PUBLISHED under R67 (condition T-B) — NOT house-adjudicated. Build S371a. What PUBLISHED means here (R72): two non-drafting AI lanes (gemini + grok) read this record's anchor citation on different objects and agreed it SUPPORTS the record's statement; no citation on the record is disputed as support; its machine certificate is current. What it does not mean: no person has signed off on this record (adjudication: NOT_ADJUDICATED), the drafting lane's own reads count for nothing, and 3 of 3 unblocked uses were REVIEWED — the rest were read by one lane or none. Every label shown is the label as printed in the suite of record (Rev33.1_S369 (PDF sha256 b64ddcd9e16a6dcd…)); no house tier is assigned. The state is recomputed from the uses on every build and is withdrawn if they stop justifying it. Receipt: condition R67-TB · anchor SU-fecd760742b07c5d809910f8 · master 0b0b838e8c4d1bc5 · S328.

LIB2-053 · Frobenius compatibility fixes the finite trace ratio

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 8

Label sentence at the locator (PDF p.232 (bytes of record)):

the constraint variety is exactly {a = b} and r = 7/3 is unique.

Statement

On the reflected module 1 ⊕ 3 ⊕ 3̄, the registered Frobenius identity forces the trace weights a = b, uniquely fixing the readout r = 2 + b/(3a) = 7/3.

Parts of the statement (2)

Each part is a clause of the statement above, cut so that one part makes one claim. A reader naming the clause a quote supports can name the part.

p1 · the registered Frobenius identity forces the trace weights a = b (one claim)
p2 · uniquely fixing the readout r = 2 + b/(3a) = 7/3. (one claim)

Scope

carrier	The reflected module 1 ⊕ 3 ⊕ 3̄ and its trace weights
domain	The nonzero normalized trace readout of Theorem 4.3.
hypotheses	Use the reflected trace-weight class τa,b and the exact registered Zorn product.; Impose the Frobenius compatibility identity in the source normalization.
quantifier	The registered construction only.
real form	Split-octonion Zorn product

What this does not show. The unique finite trace normalization is not an LSZ residue, a low-energy mass theorem or a derived physical export.

Scientific status: UNDER REVIEW — the house has not adjudicated CURRENT / CONTESTED for this record (charter §10.3); a drafted claim is a claim under review, not a result.

Sources in the suite of record

Key — use ≠ record. A review state printed on a source use below names that use — one citation of the suite, read by the lane named in its warrant — not this record. The record's own review state is the one in the table above and is unchanged by any use-level state; a use may be LANE_PROPOSED or REVIEWED while the record it sits on remains IN_REVIEW (R45, R49).

Quotes are verbatim from the sha-pinned text extraction of the Rev33.1 PDF (A1584 §2.2, S309): mathematical typography — radicals, exponents, ≅ — can appear displaced in the extracted line. The PDF page is authoritative; the quote is what the machine gate matched.

Appendix K, §4, Theorem 4.3: reflected trace weight — PDF p.244 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

r = 2 + b/(3a).

Appendix K, §4, Theorem 4.3: closure constraint — PDF p.244 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

split-octonion (Zorn) product forces a = b; the twelve nonzero closure defects are all ∝ (a − b), so the constraint variety is exactly {a = b} and r = 7/3 is unique.

Appendix K, §4, Strict physical-export fence — PDF p.244 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

This closes the last trace-weight freedom on the 7/3 road; it is not an LSZ residue, a low-energy mass theorem, or a physical export theorem.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	Appendix K §4, Theorem 4.3, S229, p.232	—	shipped	The supplied theorem states the Frobenius constraint and reports two in-house checks; their scripts and outputs are not supplied.

The numbers this record declares, and where each one's digits come from

This table covers the values this record DECLARES, not every numeral printed on this page: group labels such as E7(7), section numbers and page numbers are not declared values and are not listed here.

value as printed	page	digit source
`1`	PDF p.232 (bytes of record)	closed form: reflected module, r = 2 + b/(3a), and r = 7/3 printed in Theorem 4.3
`3`	PDF p.232 (bytes of record)	closed form: reflected module, r = 2 + b/(3a), and r = 7/3 printed in Theorem 4.3
`2`	PDF p.232 (bytes of record)	closed form: reflected module, r = 2 + b/(3a), and r = 7/3 printed in Theorem 4.3
`7/3`	PDF p.232 (bytes of record)	closed form: reflected module, r = 2 + b/(3a), and r = 7/3 printed in Theorem 4.3

Typed links

type	target	licensed by
`cited_by_section`	E-C05.1.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0166, CIT-0170
`cited_by_section`	E-C05.1.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0175
`cited_by_section`	E-C05.1.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0185
`cited_by_section`	E-C08.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0215
`cited_by_section`	E-C08.2.definitions-conventions (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0217
`cited_by_section`	E-C08.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0219, CIT-0220, CIT-0222

Why this record is PUBLISHED (R67, condition T-B)

states a predicate	yes
uses on the record · unblocked	3 · 3
uses any lane has read	3 of 3
REVIEWED SUPPORTS use on the predicate, read by two non-drafting lanes	yes (2)
a SUPPORTS use on the predicate is DISPUTED	no
machine certificate current	yes

Machine certificate (R68)

state MACHINE_CHECKS_PASSED

policy sgtoe-clearance-policy-1.0-RATIFIED · sha16 ef7d6e7690514311

bound to master aad7a3ec6ce3b510 (the master the checks ran on; issued 2026-09-26T05:06Z)

checks

check	result	reason
`schema_valid`	PASS	exercised
`basis_current`	PASS	exercised
`quote_located`	PASS	exercised
`labels_literal`	PASS	exercised
`edges_resolved`	PASS	exercised
`bindings_valid`	PASS	exercised

A certificate says the record is well-formed, current, quote-on-page, label-literal, edge-resolved and binding-consistent on the bytes it was issued on. It is not a review, and it goes STALE the moment the master moves under it (R68). It is one conjunct of the PUBLISHED condition (R67), never the whole of it.

History

March library (v1) antecedents	no legacy antecedent identified
Track-2 claim ids	C-73-01, D-73-01 — cross-reference; the Track 1 / Track 2 join sets each one against what the sealed suite prints for this record. Where they differ, the suite is the record.
candidate ids (frozen list S304)	C2-044 C2-054

Drafting-lane note

C2-044 and C2-054 are merged at the finite trace/index layer. The within-generation coefficient obstruction and the physical export problem remain separate. No kernel serial is guessed from the adjacent residue-map discussion.

Receipt

round D1253 · parsed 2026-09-06T00:06Z · machine gates passed: CONTRACT, G1-quote-on-page, G2-numerals-declared, G4-ids-resolve, DAG-acyclic · content sha256 7633c7a40ce027a15df823a8272335a2703652204d13479a18d9563e63603472

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-053 | PASS or FAIL(G1–G8) or NOT RUN | quote | PDF page | one sentence. G1 source supports the exact scoped assertion · G2 evidence class fits (numbers ≡ digit source) · G3 labels as printed, not converted · G4 comparison typed · G6 public scope · G7 history real · G8 caution present and true. Machine surfaces: index.json · capsule.md.

Generated from library_v2.jsonl. Declared volatile fields (R36): BUILD_STAMP.
BUILD_STAMP S371a · 2026-09-26T22:53Z · master 01d1a5873ede42f5 · cut 9dcc6ce9a8ee3e02