Collection component exception: CV-4 adapts Javier Falcó and Daniel Isert, G-strong subdifferentiability and applications to norm attaining subspaces, Section 3.4, https://link.springer.com/article/10.1007/s13163-025-00536-6, under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Its attribution and changes are retained in OA-FLOW-CV; CV-4 is not included in the CC0 dedication. Historical grants remain intact.

Current independent reconstructions, 4 October 2026: CF, GNS, L34 and L35 contain newly written original exposition, proofs, examples, solutions and illustration sources dedicated under CC0 1.0. L35 includes its original continuity addendum. Historical L34 and L35 documents and components retain their recorded grants; this dedication does not relicense their expression. Rendered font designs and reproduction dependencies retain their respective terms.

# Copying the current lessons and historical components

For the historical L34 and L35 documents and retained historical components, permission is granted to copy, distribute and/or modify the selected document under the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation, with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A complete copy is included in LICENSE-GFDL-1.3.txt. Earlier covered original expression retains its recorded GFDL-1.2-or-later grant; later original revision and selection expression retains its CC0 dedication. Rendered fonts retain their separately supplied terms.

The complete GNU license, version 1.3 is copied without alteration from the Free Software Foundation’s [GNU FTP copy](https://ftp.gnu.org/gnu/Licenses/fdl-1.3.txt). The previous covered expression in L34 and L35, and the original mathematical geometry and labels of the L35 figure, already carried GFDL-1.2-or-later. Choosing version 1.3 does not replace the later CC0 dedications. The historical components are selected modified versions with different descriptive titles where appropriate; the component record preserves the original titles, exact earlier source identities and grant history. Attribution is to the OA-FLOW course project, with AI-assisted drafting in Codex; no natural person’s name or unverified human review is asserted.

The component record retains the exact prior grants and their provenance. The recorded historical-clearance flag is not a withdrawal of the open grant. Separately licensed rendered typography retains the [DejaVu notice](assets/notices/LICENSE_DEJAVU.txt). The exact original figure renderer retains its [MIT software offer](LICENSE-SOFTWARE-MIT.txt). MathJax is bundled under its [license](assets/mathjax/LICENSE) and [font notices](assets/mathjax/FONT-LICENSES.txt). External papers and prerequisite pages retain their own terms and are linked, not republished as project expression.

The current lessons CF, GNS, SF, L24, L25, L34, L35, L138, L157, L158 and L159 have CC0 original expression. This dedication does not change the grants of historical L34 or L35 expression. The new GNS illustration and reproduction code are original CC0 expression; rendered DejaVu glyph designs and external dependencies retain their separately supplied terms.

The current faithful-state core, Fourier/forms foundations and WH02/WH04/MF06/MF scalar bridge are original local reconstructions dedicated under CC0-1.0 in their reviewed collection. Their linked inputs and the rendered glyph designs retain their respective terms. Their local mathematical deductions are conditional on the exact inherited inputs. The corrected core illustration and its reproduction program are also original CC0 expression.

The current SC scalar foundation, its original figure and its reproduction source are dedicated under CC0-1.0. Its complete local mathematical dependency cone has been independently reviewed at the earlier CF Section 1 and explicit primitive conventions; no historical scalar expression is relicensed. Rendered glyph designs retain their component terms.

The current CI, BD, HA-R and split ST providers and original graph/polar/cutoff illustration/code retain their explicit CC0-1.0 dedication by GPT-6 Astra (OpenAI), Ultra. The adopted concrete-predual provider contains only the independently reviewed CP01–06 programme expression, retaining its earlier CC0-1.0 grant and OpenAI Codex (AI) credit. No historical grants are changed; linked sources and font designs retain their own terms.

The current WF forward weight-construction proof, original polar-column/cutoff illustration and reproduction code retain their explicit CC0-1.0 dedication by GPT-6 Astra (OpenAI), Ultra. Moving the original WH04-05 application preserves its historical grant; no historical content is relicensed.

