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 4 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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-e5d69948600c8e1999b358f0 · master f5ddaeb87ec32678 · S338.

LIB2-017 · The boundary and selector tens have no equivariant linear intertwiner

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.296 (bytes of record)):

The boundary ten (the tangent module of the priced ten-continuous boundary object of Appendix E’s closure section) and the selector ten (the Π10 sector) are inequivalent Kdyn -modules: their Casimirs are 14 I and 16 I exactly, so HomKdyn = 0 by Schur

Statement

The boundary-adjoint ten and selector ten are inequivalent Kdyn modules: the boundary-adjoint ten has Casimir 1/4 and the selector ten has Casimir 1/6, and HomKdyn = 0.

Parts of the statement (5)

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 boundary-adjoint ten and selector ten are inequivalent Kdyn modules (one claim)
p2 · the boundary-adjoint ten has Casimir 1/4 and the selector ten has Casimir 1/6 (cut further below)
p2-p1 · the boundary-adjoint ten has Casimir 1/4 (one claim)
p2-p2 · the selector ten has Casimir 1/6 (one claim)
p3 · HomKdyn = 0. (one claim)

Scope

carrier	Boundary-adjoint ten and selector Π10 sector
domain	Linear Kdyn-equivariant maps between the named modules.
group	Kdyn
hypotheses	The boundary tangent module, selector sector and registered Casimir normalization are fixed.
quantifier	The boundary and selector modules in the declared class.
real form	Registered real Kdyn modules

What this does not show. The linear-intertwiner obstruction does not exclude the separately counted nonlinear or symmetry-breaking bridge classes.

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, §9.2, Theorem 9.2: declared-class negative — PDF p.313 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: 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 · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

The boundary ten (the tangent module of the priced ten-continuous boundary object of Appendix E’s closure section) and the selector ten (the Π10 sector) are inequivalent Kdyn -modules: their Casimirs are 14 I and 16 I exactly, so HomKdyn = 0 by Schur

The text extraction above lost mathematical typography. As the TeX source prints it (appendix_s_selector_ledger.tex:706–707): their Casimirs are ¼ I and ⅙ I exactly (R79-c; A1630 F2)

Appendix X, Carrier fence beside clause 27: boundary adjoint — PDF p.371 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

Casimir 1/4, self-intertwiner R·I, Hom = 0 to the physical ten

Appendix X, Carrier fence beside clause 27: selector Casimir — PDF p.371 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: 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 · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

The physical/vector ten (the so(5, 5) vector inside V56 , Kdyn -Casimir 1/6) is isomorphic to the selector ten (two-host certified; kernel s1067)

Appendix S, §9.2, Linear-bridge boundary — PDF p.313 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: 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 · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

The dimension match identifies nothing; any future boundary↔selector bridge must be nonlinear or symmetry-breaking, and priced.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s1052, A1515 ask-3, Appendix S §9.2, p.296; s1067/s1070 carrier fence, p.349	—	unknown	The suite reports this computation; the kernel and its output are not supplied in this round.

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
`1/4`	PDF p.349 (bytes of record)	suite text p.349 only (no kernel line found)
`1/6`	PDF p.349 (bytes of record)	suite text p.349 only (no kernel line found)
`0`	PDF p.296 (bytes of record)	closed form: HomKdyn = 0 in Theorem 9.2

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-016 The physical-vector ten and selector ten are isomorphic modules	—

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 (3)
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?
`A1632-F3a` A1632	QUOTE_RENDERING	CONFIRMED	The quote reads '14 I and 16 I' because the PDF text layer drops the fraction bar; the source prints ¼ I and ⅙ I.	appendix_s_selector_ledger.tex:706 (\tfrac14 I).	no — the predicate is unaffected
`A1632-F3f` A1632	QUOTE_RENDERING	CONFIRMED	Use 2's quote ends "Hom = 0" and drops the next words "to the physical ten", so the fragment reads as if Hom from the boundary ten to itself vanished beside a self-intertwiner ℝ·I. The complete statement is Hom(boundary ten, physical ten) = 0.	sealed extract p.349 (house-located: "to the physical ten" follows the quote).	no — the predicate is unaffected
`HOUSE-S330-F01` s1175	PROPAGATION	CLOSED 2026-09-15	The sealed suite prints the two tens' Casimirs as TWO DIFFERENT, NON-PROPORTIONAL PAIRS, with the two modules in OPPOSITE ORDER. Appendix S Theorem 9.2 (p.296): 'The boundary ten ... and the selector ten (the Pi10 sector) are inequivalent K_dyn-modules: their Casimirs are 14 I and 16 I exactly' - boundary 14, selector 16, so selector > boundary. The front matter (p.4): 'The two tens are proved inequivalent (Casimirs 1/4 vs 1/6)' and 'physical = selector at Casimir 1/6 != boundary ad K_dyn at 1/4' - selector 1/6, boundary 1/4, so selector < boundary. 14:16 is not 1/4:1/6 under any positive rescaling (s1175 T1e), and 14 < 16 while 1/4 > 1/6, so no normalization reconciles them. ★ THE THEOREM IS UNAFFECTED: distinct Casimirs force the intertwiner to zero under either pair (T1b, T1c), so Hom = 0 and LIB2-017's no-bridge conclusion stands. What fails is Theorem 9.3, 'the obstruction size is the selector's own Casimir' - it names a number the reader cannot determine from the suite, because the suite gives the selector two. How it was closed: WITHDRAWN by PI ruling R114 D-3 (S337): an extraction artifact, not a finding. The text layer renders the typeset "¼ I and ⅙ I" of Theorem 9.2 (p.296) as "14 I and 16 I"; the tex prints \tfrac14 I and \tfrac16 I (appendix_s_selector_ledger.tex:706–707), in the same boundary/selector order as p.4 and p.349, so there is no opposite order, no non-proportional pair, and Theorem 9.3's selector Casimir is ⅙. Measured on the rendered page at S335 (Trackers/F01_EXTRACTION_ARTIFACT_FINDING_S335.md) and read the same way independently by A1666 (Grok), A1667 (Gemini) and A1668 (ChatGPT). The summary above is kept as raised.	Appendix S §9.2 Theorem 9.2 and Theorem 9.3, p.296; front matter p.4 (two separate sentences); house kernel s1175 T1b-T1g. paper: REV33.2_PENDING S330·s1175 — reconcile the two printed Casimir normalizations and fix which module carries which value, then re-state Theorem 9.3 with the numeral it actually means.	closed

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-TENS-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	A1515 s1052 s1067 s1070
candidate ids (frozen list S304)	C2-109

Drafting-lane note

Boundary-wall child of C2-109. The Casimir fractions are readable at p.349; p.296's flattened fraction glyphs are retained verbatim in its quote. The least-obstruction numeral is not restated here.

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 5379d27a50eaecdb5f3ced5559197c543552840222775372d0d082eddacc107b

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-017 | 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