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 4 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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-13d3b0313b7b07ac7bde2919 · master 1aa73892adc5691e · S364.

LIB2-113 · Reynolds preservation of the registered raw coefficient ray

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 9

Label sentence at the locator (PDF p.230 (bytes of record)):

Hence democracy is not an accident of normalization — it is Reynolds-forced.

Statement

The loaded U(1)Y Reynolds average PY=0 is the identity on the span of the four displayed Yukawa channel tensors, each of total hypercharge 0, so it retains every coefficient vector on that span without reweighting — in particular the common ray (1,1,1,1) of the registered raw tensor. This is preservation, not selection: nothing in the projection excludes an unequal quartet on the same span.

Scope

carrier	The span of the four displayed Yukawa channel tensors, all of total hypercharge 0 (s1171 T1)
domain	UV/matching coefficients, not low-energy equality.
group	U(1)Y (loaded hypercharge), acting trivially on the four-channel span; the multiplicity-one premise is exhibited on the model group S4 (Appendix K §3.3, p.234), not on this action
hypotheses	None beyond total hypercharge 0 on the four displayed tensors: the retention statement needs no multiplicity-one and no channel-transitivity premise.; Split G2(2) setting as registered; the §2.2 transitivity argument is NOT used (A1717-F02).
quantifier	Every coefficient vector on that span; the (1,1,1,1) ray is named as the instance the suite carries
real form	Split G2(2) setting

What this does not show. This UV coefficient ray does not predict equal low-energy masses or select a symmetry-breaking compensator. Retention is not protection: excluding an unequal quartet is a separate claim, and it holds only under the trivial multiplicity-one premise, which Appendix K p.234 states as a premise exhibited on the model group S4 and does not derive for the registered four-channel action.

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, §3.3, Reynolds-forced equal weights — PDF p.241 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → SUPPORTS · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

(Rev32.9, A1652 F01b/S330.7: through Rev32.8 this paragraph derived the ray from “a group average over a symmetry that acts transitively on the channels”, which is unavailable for both projectors.)

Appendix K, §3.3, Democratic projected ray — PDF p.241 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

The Reynolds projector selects the singlet sector and does not reweight within it; PY =0 is the identity on the span of the four displayed tensors, which all carry total hypercharge 0 (s1171 T1).

Appendix K, §2.2, Matching-scale scope — PDF p.240 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

This is the G2 tight-frame value. It is a UV normalization statement, not a low-energy prediction.

Appendix K, §4, Remark 4.4: multiplicity-one fence — PDF p.244 (bytes of record)
review state: LANE_PROPOSED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

the residue map is multiplicity-one fenced, and an explicit m = 2 counter-model shows the bound is saturated rather than an artifact of the search.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s239/s240 and s243; Appendix K §§3.3,4, pp.229–230,232	—	unknown	The source reports Reynolds projection and its multiplicity-one strengthening; the kernels and countermodel payload 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.229 (bytes of record)	closed form: PY=0 Traw ∝ (1,1,1,1), printed in Appendix K §3.3

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	4 · 4
uses any lane has read	4 of 4
REVIEWED SUPPORTS use on the predicate, read by two non-drafting lanes	yes (1)
a SUPPORTS use on the predicate is DISPUTED	no
machine certificate current	yes

Referee findings (R73)

Raised by a lane acting as referee and re-measured by the house before being listed (a lane's word alone is not a finding). Only a CONFIRMED finding against the record's predicate blocks PUBLISHED; the others are printed so a reader sees them.