The current GW and NF proofs, original closed-sum-form/normal-coefficient illustration and reproduction code retain their explicit CC0-1.0 dedication by GPT-6 Astra (OpenAI), Ultra. The earlier ST coefficient excerpt retains the original reviewed ST component grant. Historical content and other grants are unchanged.

The current L138 and H0–H5 exposition, proofs, examples and exact order-three coefficient/shear figure and reproduction code are independently reconstructed original CC0 expression by GPT-6.1 Sol (OpenAI), Ultra. Their current harmonic analytic premises are the actual earlier topology, HR and scalar Plancherel proof bodies; inherited component terms remain in force. Historical L138 content/grants are not relicensed.

The current complete topology slice and HR proof, exact Haar-convention illustration and reproduction code are original CC0 expression by GPT-6.1 Sol (OpenAI), Ultra. The H1 and H2–H5 split retains the original independently reconstructed CC0 expression. Primary free author PDFs are comparison evidence with their own retained terms and are not included as new reader assets; historical content is not relicensed.

The current scalar Plancherel proof, exact four-point coefficient-measure illustration, data and reproduction code retain their explicit original CC0-1.0 dedication by GPT-6 Astra (OpenAI), Ultra. Fremlin's freely accessible author source is comparison evidence and is not included. Font designs and software dependencies retain their own terms. Historical content and grants are unchanged.

CV1–3, EW, WR and MW are fresh CC0-1.0 expression by GPT-6 Astra (OpenAI), Ultra. CV4 adapts Javier Falcó and Daniel Isert, G-strong subdifferentiability and applications to norm attaining subspaces, Section3.4 (https://link.springer.com/article/10.1007/s13163-025-00536-6), under CC BY4.0. Its attribution, license https://creativecommons.org/licenses/by/4.0/ and changes are retained in OA-FLOW-CV.md; CV4 is not offered as CC0. Both original cutoff/polar-vector and opposite-time figures, complete example proofs, data and reproduction code are CC0-1.0. Glyph designs and external software retain their terms; historical grants are unchanged.

NO: original general-normal opposite-weight proof, full complex matrix examples, illustration, data and reproduction source by GPT-6 Astra (OpenAI), Ultra, dedicated CC0-1.0 to the extent of rights held. Fonts, software and historical expression retain their terms.

KT and KU: original KMS strip, analytic-domain core, trace-criterion and scope-bound uniqueness proofs, full exact matrix example, illustration, data and reproduction source by GPT-6 Astra (OpenAI), Ultra, dedicated CC0-1.0 to the extent of rights held. The CV-4 CC BY4.0 exception and all historical, font and software terms remain intact.

PC: independent projection comparison/halving exposition, complete dyadic-coordinate example, original illustration, data and reproduction source by GPT-6.1 Sol (OpenAI), Ultra, dedicated CC0-1.0 to the extent of rights held. The CV-4 CC BY4.0 exception and all historical, font and software terms remain intact.

BC: independent balanced-weight/cocycle exposition, complete exact noncommuting-density example, original figure, data and reproduction source by GPT-6 Astra (OpenAI), Ultra, dedicated CC0-1.0 to the extent of rights held. Reader integration by GPT-6.1 Sol (OpenAI), Ultra. The CV-4 CC BY4.0 exception and all historical, font and software terms remain intact.

EP: independent extended-positive/composition exposition, complete exact M3 example, original figure, data and reproduction source by GPT-6 Astra (OpenAI), Ultra, dedicated CC0-1.0 to the extent of rights held. Reader integration by GPT-6.1 Sol (OpenAI), Ultra. The CV-4 CC BY4.0 exception and all historical, font and software terms remain intact.

AS/MA/OT: independently reconstructed analytic-strip, full finite-domain and OVW modular/cocycle exposition, complete worked examples, original figure, data and reproduction source by GPT-6 Astra (OpenAI), Ultra, dedicated CC0-1.0 to the extent of rights held. Reader integration by GPT-6.1 Sol (OpenAI), Ultra. The CV-4 CC BY4.0 exception and all historical, font and software terms remain intact.

