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: N/A — this record declares no suite labels to check · 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.

LIB2-311 · Find a non-residue physical realization of the finite index normalization

class OPENmath status (as printed) —attachment (as printed) —scorecard tier word (as printed) none printedhouse tier not yet assignedreview state IN_REVIEWentry version 7

Statement

Can the finite 7/3 index normalization acquire a physical realization through a non-residue, index-theoretic exceptional-field-theory construction?

Scope

carrier	The finite trace/index normalization and a possible exceptional-field-theory realization
domain	The non-residue physical export of the finite trace/index result, outside the excluded metric-weighted residue route.

What this does not show. The finite index theorem is not itself a low-energy mass relation, and the signed-residue route remains excluded.

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, Amplitude-bridge boundary: surviving question — PDF p.222 (bytes of record)
review state: REVIEWED · role CONTEXT · warrant: gemini read SUITE_TEXT_EXTRACT → CONTEXT · grok read THE_RECORD → CONTEXT

What stays open is only whether a non-residue, index-theoretic exceptional-field-theory realization exists; the 7 survives as the finite-carrier index (Appendix K), not as a signed amplitude.

Appendix I, §8, Lemma 8.3: precise excluded 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
registry	Appendix I §8, amplitude-bridge boundary and Lemma 8.3, p.212	—	shipped	The source expressly restricts the remaining question to a non-residue realization. No physical amplitude, index export or mass-matching calculation is performed.

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
`7/3`	PDF p.212 (bytes of record)	suite text p.212: Lemma 8.3 distinguishes the excluded residue route from other possible physical realizations

Open problem

charter ref	Rev32.7 Appendix I §8, amplitude-bridge boundary and Lemma 8.3, p.212
failure or reopen condition	A route that still uses the excluded metric-weighted residue does not reopen the question; the no-go does not exclude every different physical construction.
obstruction	The metric-weighted residue route on the split imaginary-octonion channels is closed negative; an unweighted finite index is a different object.
question	Does the non-residue index-theoretic physical realization left open by the source exist?
success condition	Construct the physical non-residue, index-theoretic realization rather than re-identify the finite multiplicity with the excluded signed residue.

Typed links

type	target	licensed by
`related_to` (never evidential)	LIB2-053 Frobenius compatibility fixes the finite trace ratio	—
`related_to` (never evidential)	LIB2-107 The signed metric-weighted residue cannot supply the positive seven count	—
`related_to` (never evidential)	LIB2-130 The bottom bridge retains its tau anchor and cross-scheme offset	—
`related_to` (never evidential)	LIB2-131 The charm bridge remains constituent-anchored and cross-scheme	—

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.

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`	N/A	class OPEN not governed by the source_labels rule
`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

The broad pole/LSZ language in C2-044/C2-054 is narrowed to the surviving non-residue question explicitly printed at p.212. G-057 is the finite index; G-111 is the signed-residue obstruction. No new physical-export map 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 5a34f41f495ac921569b110b26094224b18deab2708b156b029877b55151893b

Review this entry

Reviewer verdict line (one per entry, as text): LIB2-311 | 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