "proof_scope": [ "Theorem6.1 entire torus Kronecker statement/proof and generation construction: lines214–232; compact proof using own Peter–Weyl also supplied in RT-CPT06" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI) in Codex, Ultra setting, October 2026. Self-checked by GPT-6.1 Sol (OpenAI). Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "RT-FIN", "lesson": "RT-FIN-06", "source_sha256": "98475fe12e0c38592a1847d7fd308f0f60ae336f3a5c9f1b274bf360572b7efd", "editable_source": "reader/courses/RT-FIN/src/RT-FIN-06.md", "reader": "reader/courses/RT-FIN/RT-FIN-06.html", "proof_scope": [ "Theorem3.1 both full adjunction proofs, function/tensor model conversions, naturality and character identity: lines117–204", "Exercise4 full opposite-corner Gelfand proof, zero-or-one condition: lines417–457" ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI) in Codex, Ultra setting, October 2026. Self-checked by the AI that wrote it. Public domain (CC0).*", "role": "Selected prerequisite proof home; broader applications of its parent course are not claimed as part of the compact-group course." }, { "course": "DG-FND", "lesson": "linear-and-affine-connections", "original_source_sha256": "7b0e68e44aab892a0c093af04db2f2038aee159f6f82477e69ca87e460373aae", "source_sha256": "eb81f92ffd40865e60cd42fbed6feee4d4448d9bfe961424ca541b23028e158f", "editable_source": "reader/courses/DG-FND/src/linear-and-affine-connections.md", "reader": "reader/courses/DG-FND/linear-and-affine-connections.html", "proof_scope": [ "Complete sections 1–2, including all supplied proofs; source introduction limited to title and authorship notice." ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI), Ultra effort, October 2026. Draft; self-checked by the writing AI, GPT-6.1 Sol, at Ultra effort. Original text and figure dedicated to the public domain under CC0 1.0.*", "role": "Exact geometric background excerpt, additionally read for the publication navigation repair." }, { "course": "DG-FND", "lesson": "geodesics-normal-coordinates-and-curvature", "original_source_sha256": "e7d1035d71da8c0dbc648cb17a3bd1a36c10c5d250da132b699560f0aa6c5f7a", "source_sha256": "164cfd837f18631db1bdf8215d6f2272e7e1caa1168704bfdcf67cdf00bbfa9a", "editable_source": "reader/courses/DG-FND/src/geodesics-normal-coordinates-and-curvature.md", "reader": "reader/courses/DG-FND/geodesics-normal-coordinates-and-curvature.html", "proof_scope": [ "Complete sections 1–2, including all supplied proofs; source introduction limited to title and authorship notice." ], "authorship_notice": "*Written by GPT-6.1 Sol (OpenAI), Ultra effort, October 2026. Draft; self-checked by the writing AI, GPT-6.1 Sol, at Ultra effort. Original text dedicated to the public domain under CC0 1.0.*", "role": "Exact geometric background excerpt, additionally read for the publication navigation repair." } ], "scope": "Exact selected proof homes and two geometric excerpts. Wider parent-course applications are additional reading, not extra compact-course completion claims. The published Banach and C*-algebra foundations are required by the general spectral proof route and linked separately; the compact-averaging Schur proof uses the included exact prerequisites.", "compact_schur_alternative": "reader/compact-schur-proof.html", "integration": { "model": "GPT-6.1 Sol", "provider": "OpenAI", "reasoning_effort": "Ultra", "date": "2026-10-03", "independent_review": false }, "component_exception": "The Hopf–Rinow chapter’s attributed Clifton half-cylinder subsection retains CC BY 4.0; its source notice names Jacob W. 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