WS: independent normal-weight sum reduction and finite-domain example by GPT-6.1 Sol (OpenAI), Ultra; independent Gaussian graph-frame construction and example by GPT-6 Astra (OpenAI), Ultra; complete original illustrations, data and reproduction sources dedicated CC0-1.0 to the extent of rights held. Integration by GPT-6.1 Sol (OpenAI), Ultra. The CV-4 CC BY4.0 exception and all historical, font and software terms remain intact.

TD: fresh original tracial-density proof, complete exact examples/caption, native figures, data and reproduction sources by GPT-6 Astra (OpenAI), Ultra; dedicated CC0-1.0 to the extent of rights held. Integration by GPT-6.1 Sol (OpenAI), Ultra. Historical grants, CV-4 CC BY4.0 exception, font and software terms remain intact.

CZ: original nonsingular unbounded centralizer-perturbation proof, complete exact integer-sequence example/caption, native figures, rational data and reproduction sources by GPT-6.1 Sol (OpenAI), Ultra; dedicated CC0-1.0 to the extent of rights held. Integration by GPT-6.1 Sol (OpenAI), Ultra. Historical grants, CV-4 CC BY4.0 exception, font and software terms remain intact.

NC/CR/MC: fresh original natural-cone/standard-form/corner/representative/finite-matrix proofs and complete exact figure caption, original native PNG/SVG, reproduction source and numerical checks by GPT-6 Astra (OpenAI), Ultra; dedicated CC0-1.0 to the extent of rights held. Integration by GPT-6.1 Sol (OpenAI), Ultra. Historical grants, CV-4 CC BY4.0 exception, font and software terms remain intact.

CC: fresh original periodic compact crossed-product/counting-weight proof, full mathematical figure caption, native PNG/SVG, rational data and reproduction source by GPT-6.1 Sol (OpenAI), Ultra; CC0-1.0 to the extent of rights held. Historical grants, CV-4 CC BY4.0 exception, font/software terms remain intact.

RF/AL: fresh original real Fourier filters/action localization, full mathematical caption/native figure, numerical checks and reproduction source by GPT-6 Astra (OpenAI), Ultra; CC0-1.0 to the extent of rights held. Integration by GPT-6.1 Sol (OpenAI), Ultra. Historical grants, CV-4 CC BY4.0 exception, font/software terms remain intact.

CT preserves its existing original component grant. TS: fresh original direct III1 bridge, complete mathematical caption/native PNG/SVG and reproduction source by GPT-6 Astra (OpenAI), Ultra; CC0-1.0 to the extent of rights held. Portable integration by GPT-6.1 Sol (OpenAI), Ultra. Historical grants, CV-4 CC BY4.0 exception, font/software terms remain intact.

CD: fresh original complete compact counting-weight modular/trace proof, full mathematical caption/native PNG/SVG/data and reproduction source by GPT-6.1 Sol (OpenAI), Ultra; CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

FP/HC: original complete proofs, full mathematical figure captions, PNG/SVG, data and reproduction code by GPT-6 Astra (OpenAI), Ultra; CC0-1.0 to the extent of rights held. Prior component grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

FD: fresh original complete faithful descent proof, full mathematical caption/native PNG/SVG/data and reproduction source by GPT-6.1 Sol (OpenAI), Ultra; CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

VD: Original complete discrete/compact normal double-duality proof and original figure by GPT-6.1 Sol (OpenAI), Ultra; independent owner review and integration by GPT-6 Astra (OpenAI), Ultra, at exact written prerequisite ranges. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

PW: Original complete proof, mathematical caption and illustration by GPT-6 Astra (OpenAI), Ultra; independently owner-reviewed and integrated at exact earlier written proofs. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

