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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-e120bafe8a694346586127c2 · master 6d82da907c52e8e6 · S329.

LIB2-078 · The frame-free real 56 has no invariant rank-one Higgs projector

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.182 (bytes of record)):

There is no G0 -invariant rank-one projector on the 56: the only invariant idempotents have rank 0 or 56.

Statement

The bare real 56 admits no E7(7)-invariant rank-one projector; its invariant idempotents have ranks only 0 or 56.

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 bare real 56 admits no E7(7)-invariant rank-one projector (one claim)
p2 · its invariant idempotents have ranks only 0 or 56. (one claim)

Scope

carrier	Real Freudenthal carrier F = R ⊕ R ⊕ J3(Os) ⊕ J3(Os)
domain	The unmarked real carrier, without a boundary selecting a line.
group	G0 = Aut(F,ω,Q)0
hypotheses	The full frame-free E7(7) action is retained.; The source computes its real commutant as R·I.
quantifier	Every invariant idempotent for the registered full action.
real form	E7(7)

What this does not show. The obstruction does not exclude a Higgs orientation supplied by a loaded boundary or selected by additional symmetry-breaking structure.

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, §7, Theorem 7.1: invariant projectors — PDF p.188 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

There is no G0 -invariant rank-one projector on the 56: the only invariant idempotents have rank 0 or 56.

Appendix F, §7, Commutant proof — PDF p.189 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS

An invariant idempotent lies in the commutant, so its only values are 0 and I, i.e. ranks {0, 56}; no rank-one invariant line exists.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
analytic	Appendix F §7, Theorem 7.1, commutant argument, p.182	—	shipped	The idempotent argument is printed, conditional on the registered real commutant.
computational	s796, cited in Appendix F §7, p.182	—	unknown	The generator and commutant computation is reported, not rerun or supplied as arrays in this drafting round.

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
`56`	PDF p.182 (bytes of record)	suite text p.182 only (no kernel line found)
`7`	PDF p.182 (bytes of record)	suite text p.182 only (no kernel line found)
`0`	PDF p.182 (bytes of record)	suite text p.182 only (no kernel line found)

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-006 The registered symplectic exceptional substrate	—

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 (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	B-HIG-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	s796
candidate ids (frozen list S304)	C2-041

Drafting-lane note

C2-041 states the frame-free obstruction, not absence of Higgs fields in the loaded construction. Theorem 7.1 is a local heading, not a scorecard tier word.

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 02a37a6ebb0556d14d97e0e4b160dfcdc735e1115e658118c5c49ddcf270823a

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-078 | 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