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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-f5da5c448d7facafbb1a2d48 · master 7147ae21feb6c82a · S338.

LIB2-170 · A reflection-positive Cartan state exists at finite regulator

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.305 (bytes of record)):

A normalized reflection-positive state exists at the finite Cartan regulator tier: a heat-kernel × Haar product on Spin(5) edges,

Statement

The registered heat-kernel × Haar product on Spin(5) edges gives a normalized reflection-positive state, an OS Hilbert space and a positive transfer operator at finite regulator.

Parts of the statement (3)

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 heat-kernel × Haar product on Spin(5) edges gives a normalized reflection-positive state (one claim)
p2 · an OS Hilbert space (one claim)
p3 · a positive transfer operator at finite regulator. (one claim)

Scope

carrier	The finite Cartan regulator with a heat-kernel × Haar edge measure
domain	Finite-regulator state, OS Hilbert space and transfer operator only.
group	Spin(5)
hypotheses	Use the registered compact Spin(5) edge measure, crossing split and nonnegative Peter–Weyl coefficients.
quantifier	The registered construction and its stated premises.

What this does not show. Finite-regulator existence does not establish the continuum limit, Einstein universality or a selected coherent boundary state.

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, §7, Named datum 7.1: finite state — PDF p.321 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

A normalized reflection-positive state exists at the finite Cartan regulator tier: a heat-kernel × Haar product on Spin(5) edges,

Appendix T, §7, Hilbert space and transfer operator — PDF p.322 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

The OS Hilbert space and a positive transfer operator exist at finite regulator.

Appendix T, §7, Argument and computation distinction — PDF p.322 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

The standard lattice argument is argument-tier and accepted as typed; the machine controls are exact in both lanes.

Appendix T, §7, Boundary-state choice — PDF p.322 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

a symmetric finite-volume state has vanishing coframe expectation — the AdS coherent boundary state is a choice, typed as such.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	A1442; Appendix T §7, Named datum 7.1, p.305	—	shipped	The suite states finite-regulator existence via the lattice argument; its argument tier is preserved.
computational	s920; Appendix T §7, p.305	—	unknown	The positive Gram controls are source-reported. The kernel, finite regulator data and original outputs 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
`5`	PDF p.305 (bytes of record)	suite text p.305: heat-kernel × Haar product on Spin(5) edges; no kernel line found

Premises this record rests on (qualified uses)

Each row is a house-declared use of a registered premise (R37). DECLARED is the house's editorial judgment only; a use becomes REVIEWED when two non-drafting lanes, reading different objects, agree the premise is LOAD_BEARING for this record's result. REJECTED rows were retired by ruling and are shown for provenance.

use	state	premise	role	why the house declared it · reads
`USE-0028`	REVIEWED by lanes (R49c)	PRM-014 (PRM-014/r2) — Finite regulator	hypothetical_assumption	Proposed by the drafting lane (A1634): The state, OS Hilbert space and positive transfer operator are stated only at finite Cartan regulator. The record carries that regulated existence theorem, not a continuum-limit statement. — House reading: House read App T:365–370: the state, OS Hilbert space and transfer operator are asserted only at the finite Cartan regulator. The result is conditional on the regulator convention. gemini · LOAD_BEARING · SUITE_TEXT_EXTRACT (D1350) grok · LOAD_BEARING · THE_RECORD (D1349)

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-169 The Euclidean MM/EH action has the stated conformal instability	—
`rests_on_premise`	PRM-014 Finite regulator	appendix_t_cartan_observation.tex:366 — "A normalized reflection-positive state exists at the finite Cartan regulator tier:"

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 (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	F-RP-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	A1442 s920
candidate ids (frozen list S304)	C2-094

Drafting-lane note

C2-094 is distinct from the finite Gaussian checkpoint G-169. Source-reported exact machine controls are not substituted for the separately identified lattice argument or an unbuilt continuum proof.

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 ac55344f3cc1cf8beb5682b46536fc148025bb9beec04402f6915b2d03206195

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-170 | 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