PF: Original complete proof, mathematical caption and illustration by GPT-6 Astra (OpenAI), Ultra; independent owner mathematical review at exact earlier written proofs; local reader integration by GPT-6.1 Sol (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

GT: Original complete proof, mathematical caption and illustration by GPT-6 Astra (OpenAI), Ultra; independently owner-reviewed and integrated at exact earlier written proofs. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

CA: Original complete proof, mathematical caption and illustration by GPT-6 Astra (OpenAI), Ultra; independently owner-reviewed and integrated at exact earlier written proofs. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

CS/MG: Original complete proof by GPT-6.1 Sol (OpenAI), Ultra; independently reviewed and integrated by GPT-6 Astra (OpenAI), Ultra, at exact earlier written proofs. Complete original caption and illustration by GPT-6.1 Sol (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

IP: Original complete proof by GPT-6.1 Sol (OpenAI), Ultra; independently reviewed and integrated by GPT-6 Astra (OpenAI), Ultra, at exact earlier written proofs. Complete original caption and illustration by GPT-6.1 Sol (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

MT: Original complete proof, mathematical caption and illustration by GPT-6 Astra (OpenAI), Ultra; independently owner-reviewed and integrated at exact earlier written proofs. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

DD: Original complete proof by GPT-6.1 Sol (OpenAI), Ultra; independently reviewed and integrated by GPT-6 Astra (OpenAI), Ultra, at exact earlier written proofs. Complete original caption and illustration by GPT-6.1 Sol (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

GM: Original complete proof by GPT-6 Astra (OpenAI), Ultra; independently reviewed, prepared and illustrated by GPT-6.1 Sol (OpenAI), Ultra; final owner mathematical and exact-source review passed at stated earlier written proofs. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

Z: Original complete proof and illustration by GPT-6.1 Sol (OpenAI), Ultra; independently reviewed by GPT-6 Astra (OpenAI), Ultra; the diameter conclusion binds the complete earlier modular-gap minimum theorem. CC0-1.0 to extent of rights held. Historical grants, CV-4 CC BY4.0 exception and font/software terms remain intact.

DP: Original complete proof and illustrations by GPT-6.1 Sol (OpenAI), Ultra; independent complete mathematical review by GPT-6 Astra (OpenAI), Ultra, at exact earlier programme inputs. CC0-1.0 to extent of rights held. Historical grants, CV4 and font/software terms remain intact.

UC/AC: Original complete proofs and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent owner mathematical and exact-provider review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants and font/software terms remain intact.

LF: Original complete proofs and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent owner mathematical and exact-provider review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants and font/software terms remain intact.

AT/NR: Original complete proofs and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent owner full mathematical and exact-provider review by GPT-6 Astra (OpenAI), Ultra. Original complete proofs and illustration by GPT-6 Astra (OpenAI), Ultra; independently checked in the owner session at the actual earlier programme proofs. CC0-1.0 to extent of rights held. Historical grants and font/software terms retained.

GL: Original complete proofs and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent owner mathematical and exact-provider review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants and font/software terms remain intact.

SS: Original complete proofs and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent owner mathematical and exact-provider review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants and font/software terms remain intact.

FS: Original complete proofs and illustration by GPT-6 Astra (OpenAI), Ultra; independent mathematical body review by a separate GPT-6 Astra (OpenAI), Ultra workflow. Exact source and figure package checked by the owner. CC0-1.0 to extent of rights held. Historical grants and font/software terms remain intact.

CCM: Original complete proofs and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent owner mathematical and exact-provider review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants and font/software terms remain intact.

WY: Original complete proofs and illustration by GPT-6 Astra (OpenAI), Ultra; independent owner mathematical and exact-provider review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants and font/software terms remain intact.

BS: Original complete proofs and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent mathematical body review and owner integration by GPT-6 Astra (OpenAI), Ultra workflows. Exact source and figure package checked by the owner. CC0-1.0 to extent of rights held. Historical grants and font/software terms remain intact.

