Exact rotational moments and a triangular-base tensor obstruction (Family 172)

A written centered-isotropic-base lemma generalizes the rotation-moment calculation in OpenAI mathematics Family 172. Three rotations of an equilateral triangle give nine distinct unit-circle points, for transcendental real 0 < t < 1/4, with exact tensor-criterion obstruction 0 = 6. The algebraic identities are proved under the stated differential-field assumptions. The non-Ramsey consequence remains conditional on the source classification theorem, which is not verified here. The self-contained packet includes source pins, written proof, an exact symbolic checker over Q(sqrt(3))(t), 54 moment entries and 72 product-rule coefficients, 15 tests, and three deliberately corrupted mechanisms rejecting under ordinary and optimized Python. A separately tasked AI review and upstream maintainer AI review are recorded with their scopes. Finite rational sampling in the maintainer review is corroboration, not a proof of unrestricted identities. This is not Lean verification or human peer review, and there is no smallest-example or global novelty claim. Original public disclosure: PR 28 on 2026-10-24 at 06:17:48 UTC, contribution commit c9c0b02678b7b1374973d8e554567718e7707c08. Approved by Pico on 2026-10-24 at 08:26:56 UTC; merged on 2026-10-24 at 08:28:07 UTC (ec0006e88e1a88cf3a82e1cf379e57e87a8375b9). The separate checker at f56602917554df5800299cf8f00bd62243066436 was rerun and its reported output reproduced. It is linked and hashed, not redistributed; no applicable license for that separate script was found. Alexander Richard Towell, with substantial OpenAI Codex assistance. OpenAI supplied the square construction, classification claim and derivation mechanism; Pico (operated by Hakon Amdal) supplied earlier computations and review; earlier Palvolgyi seven-point work is credited by the source. No assertion of legal priority or theorem certification follows from this DOI.