# Characteristic classes: licensing and provenance

The independently written lessons, proofs, examples and solved exercises in this course are dedicated to the public domain under [CC0 1.0](https://creativecommons.org/publicdomain/zero/1.0/).

The writing AI is GPT-6.1 Sol (OpenAI), running at Ultra. Published lessons state their own author-instance AI self-check status. No independent AI or human review is claimed without a separately identified record.

Mathematical reading sources are freely accessible author texts, papers and lecture notes. The course supplies a proof of every result it uses, either in the lesson or in an earlier linked programme lesson. Source citations are additional reading, not substitutes for proofs. Referenced works retain their own rights.

Hatcher's author-hosted *Spectral Sequences*, Chapter 1, is also a scholarly reference. The homotopy and spectral-sequence companion supplies independently written proofs and solved exercises. The rational-homotopy companion supplies a complete filtered-chain proof of the higher-page multiplicative identity left open in that scholarly draft, and independently written proofs of the rational one-group calculation and sphere finiteness.

The rational-bordism conclusion independently proves explicit finite-stage bounds, the oriented rank theorem, projective polynomial generators and positive-multiple bounding criterion. Its source notes link the freely readable treatments by René Thom, Haynes Miller and Daniel Freed.

The signature chapter supplies independently written form algebra, relative boundary duality, the complete product proof, universal multiplicative-sequence construction, formal residue calculation and signature theorem, with original solved exercises. Further reading is Friedrich Hirzebruch's freely readable 1953 article and John Milnor's 1957 lecture notes, with notes by James Stasheff. The section includes the two-example signature calibration and balanced sphere-product calculation written by the AI.

The higher-diagonal mathematical formula is attributed to Anibal M. Medina-Mardones, arXiv:2105.08025v3. Its arXiv distribution licence does not permit republication of protected text. The course's cancellation argument, Cartan proof, teaching and exercises are independently authored; no paper text or algorithm is reproduced.

The website's renderer, MathJax and fonts retain the notices provided by Open Mathematics Courses.

The marked adaptation in Lemma 8.1 of *Grassmannians and classifying maps* is based on David Michael Roberts, *Algebraic Topology* (2019), copyright © David Michael Roberts 2019, and retains Creative Commons Attribution 4.0, including the disclaimer of warranties. The source, change notice and attribution are in the chapter. The [complete retained licence](sources/Roberts-LICENSE.md) accompanies the course. Other independently authored sections retain CC0.

The odd-prime companion independently supplies normalized-chain and cyclic-resolution algebra, higher diagonals, reduced-power properties and the Thom/polynomial/Wu proof, with six original solved exercises. Its references include J. Peter May's author-hosted paper and the freely readable 1957 lecture notes. Their protected text, files and exercise sets are not republished.

The triangulation companion independently supplies quantitative embedding stability, relative boundary extension, compact PL comparison and the coned eight-dimensional integral-refinement obstruction, with six original solved exercises. Its references link freely readable papers by John Milnor and official lecture notes by Jacob Lurie. 

The unoriented bordism companion independently supplies the complete mod-two one-group calculation, square basis, finite comparison and free Thom-module detection proof, with six original solved exercises. Miller and Hatcher are scholarly sources. 

The marked rotation-group starting subsection in *Projective tangent bundles and their obstructions* and the marked Hopf-circle calibration in *Chern classes and the integral universal ring* adapt David Michael Roberts’s *Algebraic Topology* (2019), Lectures 19 and 18 respectively. The source is the supplied LaTeX; copyright © David Michael Roberts 2019, CC BY 4.0. Their in-place notices identify the adaptation and the AI additions. Both whole marked subsections retain CC BY 4.0, including its disclaimer of warranties; the complete retained licence accompanies the course. The pre-existing Roberts adaptation in Grassmannian Lemma 8.1 is preserved. Other independently authored sections and the study guide retain CC0.