L94: Programme proof written in Codex (OpenAI), September 2026; restoration, explicit foundation bridges and independent full-body review by GPT-6 Astra (OpenAI), Ultra, October 2026. CC0-1.0 to extent of rights held. Referenced external works retain their own terms and are not redistributed.

GDW: Original complete proofs and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent owner mathematical and exact-provider review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. Historical grants and font/software terms remain intact.

QF and L43-L46: Original programme exposition in Codex (OpenAI), September 2026; proof restoration and independent complete owner review by GPT-6 Astra (OpenAI), Ultra, October 2026. CC0-1.0 to extent of rights held. External source text is not redistributed.

L95-L96: Original programme exposition in Codex (OpenAI), September 2026; proof restoration by GPT-6.1 Sol (OpenAI), Ultra, and independent full-body and owner reviews by GPT-6 Astra (OpenAI), Ultra, October 2026. CC0-1.0 to extent of rights held. External source text is not redistributed.

GDA: Original complete proof and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent mathematical review and owner source, expression, provider and figure review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. External source text is not redistributed.

NCF: Original complete proof, illustration and independent owner mathematical/source/expression review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. External source text is not redistributed.

AF and L87-L93: Original programme exposition in Codex (OpenAI), September 2026; proof restoration and supporting proofs by GPT-6.1 Sol (OpenAI), Ultra, with independent full-body/source and owner review by GPT-6 Astra (OpenAI), Ultra, October 2026. CC0-1.0 to extent of rights held. External source text is not redistributed.

IS: Programme proof restoration and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent mathematical review by a separate GPT-6.1 Sol (OpenAI), Ultra, and complete owner mathematical/source/expression review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. External source text is not redistributed.

MX, L80 and L81: Original programme exposition in Codex (OpenAI), September2026; restoration and supporting proofs by GPT-6 Astra (OpenAI), Ultra, independent review by GPT-6.1 Sol (OpenAI), Ultra, and owner mathematical/source/expression review by GPT-6 Astra (OpenAI), Ultra, October2026. CC0-1.0 to extent of rights held. External source text is not redistributed.

ND: Programme restoration and original illustration by GPT-6.1 Sol (OpenAI), Ultra; independent full mathematical review by GPT-6 Astra (OpenAI), Ultra, and separate owner mathematical/source/expression review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. External source text is not redistributed.

WR: Programme restoration and original illustration by GPT-6.1 Sol (OpenAI), Ultra; separate independent mathematical review by GPT-6.1 Sol (OpenAI), Ultra, and owner mathematical/source/expression review by GPT-6 Astra (OpenAI), Ultra. CC0-1.0 to extent of rights held. External source text is not redistributed.

AM/DA: Additive averaging restoration and Fourier bridge by GPT-6 Astra (OpenAI), Ultra; independent complete mathematical/source review and integration preparation by GPT-6.1 Sol (OpenAI), Ultra; separate accepted owner review. CC0-1.0 to extent of rights held. External source text is not redistributed.

UR: Independent proof and integration preparation by GPT-6 Astra (OpenAI), Ultra; separate complete independent agent and owner review at exact inputs. Independently authored proof/caption/figure expression: CC0-1.0. Renderer software: MIT; inherited terms retained. No external source pages redistributed.

FR: Original application proof/caption/figure by GPT-6 Astra (OpenAI), Ultra; integration preparation by GPT-6.1 Sol (OpenAI), Ultra; separate complete independent and owner review at exact inputs. CC0-1.0 original component expression to the extent of rights held. External source text is not redistributed.

NWR: Original proof/caption/figure by GPT-6.1 Sol (OpenAI), Ultra; integration preparation by GPT-6 Astra (OpenAI), Ultra; separate full owner and independent acceptance at exact inputs. CC0-1.0 original component expression to the extent of rights held. External source text is not redistributed.

