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 2 of 2 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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-81c9c1478201a31559a4d0d3 · master bd2d1a4de7da2b44 · S338.

LIB2-195 · The frozen symplectic braid representation has a nonscalar centre

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 11

Label sentence at the locator (PDF p.313 (bytes of record)):

exactly and are symplectic: a genuine representation B3 → Sp(V56 ). The centre is computed and is not scalar — (B1 B2 )3 = I − 2Pact — so there is no global PSL(2, Z); only the active sector projectivizes.

Statement

The registered B1 and B2 give a symplectic representation B3 → Sp(V56) with nonscalar centre (B1B2)³ = I − 2Pact; only the active sector projectivizes to PSL(2,Z).

Parts of the statement (4)

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 B1 and B2 give a symplectic representation B3 → Sp(V56) with nonscalar centre (B1B2)³ = I − 2Pact (cut further below)
p1-p1 · The registered B1 and B2 give a symplectic representation B3 → Sp(V56) (one claim)
p1-p2 · with nonscalar centre (B1B2)³ = I − 2Pact (one claim)
p2 · only the active sector projectivizes to PSL(2,Z). (one claim)

Scope

carrier	The registered braid generators on the frozen real V56 carrier
domain	The frozen symplectic braid representation, not the winding-category functor.
hypotheses	Use the registered B1, B2 and active-sector projector in Appendix T §14.2.
quantifier	The registered construction and its stated premises.

What this does not show. The representation does not supply the missing functor to the winding category or identify the trace-three word with a physical lepton neck.

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 T, §14.2, Braid representation and centre — PDF p.331 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read OUR_QUOTE_AS_PRINTED → SUPPORTS · gemini read OUR_QUOTE_AS_PRINTED → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

exactly and are symplectic: a genuine representation B3 → Sp(V56 ). The centre is computed and is not scalar — (B1 B2 )3 = I − 2Pact — so there is no global PSL(2, Z); only the active sector projectivizes.

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_t_cartan_observation.tex:894-897): exactly and are symplectic: a genuine representation B₃→Sp(V₅₆). The centre is computed and is not scalar — (B₁B₂)³=I-2P_act — so there is no global PSL(2,ℤ); only the active sector projectivizes. (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix T, §14.2, Missing winding-category interface — PDF p.331 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read OUR_QUOTE_AS_PRINTED → CONTEXT · gemini read OUR_QUOTE_AS_PRINTED → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

The braid result lives in RepR (so(2, 1)) on V56 , not in the corpus F4 /winding category, and no functor between the two has been constructed

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s1026/s1032; A1499, Appendix T §14.2, p.313	—	unknown	The source reports the braid relation, symplecticity and central involution; the generators and original verifier 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.313 (bytes of record)	closed form: B3 → Sp(V56) and (B1B2)3 = I − 2Pact in Appendix T §14.2
`2`	PDF p.313 (bytes of record)	closed form: B3 → Sp(V56) and (B1B2)3 = I − 2Pact in Appendix T §14.2
`3`	PDF p.313 (bytes of record)	closed form: B3 → Sp(V56) and (B1B2)3 = I − 2Pact in Appendix T §14.2
`56`	PDF p.313 (bytes of record)	closed form: B3 → Sp(V56) and (B1B2)3 = I − 2Pact in Appendix T §14.2

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-015 The golden braid-word square root on the frozen carrier	—
`related_to` (never evidential)	LIB2-194 The frozen Clifford law makes every registered carrier-map Gram isotropic	—
`related_to` (never evidential)	LIB2-143 The exhibited winding-to-Fibonacci functor defines the finite cluster image	—
`cited_by_section`	E-C05.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0193
`cited_by_section`	E-C05.2.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0205
`cited_by_section`	E-C05.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0197
`cited_by_section`	E-C05.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0214

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

states a predicate	yes
uses on the record · unblocked	2 · 2
uses any lane has read	2 of 2
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

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
serials	A1499 s1026 s1032
candidate ids (frozen list S304)	C2-104

Drafting-lane note

Representation subject associated with C2-104, distinct from the golden word's square root G-019. The nonscalar centre and absent cross-category map prevent a global projective or physical identification.

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 70fa18092207fb1df5172f088b93538fe3d78c8f138e23f59921ec3a7a57ac92

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-195 | 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