finding	scope	state	what	evidence	affects this record's predicate?
`A1652-F01` A1652	PROOF	CONFIRMED	The four displayed Yukawa tensors all carry total hypercharge 0, so the loaded U(1)_Y Reynolds average is the IDENTITY on their span (s1171 T1: rank 4; (1,2,3,4) unchanged). The sealed text at App K §3.2 p.229 infers the democratic ray from the projector's 'being an average', and §3.3 supplies a transitivity premise for P_{Y=0} that it does not establish. A transitive S4 average is rank 1 and does collapse (T1c/T1d); controls show the operative property is TRANSITIVITY, not averaging. The record's conditional conclusion is not refuted; its printed proof is.	Appendix K §3.2 p.229 ('which, being an average, returns the democratic ray') and §3.3 p.229; house kernel s1171 T1a-T1d + two non-vacuity controls, 29/29 gates. paper: REV33.2_PENDING S330·A1652	no — the predicate is unaffected
`A1652-F01b` A1652	PROOF	CONFIRMED	SHARPENING OF A1652-F01, and it changes the repair. (1) 'Reynolds-forced' is used in ONE appendix in TWO senses: PRODUCED-BY (p.222 'this forces the democratic ray'; p.229 §3.2 'being an average, returns the democratic ray') and PROTECTED-BY (p.225 Prop 3.2 'no operation invariant under the averaged symmetry can split it'). PRODUCED-BY is false for both projectors the suite names. PROTECTED-BY is true ONLY when the trivial multiplicity is one — a Schur statement, not an orbit-average statement — and s1172 T2 exhibits diag(2,1,1,1) as an invariant operator that splits the ray at multiplicity 4, so Prop 3.2 FAILS for P_{Y=0} as §3.2 names it. (2) The §3.3 transitivity premise is unavailable for BOTH named groups: U(1)_Y fixes all four channels, and \|C3 x C3\| = 9 while a transitive action on 4 channels needs an orbit of size 4, which does not divide 9 (s1172 T1; controls at orders 12 and 6 fire). The 'find the transitive group' repair path is therefore CLOSED inside the structure the suite names. (3) ★ THE SUITE STATES THE CORRECT VERSION ITSELF, FOUR PAGES EARLIER: p.225 item 3 — 're-projecting the democratic sum with P_{Y=0} keeps (1,1,1,1): the Reynolds projector SELECTS, IT DOES NOT REWEIGHT.' (4) The class identification at p.224 Thm 3.1 ('P_code and P_{Y=0} are the same operator CLASS') is then used as an OBJECT identification when the conclusion is attributed to P_{Y=0} — the S299 signature-is-not-identification rule, in the suite's own text.	Appendix J p.222, p.224 Thm 3.1, p.225 item 3 and Prop 3.2, p.226; Appendix K p.229 §3.2/§3.3, p.232 Remark 4.4 (s243 multiplicity-one); house kernel s1172, 14 gates. paper: REV33.2_PENDING S330·A1652 row S330.1 (rewritten by this finding — see Trackers/F01_DISPOSITION_S330.md)	no — the predicate is unaffected
`A1653-F01` A1653	MATERIALLY_AMBIGUOUS_REFERENT	CLOSED 2026-09-17	LIB2-113's statement does not fix which object it is about, so the scope of a finding against it cannot be typed. The two readings are not merely different — they place the defect in different places. A1655 sharpened this further: the word 'leaves' hides THREE propositions — preservation (P_Y d = d), particular evaluation (P_Y T_0 = lambda d for one specified raw tensor), and universal equalization (P_Y(C) subset R d). Identity on the span PROVES the first, DOES NOT DISPROVE the second, and REFUTES the third. A disambiguation must therefore record WHICH OPERATOR, on WHICH INCOMING DOMAIN, with WHICH QUANTIFIER, making WHICH CLAIM — preservation, evaluation or selection. 