Claims & Evidence Registrar › H07
Label sentence at the locator (PDF p.307 (bytes of record)):
A sum of two simple bivectors has rank 4, so no linear projector can impose simplicity: nonlinearity is unavoidable.
Some sums of simple bivectors are nonsimple (e1∧e2 + e3∧e4 has rank 4), so no linear projector retracts onto the full simple-bivector variety; keeping the full condition needs a nonlinear construction.
| carrier | The bivector simplicity condition in the finite Cartan regulator |
|---|---|
| domain | The linear-projector route to simplicity, not the nonlinear measure that follows. |
| hypotheses | Use the simple-bivector condition and sum considered in Theorem 8.6. |
| quantifier | The registered construction and its stated premises. |
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.
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, Theorem 8.6: linear-projector obstruction — PDF p.324 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS · grok read THE_RECORD → SUPPORTS · gemini read SUITE_TEXT_EXTRACT → SUPPORTS
Some sums of simple bivectors are nonsimple (e1 ∧ e2 + e3 ∧ e4 has rank 4, while e1 ∧ e2 + e1 ∧ e3 is simple), so no linear projector retracts onto the full simple-bivector variety: keeping the full condition needs a nonlinear construction
| kind | reference | line / key | availability | note |
|---|---|---|---|---|
| computational | s922-T6; A1444, Appendix T §8, Theorem 8.6, p.307 | — | unknown | The source reports the rank example and linear-projector obstruction; the original bivectors and computation are not supplied. |
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 |
|---|---|---|
4 | PDF p.307 (bytes of record) | suite text p.307 only (no kernel line found) |
| type | target | licensed by |
|---|---|---|
related_to (never evidential) | LIB2-190 No positive path in the declared heat-kernel family reaches pure MM/EH | — |
| states a predicate | yes |
|---|---|
| uses on the record · unblocked | 1 · 1 |
| uses any lane has read | 1 of 1 |
| 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 |
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? |
|---|---|---|---|---|---|
A1677-F02A1677 | PREDICATE | CLOSED 2026-09-17 | 'A sum of two simple bivectors has rank 4' is false as a universal (e₁∧e₂ + e₁∧e₃ is simple). Only some sums are nonsimple (e₁∧e₂ + e₃∧e₄ has rank 4); the no-linear-projector conclusion follows from that weaker fact. How it was closed: R133 D-2 (PI, S342): Rev32.9 fix S338.7 landed; LIB2-191 re-typed by R130 row 19; its use REVIEWED in round 22. | appendix_t_cartan_observation.tex:516 (Rev32.7) paper: REV32.9_CHANGELOG S338.7 (landed in Rev32.9) | closed |
| 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 |
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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.
| 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 | A1444 s922 |
| candidate ids (frozen list S304) | C2-094 |
Simplicity-obstruction subject associated with C2-094. The source's rank example is not generalized here into a statement that every sum of two simple bivectors has that rank.
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 56a1f9dda5420b910e6e700cac9f79b61cb5065d684a4e857969c5903169dae8
Reviewer verdict line (one per entry, as text): LIB2-191 | 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