# AI provenance - Explicit String Vacua and the Geometric Selection Conjecture

Human authors: Deep Bhattacharjee, Ushashi Bhattacharya.
Submitting contributor: Deep Bhattacharjee, ORCID 0000-0003-0466-750X.

Text classification: to be chosen by the submitting author on the form (version 1 of the record, hexagon:2610.00493v1, was submitted as partly checked and understood by a human; this version has been read in full by the submitting author before upload if the stronger declaration is chosen).
Human-understanding declaration: to be chosen by the submitting author on the form.
Basis: the submitting author's own declaration on the Hexagon form, not a claim verified by the assistant.

Claude Code (Anthropic) assisted the preparation of the manuscript, the merger of the two earlier Hexagon parts, the proofs and the writing of Section 16 (including the extension-branch results of Section 16.3 and the acceptance windows of Definition 9.1), the Python checks of the finite arithmetic and the submission package. The Anaxia engine (creelie/eBLLM, release 3.1.0, 10.5281/zenodo.23484160) supplied the ten tetraquadric line-bundle classes of Proposition 16.4 and the atlas record that conditions C7 to C9 of the conjecture are fixed by comparison with measurement; it is cited in the paper.

Documented tools: Anthropic Claude / Claude Code; Python 3 (exact rational arithmetic, 511 + 45 + 61 checks in the repository, the last with SymPy); LaTeX / pdfLaTeX (amsart); Matplotlib for the figures. Exact historical model versions are not inferred from tool names.

Verification scope: every statement of the paper is proved in the text by hand; the programs check finite arithmetic (the matrix certificates, the charge matrices, the Yukawa flow bounds and the slope spaces, extension groups and wall certificates of the extension branch) and no statement rests on them alone. No Lean formalisation is claimed for this paper.

The authors retain responsibility for the final mathematics, citations and approval of the manuscript. AI systems are not added as human contributors. The package creation step prepared the source archive and the submission metadata; it did not submit the manuscript to Hexagon. No private prompts, chat history or hidden reasoning traces are included or represented as an exported transcript.

Earlier Hexagon versions: https://hexagonmath.org/2610.00493v1 (mirror clause), https://hexagonmath.org/2610.00446v1 (spectral calculations)
Research manuscript/source DOI: https://doi.org/10.5281/zenodo.23688897 (release v3.1.0; all versions https://doi.org/10.5281/zenodo.23567114)
Repository: https://github.com/creelie/geometric-selection-conjecture