'Multiplicity one' cannot stand in for that specification, and a one-dimensional invariant space does not by itself name the democratic line (s1173 T1 is the counterexample). ★ The record documented its own weak points and nobody read them: scope.hypotheses[0] imports 'the source's channel-transitivity premise', which s1172 shows is unavailable for both groups the source names; scope.hypotheses[1] restricts transitivity to a 'norm-class orbit', which is precisely the vectors-vs-triples move s1171 T2 refutes. How it was closed: R138 D-1 (PI, S343): closing condition met by R137 (operator PY=0; domain = span of the four displayed hypercharge-0 Yukawa channel tensors; quantifier = every coefficient vector on that span; claim = PRESERVATION; scope.group = U(1)Y) and confirmed by round 24 (A1718 Grok THE_RECORD + A1719 Gemini SUITE_TEXT_EXTRACT: SUPPORTS on SU-13d3b031 with the same conjunct, CONTEXT on the other three; 0 disputes).	The record's own scope.group and scope.hypotheses fields; Trackers/P2_GATE_CENSUS_S330.md; kernels s1171 T1/T2, s1172 T1/T2, s1173 T1. paper: none — this finding closes by rewriting the RECORD, not by a suite row. The suite rows are S330.7 (and superseded S330.1).	closed
`A1711-F03` A1711	PREDICATE	CLOSED 2026-09-17	A projector that is the identity on the four-tensor span preserves any ray; "leaves (1,1,1,1)" must be read as retention of the registered raw coefficients (p.229), not selection. How it was closed: R135 D-2 (PI, S342): R132 D-3 re-type applied and the LIB2-113 uses re-read in round 23.	SUITE_TEXT_S341 pp.229, 233	closed
`A1717-F01` A1717	PROOF	CONFIRMED	App K p.233 credits the equality to averaging ('which, being an average, returns the democratic ray'; heading 'democracy is Reynolds-forced') while the same page says PY=0 is the identity on the span of the four displayed tensors. An identity cannot distinguish an equal quartet from an unequal one: the causal wording overstates what the operator does.	SUITE_TEXT_S341 p.233 (end of App K 3.2; heading 3.3) paper: REV32.10 S342.4	no — the predicate is unaffected
`A1717-F02` A1717	PROOF	CONFIRMED	App K 2.2 (p.232) infers constancy of the cubic coupling across four channel TRIPLES from G2(2) transitivity evaluated on the seven rotated copies of a SINGLE channel. Simultaneous orbit membership of ordered triples is the missing step; the review's exact Zorn control shows equal Gram data does not fix the trilinear (1 vs 5/3).	SUITE_TEXT_S341 p.232 (App K 2.2, Lemma 2.2 / Proposition 2.3) paper: REV32.10 S342.5	no — the predicate is unaffected
`A1717-F03` A1717	PROPAGATION	CONFIRMED	App K p.232 cites 'the four gauge-allowed channels of 2.3'. Section 2 prints 2.1, 2.2 and Proposition 2.3, then 3 begins on p.233: there is no subsection 2.3. The intended locator is unidentified and must not be silently read as Proposition 2.3.	SUITE_TEXT_S341 p.232; heading sweep pp.228-237 paper: REV32.10 S342.6	no — the predicate is unaffected
`A1720-F01` A1720	PROPAGATION	CONFIRMED	Appendix K Remark 4.4 (p.236) attaches [LIB2-113] to the s243 residue-map upgrade of Theorem 3.1 ('the residue map is multiplicity-one fenced, and an explicit m = 2 counter-model shows the bound is saturated'). Under R137 the record asserts only that the loaded U(1)Y Reynolds average is the identity on the four-channel span; it says nothing about Theorem 3.1, the residue map or s243, and no other record carries s243. The tag makes the record read as certifying a different theorem.	Rev32.9_S341 p.236 Remark 4.4; LIB2-113 statement/caution under R137; A1720 review §3. paper: REV32.10_CHANGELOG S343.1 (landed in Rev32.10)	no — the predicate is unaffected

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-DEM-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	s239 s240 s243
candidate ids (frozen list S304)	C2-046

Drafting-lane note

C2-046 retains the declared category and per-orbit-class transitivity premise. Uniqueness of the underlying trilinear is not assumed. The source's prose theorem language is not a scorecard tier.

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 36236cbc0673f708d32f73e1b72963cd3acbd1dcb1c25c686772f144c071335e

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-113 | 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