IN_REVIEW — NOT CITABLE. Under coalition review; not house-adjudicated. This page was generated (build S371a) from a drafting-lane record. Clearance here is a MACHINE CERTIFICATE under the ruled policy (v1.0 RATIFIED, R68), not a review: it is MACHINE_CHECKS_PASSED — contract · quote-on-page · declared numerals · id resolution · acyclic graph · basis current — and that is a statement about the intake gates, not scientific clearance. It is NOT HOUSE_ADJUDICATED: no person has signed off on this record, and 0 of 357 records have been. No tier has been assigned by the house; every label shown is the label as printed in the suite of record (Rev33.1_S369 (PDF sha256 b64ddcd9e16a6dcd…)). Adversarial review by a lane that did not draft it is also still owed. Nothing on this page may be cited as a result of the programme until its state reads PUBLISHED — a state written only by the R67 transition producer when a REVIEWED SUPPORTS use, read by two non-drafting lanes, stands on the record's predicate.

LIB2-010 · The algebra generated by the complementary tangent plane

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state IN_REVIEWentry version 10

Label sentence at the locator (PDF p.181 (bytes of record)):

It generates g′ = [16, 16] ⊕ 16 of dimension 28, closing at 7.4 × 10−15 , with compact part of dimension 12, trivial center, rank 4, and Cartan character +4: g′ ∼ = so(4, 4), [16, 16] ∼ = so(4) ⊕ so(4).

Statement

The missing-16 plane generates a 28-dimensional algebra identified with so(4,4), whose compact part is so(4) ⊕ so(4) of dimension 12.

Parts of the statement (4)

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 missing-16 plane generates a 28-dimensional algebra identified with so(4,4) (cut further below)
p1-p1 · The missing-16 plane generates a 28-dimensional algebra (one claim)
p1-p2 · identified with so(4,4) (one claim)
p2 · whose compact part is so(4) ⊕ so(4) of dimension 12. (one claim)

Scope

carrier	g′ = [16,16] ⊕ 16 generated by the registered complementary plane
domain	Generated Lie-algebra identification; its associated symmetric-space identification is local.
group	SO(4,4)
hypotheses	The registered plane, brackets and source normalization are used.
quantifier	The algebra generated by this plane.
real form	so(4,4) with compact part so(4) ⊕ so(4)

What this does not show. This local Lie-algebra identification does not prove geodesic completeness, embedding closedness or a global quotient identification.

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, Generated-algebra identification — PDF p.187 (bytes of record)
review state: LANE_PROPOSED · 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

Cartan character +4 — a tuple that by itself does not distinguish so(4, 4) from g2(2) ⊕ g2(2)

Paper 4, §4.2, Local versus global identification — PDF p.73 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → CONTEXT · gemini read SUITE_TEXT_EXTRACT → CONTEXT

The equality sign in “= SO(4, 4)/(SO(4) × SO(4))” is therefore to be read as a local isometry, not as a global identification of manifolds.

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)
`28`	PDF p.181 (bytes of record)	suite text p.181 only (no kernel line found)
`4`	PDF p.181 (bytes of record)	suite text p.181 only (no kernel line found)
`12`	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)	LIB2-009 The complementary tangent plane closes as a Lie-triple system	—
`cited_by_section`	E-C03.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0032
`cited_by_section`	E-C03.2.computations (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0041
`cited_by_section`	E-C03.2.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0039
`cited_by_section`	E-C03.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0037
`cited_by_section`	E-C03.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0045

Why this record is not 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	no (0)
a SUPPORTS use on the predicate is DISPUTED	no
machine certificate current	yes

Not PUBLISHED because no use on it has been read as SUPPORTS by two non-drafting lanes on different objects. The transition is written only by the R67 producer and recomputed by a gate on every build; no person promotes a record by hand.

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-F5` A1632	CERTIFICATE	CLOSED 2026-09-10	The invariant tuple printed as the identification (dim 28, compact 12, trivial centre, rank 4, character +4) is also satisfied by g₂₍₂₎⊕g₂₍₂₎; a bracket-level certificate is owed. How it was closed: Closed on the mathematics by house kernel s1167 (Kernels/current/s1167_so44_embedded_missing16_certificate.py, run on the REGISTERED missing-16 plane from _S77_cache.npz): the generated algebra is absolutely simple (dim End = 1; g2(2)+g2(2) and complex type give 2, controls C1/C2), dim 28, Killing (16,12), split rank 4, 24 restricted roots of one length, multiplicity 1 ⇒ so(4,4). Paper row still open: Appendix F prints the tuple, not this certificate. Note: the older A_SUB_010 certificate tests the textbook so(4,4), not the embedded plane.	appendix_f_gauge_boundary.tex:517–518; tuple count for g₂₍₂₎⊕g₂₍₂₎. paper: REV32.9_CHANGELOG S327·A1632 item 4 (landed in Rev32.9)	closed
`A1632-F4` A1632	PROPAGATION	CONFIRMED	Appendix F states globally that the missing-16 is the totally geodesic submanifold; the p.69 correction (this record's use 2) limits it to a local isometry. The record carries the 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

The real-form child of C2-033 is kept separate from the Lie-triple predicates. The quote retains the extraction's displaced isomorphism signs; no new Killing-inertia or global-topology certificate is invented.

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 88ab4c09fac97ff248ef3522e75e772160c7c4dd5b39112ff6b64088e7f00dd7

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-010 | 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