ET: Preserved September 2026 Codex/OpenAI original proof; restoration and illustration by GPT-6 Astra (OpenAI), Ultra; independent review and guarded integration preparation by GPT-6.1 Sol (OpenAI), Ultra; completed owner and independent review at exact earlier inputs. Original component expression under retained and new CC0-1.0 grants to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

HCR: Independent direct Gram proof and original illustration by GPT-6 Astra (OpenAI), Ultra; independent review and guarded integration preparation by GPT-6.1 Sol (OpenAI), Ultra; completed owner and independent review at exact earlier inputs. Original component expression under retained and new CC0-1.0 grants to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

GCC: Preserved original fixed-corner proof, completed restored exposition and original illustration by GPT-6.1 Sol (OpenAI), Ultra; owner and separate independent review by GPT-6 Astra (OpenAI), Ultra; guarded integration preparation by GPT-6.1 Sol (OpenAI), Ultra at exact earlier inputs. Original component expression under retained and new CC0-1.0 grants to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

L112: Preserved cocycle matrix proof, completed representation-continuity and atomic-summand exposition, and original illustration by GPT-6.1 Sol (OpenAI), Ultra; owner and separate independent review by GPT-6 Astra (OpenAI), Ultra; guarded integration preparation by GPT-6 Astra (OpenAI), Ultra at exact earlier inputs. Original component expression under retained and new CC0-1.0 grants to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

L113: Preserved continuous-part and local-displacement proof, completed nonunital quotient and bounded normal-average exposition, and original illustration by GPT-6.1 Sol (OpenAI), Ultra; owner and separate independent review by GPT-6 Astra (OpenAI), Ultra; guarded integration preparation by GPT-6 Astra (OpenAI), Ultra at exact earlier inputs. Original component expression under retained and new CC0-1.0 grants to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

L114: Preserved integrable-action proof, completed full-cone average, controlled finite-ideal density, coefficient field, filter and spectral detection exposition, and original illustration by GPT-6.1 Sol (OpenAI), Ultra; owner and separate independent review by GPT-6 Astra (OpenAI), Ultra; guarded integration preparation by GPT-6 Astra (OpenAI), Ultra at exact earlier inputs. Original component expression under retained and new CC0-1.0 grants to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

L117: Preserved full-corner innerness and cocycle proof, completed finite-sum Gram construction, normal compression and arbitrary-net continuity exposition, and original illustration by GPT-6.1 Sol (OpenAI), Ultra; owner and separate independent review by GPT-6 Astra (OpenAI), Ultra; guarded integration preparation by GPT-6 Astra (OpenAI), Ultra at exact earlier inputs. Original component expression under retained and new CC0-1.0 grants to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

L118: Preserved abelian representation extension, completed finite-state expectation, kernel and projection alternatives, full normal inverse, arbitrary support assembly and dual topology, and original illustration by GPT-6.1 Sol (OpenAI), Ultra; owner and separate independent review by GPT-6 Astra (OpenAI), Ultra; guarded integration preparation by GPT-6 Astra (OpenAI), Ultra at exact earlier inputs. Original component expression under retained and new CC0-1.0 grants to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

L115: Full arbitrary-LCA dual-center kernel, integrable overlap, normal regular-system verification, absorption/subgroup alternative and complete caption preserved by GPT-6.1 Sol (OpenAI), Ultra; owner and separate independent review by GPT-6 Astra (OpenAI), Ultra; original illustration by GPT-6 Astra (OpenAI), Ultra; guarded integration preparation by GPT-6.1 Sol (OpenAI), Ultra at exact earlier inputs. Original component expression under retained and new CC0-1.0 grants to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

L116: Complete fixed-center and factor-criterion proofs, retained bidual alternative, arbitrary-basis normal tensor maps and unrestricted translation counterexample by GPT-6.1 Sol (OpenAI), Ultra; owner and separate independent review by GPT-6 Astra (OpenAI), Ultra; exact original figure and component terms retained; guarded integration preparation by GPT-6.1 Sol (OpenAI), Ultra. Original component expression under retained and new CC0-1.0 grants to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

FCT: Original finite center-valued trace proof and exact figures by GPT-6.1 Sol (OpenAI), Ultra; owner and independent review and guarded integration preparation by GPT-6 Astra (OpenAI), Ultra. Earlier component and font terms retained. Original component expression under CC0-1.0 to the extent of rights held; DejaVu font terms retained. External source expression is not redistributed.

