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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-2530c9870315f7f83e976265 · master 94096cf0b0ea8052 · S330.

LIB2-112 · Exactly half of the raw trilinear norm lies in forbidden mirror sectors

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.229 (bytes of record)):

the raw octonionic trilinear τ carries exactly half of its squared norm as Y = ±1 “forbidden mirror” leakage:

Statement

Exactly half of the raw trilinear squared norm lies in total-hypercharge ±1 mirror sectors, and the loaded U(1)Y Reynolds projector removes that leakage.

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 · Exactly half of the raw trilinear squared norm lies in total-hypercharge ±1 mirror sectors (one claim)
p2 · the loaded U(1)Y Reynolds projector removes that leakage. (one claim)

Scope

carrier	The raw and hypercharge-projected split-octonion trilinears
domain	The forbidden-mirror component norm and its removal.
group	Loaded U(1)Y
hypotheses	Use the loaded hypercharge assignments and the squared component norm of the A1048 census.
quantifier	The registered construction and its stated hypotheses.

What this does not show. Removing forbidden mirror components does not derive the hypercharge loading or create a non-democratic hierarchy.

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, §3.2, Half-norm mirror leakage — PDF p.240 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

the raw octonionic trilinear τ carries exactly half of its squared norm as Y = ±1 “forbidden mirror” leakage:

Appendix K, §3.2, Projection removes the leak — PDF p.240 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

The loaded U (1)Y Reynolds projector PY =0 removes this leak exactly

Appendix K, §3.2, Raw cubic versus physical Yukawa — PDF p.241 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

the raw J3 cubic is not the physical Yukawa tensor without the U (1)Y projection;

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	A1048, Appendix K §3.2, p.229: raw/projected component-norm census	—	unknown	The source reports exact half-norm leakage and projection removal; no component census is rerun.

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.229 (bytes of record)	suite text p.229: Y = ±1 forbidden-mirror sectors and loaded U(1)Y projection
`1`	PDF p.229 (bytes of record)	suite text p.229: Y = ±1 forbidden-mirror sectors and loaded U(1)Y projection

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-111 The loaded hypercharge projection gives the four Yukawa tensors	—

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-LEAK-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.
serials	A1048
candidate ids (frozen list S304)	C2-047

Drafting-lane note

C2-047 is the norm-leakage result, not an assertion that the unprojected cubic is already a physical Yukawa. The fraction is stated as the source's word half rather than repaired from its flattened equation.

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 e5920ca55686be5adda756d319d95a24ff98e3fd9bb915360a14ca931aa28efb

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-112 | 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