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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-ff52bc428504d9ea871960a7 · master cb9ce26d95e37a21 · S327.

LIB2-009 · The complementary tangent plane closes as a Lie-triple system

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.181 (bytes of record)):

The missing-16 IS a Lie-triple system, to machine precision (4.9 × 10−15 over all 1,920 triples).

Statement

The registered missing-16 tangent plane is a Lie-triple system at the basepoint of E7(7)/SU(8), as reported to machine precision.

Scope

carrier	Registered missing-16 tangent plane
domain	The local tangent-plane computation in Appendix F §5.3 and Paper 4 §4.2.
group	E7(7)
hypotheses	The basepoint, tangent plane and registered ambient brackets are fixed.
quantifier	The named tangent plane at the basepoint.
real form	E7(7)/SU(8)

What this does not show. Local Lie-triple closure does not establish the global embedded quotient or a vector-coupled physical truncation.

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 F, §5.3, Missing-16 Lie-triple test — PDF p.187 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

The missing-16 IS a Lie-triple system, to machine precision (4.9 × 10−15 over all 1,920 triples).

The text extraction above lost mathematical typography. Restored from the sealed TeX source (rev32.7/tex/appendix_f_gauge_boundary.tex:514-515): The missing-16 IS a Lie-triple system, to machine precision (4.9×10⁻¹⁵ over all 1,920 triples). (R87 house restoration: rendered from the tex, not the quote; the quote above is what the machine gate matched)

Paper 4, §4.2, Rev29 local-scope correction — PDF p.73 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

the missing-16 tangent plane is a Lie triple system in e7(7) ⊖ su(8) at the basepoint, so by Cartan’s theorem it exponentiates to a totally geodesic submanifold of E7(7) /SU (8) in a neighbourhood of that basepoint, locally isometric to the symmetric space SO(4, 4)/(SO(4) × SO(4))

Appendix F, §5.3, Scope fence — PDF p.188 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

Scope fence: “consistent truncation” here is the scalar sigma-model criterion; vector-sector statements are downstream and not claimed.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
registry	Appendix F §5.3, S78b Lie-triple/generated-algebra report, p.181	—	shipped	Availability refers to the supplied suite report; no individual computational kernel or output is 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
`16`	PDF p.181 (bytes of record)	suite text p.181 only (no kernel line found)

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-007 The identity-anchored complementary scalar sector	—
`cited_by_section`	E-C03.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0031
`cited_by_section`	E-C03.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0036
`cited_by_section`	E-C03.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0044

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

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-F4b` A1632	PROPAGATION	CONFIRMED	As A1632-F4; this record's 'at the basepoint' wording is the correct local reading.	appendix_f:519–520 vs suite p.69. paper: REV32.9_CHANGELOG S327·A1632 item 3 (landed in Rev32.9)	no — the predicate is unaffected

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	A-GEO-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.
candidate ids (frozen list S304)	C2-033

Drafting-lane note

This is the closure child of C2-033. Paper 4 p.69 limits the older submanifold wording on p.181 to a neighbourhood of the basepoint. The registered computation is restated, not rerun.

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 474ec0cd2c65ba2bd6d0af39b7cd5e82bc077c49a164b5b33c19e7833ce2304f

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-009 | 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