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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-a7b9fb87816bcfee086e54f1 · master 6d82da907c52e8e6 · S329.

LIB2-089 · The physical-to-boundary quadratic bridge space is one-dimensional

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 7

Label sentence at the locator (PDF p.297 (bytes of record)):

dim HomKdyn (Sym2 P, B) = 1

Statement

For the registered physical/selector ten P and boundary ten B, dim HomKdyn(Sym²P,B) = 1.

Scope

carrier	Physical/selector ten P and boundary ten B
domain	Quadratic symmetry-respecting maps from the physical/selector module to the boundary module.
group	Kdyn
hypotheses	Use the distinct registered P and B modules and the symmetric-square domain.
quantifier	The specified equivariant Hom space.

What this does not show. The dimension count does not select a normalized physical bridge or identify the inequivalent linear modules.

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 S, §9.3, Quadratic bridge census: P to B — PDF p.313 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

dim HomKdyn (Sym2 P, B) = 1

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_s_selector_ledger.tex:744): dim Hom_(K_dyn)(Sym²P, B)=1 (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Appendix S, §9.3, Naming the two carriers — PDF p.313 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

The quadratic bridges between the physical/selector ten P and the boundary ten B are counted exactly:

Appendix S, §9.3, Choice of a bridge remains priced — PDF p.313 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

any future use of one must name which of the counted copies it takes and price the choice.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	A1523 V6/V7; D1210 return §4, Appendix S §9.3, p.297	—	unknown	The suite reports the two-host carrier census. The computational payload and individual output key 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
`2`	PDF p.297 (bytes of record)	closed form: dim HomKdyn(Sym2 P,B) = 1 in the printed quadratic-bridge census
`1`	PDF p.297 (bytes of record)	closed form: dim HomKdyn(Sym2 P,B) = 1 in the printed quadratic-bridge census

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-016 The physical-vector ten and selector ten are isomorphic modules	—
`related_to` (never evidential)	LIB2-017 The boundary and selector tens have no equivariant linear intertwiner	—

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-QUAD-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	A1523 D1210
candidate ids (frozen list S304)	C2-120

Drafting-lane note

P-to-B child of C2-120. It is distinct from the reverse quadratic Hom space and does not overturn the direct linear-intertwiner obstruction G-021.

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 bd9ad61de54d61e42b4dbf4e2a4bf6d8aeb56825634feec590a0a80d27935de1

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-089 | 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