# AI provenance: Supersymmetric Yang–Mills theories with several times reduce to ten dimensions

Author: Deep Bhattacharjee. No AI system is an author or contributor.

## How the work was produced

Deep Bhattacharjee set the task, a paper in mathematical physics that settles a published claim, and directed the work. Claude (Anthropic), through Claude Code, chose the claim of Rios, Marrani and Chester (Phys. Rev. D 99 (2019) 046004, Sec. III A) that Nishino's existence proofs for supersymmetric Yang–Mills theories in (9+m)+(1+m) carry over to (9+8n)+1, (10+8n)+2, (11+8n)+3 and (12+8n)+4. It checked that the claim had not been tested, developed the proofs that refute it, wrote the verification code and the figure scripts, and drafted and revised the paper. The paper states this in its section "Use of AI tools".

## How the results are checked

Every statement is proved in the text. Independently, `verify.py` tests the identities in explicit real and complex gamma matrices in double precision (34 checks): the decomposition of the symmetric square of a Weyl spinor for so(2r), r = 2 to 20; the cubic identity and the count N = 2(d-2) in (9,1), (5,5), (1,9), (17,1), (13,5), (9,9) and (25,1); absorption of the cubic terms for null frames in Nishino's signatures (10,2) to (13,5), (6,6), (7,7) and its failure in (17,1), (18,2), (19,3), (20,4); real null frames with k = min(s,t); and the state count of the single-time theorem. All 34 pass.

## Literature check

Every record in the INSPIRE database that cites Phys. Rev. D 99 (2019) 046004 or Phys. Lett. B 808 (2020) 135674 (thirteen and eleven records in October 2026) was read. All of them use or quote the existence of the theories; none constructs one and none tests whether Nishino's argument carries over. The result is new.

## What is not claimed

The theorem concerns theories built in the manner of Nishino, as made precise by the axioms (N1)–(N5) of the paper; a theory that violates these axioms in an essential way is not covered. The single-time theorem assumes that tensor charges vanish on the massless multiplet (hypothesis H). For the degenerate family 9+(1+8n) the theorem excludes n >= 3 and does not exclude n = 1, 2; it does not construct those theories.

## Labels given on the Hexagon form

- Text of the contribution: a mix of human-written and AI-generated.
- Human understanding at submission: some parts, but not all, checked and understood by a human.

## Where everything is

Zenodo, doi:10.5281/zenodo.23558751 (release v1.0.0 of https://github.com/creelie/cs-grav, with the LaTeX source); the verification code is also in anc/ of the source ZIP.