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 The state is recomputed from the uses on every build and is withdrawn if they stop justifying it.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-e53477a7dae3bcea4f3e3083 · master 94096cf0b0ea8052 · S330.

LIB2-107 · The signed metric-weighted residue cannot supply the positive seven count

class CLAIMmath status (as printed) NOT_PRINTEDattachment (as printed) NOT_PRINTEDscorecard tier word (as printed) none printedhouse tier not yet assignedreview state PUBLISHEDentry version 8

Label sentence at the locator (PDF p.212 (bytes of record)):

The signed residue over any sub- collection of g-orthonormal channels equals (#positive − #negative) and therefore lies in the closed range [−4, +3]

Statement

For a subcollection of registered g-orthonormal Im Os channels, the signed residue equals the positive-minus-negative channel count and lies in [−4,+3], excluding 7 as that metric-weighted residue.

Parts of the statement (3)

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 signed residue equals the positive-minus-negative channel count (one claim)
p2 · lies in [−4,+3] (one claim)
p3 · excluding 7 as that metric-weighted residue. (one claim)

Scope

carrier	Subcollections of g-orthonormal imaginary split-octonion channels
domain	The specific metric-weighted residue route; unweighted index and other physical realizations are different objects.
hypotheses	The imaginary split-octonion metric has signature (3,4).; Use the signed channel-count residue of Lemma 8.3, not arbitrary independent channel weights.
quantifier	Any subcollection of the registered g-orthonormal channels.
real form	Split octonions Os

What this does not show. This bound does not refute the finite trace/index theorem or exclude every non-residue physical realization of the ratio.

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 I, §8, Lemma 8.3: signed-residue range — PDF p.222 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

The signed residue over any sub- collection of g-orthonormal channels equals (#positive − #negative) and therefore lies in the closed range [−4, +3]

Appendix I, §8, Lemma 8.3: multiplicity versus residue — PDF p.222 (bytes of record)
review state: REVIEWED · role SUPPORTS · warrant: gemini read SUITE_TEXT_EXTRACT → SUPPORTS · grok read THE_RECORD → SUPPORTS

the integer 7 is unreachable as a signed (unitary) residue and is realized only as the unweighted multiplicity.

Appendix I, §8, Lemma 8.3: scope of the closed route — PDF p.222 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

This closes the specific residue route on Im Os ; it does not assert that no other construction could realize 7/3 physically.

Evidence (availability is not outcome)

kind	reference	line / key	availability	note
computational	s902; Appendix I §8, Lemma 8.3 sharpening, p.212	—	unknown	The source reports the signed-channel computation and bound; the original implementation and output are not attached.

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
`−4`	PDF p.212 (bytes of record)	closed form: the signed-residue interval [−4,+3] and excluded integer 7 in Lemma 8.3
`+3`	PDF p.212 (bytes of record)	closed form: the signed-residue interval [−4,+3] and excluded integer 7 in Lemma 8.3
`7`	PDF p.212 (bytes of record)	closed form: the signed-residue interval [−4,+3] and excluded integer 7 in Lemma 8.3

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-053 Frobenius compatibility fixes the finite trace ratio	—
`cited_by_section`	E-C08.2.claims-used (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0216
`cited_by_section`	E-C08.2.definitions-conventions (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0218
`cited_by_section`	E-C08.2.prior-art (Exposition section page; use UNREVIEWED)	TEXTBOOK_CITATIONS.jsonl (S312) — CIT-0221, CIT-0223

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?
`A1652-F04` A1652	PROPAGATION	CONFIRMED	The restricted count is exact — all 128 subsets of a (3 positive, 4 negative) normalized basis give signed counts in [-4,+3], full count -1, 7 unattainable (s1171 T5). But Lemma 8.3 as printed says ANY S-matrix residue weighted by g returns the signed trace, and a coupling-weighted contraction sum eta_i \|a_i\|^2 reaches 7 at amplitude sqrt(7) on a positive channel (T5f). The universal sentence overstates the lemma. The Registrar predicate is already restricted and is faithful.	Appendix I §8 Lemma 8.3 and its preceding box, p.212; house kernel s1171 T5a-T5f. paper: REV33.2_PENDING S330·A1652	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	C-73-01, D-73-01 — 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	s902
candidate ids (frozen list S304)	C2-044 C2-054

Drafting-lane note

Residue-route obstruction under C2-044/C2-054, separate from the positive finite trace theorem G-057. The claim is restricted to the source’s signed orthonormal-channel class, not all weighted residues.

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 8a6f2f9f43e7aec6849f386ba6274e0802fb0411c6903473689330c122319b14

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-107 | 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