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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-692a5fadf454d229ff75063d · master 742e6c24f3aa86af · S342.

LIB2-025 · The loaded-plane defect algebra determines the selector eigenspaces

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

Label sentence at the locator (PDF p.170 (bytes of record)):

PB forces the exact 26 ⊕ 10 eigenspace split

Statement

The loaded plane PB forces the 26 ⊕ 10 interior split, and its symplectic transport defect, with the commuting joint pair (QP,QΔ) — words of degree at most 2 in QP and QΔ — produces all five QT eigenspaces once their two-dimensional common kernel, on which every polynomial in the pair is scalar, is split by the top Hessian projector of the banked golden form η.

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 loaded plane PB forces the 26 ⊕ 10 interior split (one claim)
p2 · its symplectic transport defect, with the commuting joint pair (QP,QΔ) — words of degree at most 2 in QP and QΔ — produces all five QT eigenspaces once their two-dimensional common kernel, on which every polynomial in the pair is scalar, is split by the top Hessian projector of the banked golden form η. (one claim)

Scope

carrier	Loaded-plane projector PB and the tangent-sector selector eigenspaces
domain	Eigenspaces as subspaces; weights and nonlinear shape are separate.
hypotheses	PB is the registered loaded plane.; The transport defect is ∆T = [Tϕ,PB] = [J0,PB].; The registered joint pair is (QP,Q∆).
quantifier	The declared class only.
real form	Split-real 56-frame

What this does not show. This subspace construction does not select the loaded plane, the eigenvalue weights or a unique nonlinear action.

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 E, §7, Forced interior split — PDF p.176 (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

PB forces the exact 26 ⊕ 10 eigenspace split

Appendix E, §7, Symplectic transport defect — PDF p.176 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → CONTEXT · the lanes disagreed; resolved by PI ruling R135 as CONTEXT — a ruling whose gloss the house owes; a use resolved by ruling never anchors PUBLISHED

its symplectic transport defect ∆T = [Tϕ , PB ] = [J0 , PB ] forces the complement

Appendix E, §7, Joint-projector result — PDF p.176 (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

produces all five QT eigenspaces as subspaces once that kernel is split by the top projector of the Hessian of the banked golden form η, which s1051 adds at gate G8

Appendix E, §7, Weights and action-shape boundary — PDF p.176 (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

The eigenvalue weights on those subspaces are the subject of Appendix S’s production arc (A1515–A1516), where they are derived in-class and their action shape is priced.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s1051; A1514, Appendix E §7, p.170	—	unknown	The suite reports the projector construction; its arrays and output are not supplied here.

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
`26`	PDF p.170 (bytes of record)	suite text p.170: eigenspace dimensions and word-degree bound; no kernel line found
`10`	PDF p.170 (bytes of record)	suite text p.170: eigenspace dimensions and word-degree bound; no kernel line found
`2`	PDF p.170 (bytes of record)	suite text p.170: eigenspace dimensions and word-degree bound; no kernel line found

Typed links

type	target	licensed by
`cited_by_section`	E-C04.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0071
`cited_by_section`	E-C04.2.derivation (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0118
`cited_by_section`	E-C04.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0091
`cited_by_section`	E-C04.2.sources-receipt (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0141

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

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-F1` A1632	PREDICATE	CLOSED 2026-09-17	The commuting pair (Q_P,Q_Δ) has four joint eigenvalues, so it cannot by itself produce all five Q_T eigenspaces; the suite credits the pair alone and states a word-degree bound. How it was closed: R135 D-2 (PI, S342): the R132 re-typed statement no longer credits the commuting pair alone — the five QT eigenspaces are produced only once the top Hessian projector of the golden form η splits the two-dimensional common kernel, and the degree bound is scoped to words in (QP,QΔ). Re-read REVIEWED in round 23.	appendix_e_vacuum_selector.tex:384–386; kernel s1051 G4 builds 26/10/32 from the pair and G8 splits the 2-dim common kernel with the top projector of the detector form η. paper: REV32.9_CHANGELOG S327·A1632 item 1 (landed in Rev32.9)	closed
`A1711-F02` A1711	PREDICATE	CLOSED 2026-09-17	The R130 statement's trailing degree bound read as a bound on the whole construction; the paper scopes it to words in (QP,QΔ), which are scalar on the common kernel that the η projector splits. Continues A1632-F1. How it was closed: R135 D-2 (PI, S342): R132 D-2 re-type applied and the LIB2-025 uses re-read in round 23; A1632-F1 closes with it.	SUITE_TEXT_S341 p.174	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-SPLIT-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	A1514 s1051
candidate ids (frozen list S304)	C2-106

Drafting-lane note

The source's zero-incremental-price statement is conditional on the already loaded plane. The separate weight representation and action-shape records follow; no global physical selector is inferred.

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 6e402c44423cef27ba73ddccb1de78be49499cb2c80f8b086a894605311e7471

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-025 | 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