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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-8bc029535b368dc18ab45729 · master c7e92a7e45eaadf0 · S342.

LIB2-189 · The anisotropic heat-kernel family has nonlinear OS positivity in its cone

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 8

Label sentence at the locator (PDF p.307 (bytes of record)):

Lα,β is a positive elliptic invariant on the whole cone α > |β|, the heat semigroup is a positive Markov convolution, and the reflected-kernel factorization gives OS positivity.

Statement

In the declared anisotropic heat-kernel family with α > |β|, the positive elliptic invariant generates a positive Markov convolution whose reflected-kernel factorization gives OS positivity.

Parts of the statement (2)

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 positive elliptic invariant generates a positive Markov convolution (one claim)
p2 · whose reflected-kernel factorization gives OS positivity. (one claim)

Scope

carrier	The anisotropic heat-kernel family generated by Lα,β
domain	Nonlinear reflection positivity in the declared heat-kernel family at regulator tier.
hypotheses	Use the registered invariant operator Lα,β and its coefficient cone α > \|β\|.; Use the reflected-kernel factorization of Proposition 8.5.
quantifier	The registered construction and its stated premises.

What this does not show. This family-specific reflection positivity does not establish a general gravitational measure or a continuum Einstein limit.

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, §8, Proposition 8.5: nonlinear reflection positivity — PDF p.324 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

Lα,β is a positive elliptic invariant on the whole cone α > |β|, the heat semigroup is a positive Markov convolution, and the reflected-kernel factorization gives OS positivity.

Appendix T, §7, Proposition 7.4: heat-kernel-family qualification — PDF p.322 (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

nonlinear RP at β = ̸ 0 was closed only for the anisotropic heat-kernel family (below);

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s921-U3; Appendix T §8, Proposition 8.5, p.307	—	unknown	The source reports the operator, semigroup and factorization result; the defining kernel and original outputs are not supplied.

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-170 A reflection-positive Cartan state exists at finite regulator	—
`related_to` (never evidential)	LIB2-172 The positive completion cone has a strict coefficient domain	—

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
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	A1443 s921
candidate ids (frozen list S304)	C2-094

Drafting-lane note

Nonlinear heat-kernel subject associated with C2-094. It is distinct from the finite product state G-174 and from mere positivity of a quadratic completion. No coefficient is selected.

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 f968f54fc4ff5d174e5127863e36a508991ef0abb0b91972aa76b48d82237996

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-189 | 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