The informal proof

This is the ink layer: an argument written for a human reader and refereed. No proof kernel certifies it and no computation bounds it — the check is a referee reading the proof. It is also the layer every other row presupposes, because a kernel certifies a formal statement and something has to say that the statement is the one that was signed.

Read it

The paper (PDF, 8 pp.)	The mathematics written up to be read: the statement for general n, which this edition does not prove, and the case n = 1, which it does. Assembled from the documents below, every definition, statement and proof step lifted verbatim.
The mathematics explained	The same result at length, for a general reader, with the formulas typeset. No renderer, no network.

The record they are accountable to

The statement and the proof are separate documents on purpose: the goal was signed and hash-frozen before any proving began, so the claim “the proof proves the statement that was signed” has content that can be checked rather than assumed.

The signed goal (PDF) — also as LaTeX source
The informal proof (PDF) — also as LaTeX source
The adversarial referee’s report

How it was refereed

stage	date	what happened
adversarial mathematical referee	2026-07-20	CONFIRM-WITH-FINDINGS · read: proofv0a.tex as it then stood, pre-notation-migration · report `6e31018c647e…` · the report attack (8), byte-faithfulness to goalv0a.tex — FAITHFUL. Definitions, the algebra and its relations, and all three clauses reproduced without change; the four documented traps checked one by one. One non-blocking phrasing point.
notation migration	2026-08-10/11	read: the whole manuscript Q→q, q→v, z→t by the Sandbox-wide dictionary. Argument unchanged, symbols renamed. The no-drift property was verified mechanically by the next referee, not asserted here.
human-facing editorial referee	2026-08-12	PASS-WITH-EDITS — 2 BLOCKING, 15 EDITORIAL, 12 NIT · read: proofv0a.tex · bytes read `c42cbf8fc204…` · report `e8034b17455c…` · the report · kept at `informal/versions/proofv0a_pre-editorial_2026-08-12.tex` semantic-drift check against the byte-frozen signed anchor: NO DRIFT, verified MECHANICALLY rather than by eye. Refereed for a competent mathematician OUTSIDE this programme reading the PDF with no access to the record.
revision	2026-08-12	Both BLOCKING findings repaired — one-sentence each. The repairs are visible as three hunks against the version above: the migration paragraph restated, the clause (ii) injectivity step written out in full, and the attribution remark made exact. The middle one writes the FIRST referee's own supplied argument into the text.
acceptance	2026-08-13	by hypervisorA, as tree owner and review counterparty · document `2e9d82647107…` · the acceptance

What ink does not mean

INTERNAL. Both referees are agents of this project working under the Sandbox Rule, adversarially and recused from their own work. NO EXTERNAL PEER REVIEW HAS TAKEN PLACE. The edition says 'Peer review to date: Internal' on its face and that stays true; ink means refereed, never externally refereed.

The limit, stated on its own face

NO REFEREE READ THE SHIPPED BYTES. The last referee read c42cbf8f…, required two one-sentence repairs, and those repairs produced the shipped bbd6f055…. THIS IS NOT WITHDRAWN BY THE VERIFICATION BELOW: a delta check by the accepting seat is weaker than a referee reading the whole document, and ink means refereed. The verification sits under this limit as mitigation, never as replacement, and 'Peer review to date: Internal' stands.

What was done about it

versions/proofv0a_pre-editorial_2026-08-12.tex (c42cbf8f…, the refereed bytes) against informal/proofv0a.tex (bbd6f055…, the shipped bytes) — 29 changed lines across three sites. Verified by hypervisorA, the accepting seat, 2026-08-31 — who attacked this limit on request rather than ruling it ordinary.

The decisive test. A mechanical diff of every theorem / lemma / proposition / corollary / definition environment and every \label. EMPTY: six environments in each, identical, same labels. Carried further by the Editor to the full statement BODIES, whitespace-normalised: 6 of 6 identical. NO STATEMENT CHANGED BETWEEN THE REFEREED BYTES AND THE SHIPPED BYTES.

Every change ran toward more rigour:

the notation-dictionary paragraph expanded — expository, making Q→q, q→v, z→t explicit
the middle-equality step: the refereed text ASSERTED that Uev = Nev ⊆ U maps into U ⊗ Frac(A_t); the shipped text PROVES it — F_t injects into Frac(A_t) = ℚ(v,t) and U is free over F_t, so the inclusion is literal. A justification SUPPLIED where one was assumed.
the Lusztig remark made precise and given the sentence 'Nothing below rests on that remark' — reliance on an external remark REMOVED.

TWO SEATS, TWO INDEPENDENT IMPLEMENTATIONS, on the stronger form of the test. The Almanac Editor re-ran hypervisorA's environment/label diff before adopting it and extended it to full statement BODIES (6 of 6 identical); hypervisorA then re-implemented the body comparison by a different route and got the same result. Neither seat took the other's number.

Every delta runs toward more rigour and none touches a statement, so a referee who passed c42cbf8f could not have withdrawn that verdict on bbd6f055: the shipped bytes are strictly better supported than the bytes that earned the PASS. WHAT IT DOES NOT LICENSE: calling the shipped bytes refereed. They are not.

The row this layer carries

result	what it says
A0a-12-proof-proves-the-signed-statement	The stand-alone proof proves the statement that was signed: proofv0a.tex establishes the three clauses of goalv0a.tex — no clause weakened, none strengthened, no convention changed.

Its convention frame: Both documents are read in the CURRENT frame (q, v, t; q = v², t = z²). The first referee read the pre-migration text in the legacy frame (Q, q, z); the migration between them was verified mechanically, not by eye, and is recorded in the chain below.

Every other result in this edition is in the concordance, with the two layers that can be machine-checked: the proof ledger and the formal layer.