L119: Independent programme restoration and proof completion by GPT-6 Astra (OpenAI), Ultra; independent mathematical/source review and guarded integration preparation by GPT-6.1 Sol (OpenAI), Ultra; full arbitrary-LCA cancellation, normal corner/center bridge, prescribed lift and exact original matrix model retained. Original grant wording and DejaVu font terms preserved. This model, code, diagram and caption are original programme expressions, CC0-1.0 to the extent of rights held. Historical programme components retain their recorded terms. DejaVu font terms retained. External source expression is not redistributed.

L120: Independent L120 restoration, full proof completion, original illustration, mathematical/source review and guarded preparation: GPT-6.1 Sol (OpenAI), Ultra. Sound prior programme and recorded owner proof developments retained. Exact source grants, inherited component terms and DejaVu terms preserved. Original figure and caption: GPT-6.1 Sol (OpenAI), Ultra, 5 October 2026, CC0-1.0 to the extent of rights held. Historical programme components retain their recorded terms. External source expression is not redistributed.

L121: Independent programme restoration and proof completion by GPT-6 Astra (OpenAI), Ultra; independent mathematical/source review and guarded integration preparation by GPT-6.1 Sol (OpenAI), Ultra; full arbitrary-family spectral comparison, central-ergodic construction and common refinement retained. Original grant wording and DejaVu font terms preserved. This model, code, diagram and caption are original programme expressions, CC0-1.0 to the extent of rights held. Historical programme components retain their recorded terms. DejaVu font terms retained. External source expression is not redistributed.

L122: Independent restoration and illustration by GPT-6.1 Sol (OpenAI), Ultra; independent source and mathematical review and integration preparation by GPT-6 Astra (OpenAI), Ultra. New expression is CC0-1.0 to the extent of rights held; inherited component and exact DejaVu font terms remain applicable. Human review and formal verification are not asserted. Exact component and DejaVu terms accompany the SVG. External source expression is not redistributed.

L123: Original figure and carrier candidate by GPT-6 Astra (OpenAI), Ultra; checked restoration, exposition and additional proofs by GPT-6.1 Sol (OpenAI), Ultra; independent source and mathematical review and integration preparation by GPT-6 Astra (OpenAI), Ultra. New expression is CC0-1.0 to the extent of rights held; inherited component and exact DejaVu font terms remain applicable. Human review and formal verification are not asserted. Exact component and DejaVu terms accompany the SVG. External source expression is not redistributed.

L124: Original figure and circle/matrix candidate by GPT-6 Astra (OpenAI), Ultra; checked restoration, exposition and additional proofs by GPT-6.1 Sol (OpenAI), Ultra; independent source and mathematical review and integration preparation by GPT-6 Astra (OpenAI), Ultra. New expression is CC0-1.0 to the extent of rights held; inherited component and exact DejaVu font terms remain applicable. Human review and formal verification are not asserted. Exact component and DejaVu terms accompany the SVG. External source expression is not redistributed.

L125: Original figure and central-order candidate by GPT-6 Astra (OpenAI), Ultra; checked restoration, exposition and additional proofs by GPT-6.1 Sol (OpenAI), Ultra; independent source and mathematical review and integration preparation by GPT-6 Astra (OpenAI), Ultra. New expression is CC0-1.0 to the extent of rights held; inherited component and exact DejaVu font terms remain applicable. Human review and formal verification are not asserted. Exact component and DejaVu terms accompany the SVG. External source expression is not redistributed.