Expositions · Registrar · Pasture

C04.1 — Golden-field selectors and the admissible-gap proof

Library article. Exposition built on the Registrar. The article kind (FOUNDATION / CONDITIONAL / HISTORICAL / OPEN) says what the article does; it is not a scientific tier and it never upgrades a claim's printed label. Every number below is produced by the code on this page, not recalled.

Prior art: 2 standard · 5 programme · 1 unresolved — on the Prior art page. Nothing on these pages is claimed as new.

Sections

One page per section (R71). A section is a typed object (R69): its record uses carry the Registrar's own review vocabulary and every one is UNREVIEWED until a lane reads it; its attestation is inherited from this article unless it has earned its own.

Section	Kind	Words	Record uses	Anchors
Source basis/status · `E-C04.1.source-basis-status`	PROSE	217	—	—
Prerequisites · `E-C04.1.prerequisites`	PROSE	30	—	—
Claims used · `E-C04.1.claims-used`	CLAIMS_USED	127	6, all UNREVIEWED	—
Definitions/conventions · `E-C04.1.definitions-conventions`	PROSE	95	—	—
Derivation · `E-C04.1.derivation`	DERIVATION	630	3, all UNREVIEWED	V1–V3: The field-free route, V1, V4: Arithmetic reduction to a discre, V4: The admissible-gap proof is exhausti, V5: A rejected monotonicity argument rem, V6–V7: A spectral orbit is not an ordere
Computations · `E-C04.1.computations`	COMPUTATION	692	—	Declarative object and assertion, Reproduction settings and input contract, Complete executable code, Actual stdout
Interpretation · `E-C04.1.interpretation`	PROSE	91	—	—
What this does not show · `E-C04.1.what-this-does-not-show`	PROSE	54	—	—
Prior art · `E-C04.1.prior-art`	PRIOR_ART	213	6, all UNREVIEWED	—
Sources/receipt · `E-C04.1.sources-receipt`	RECEIPT	256	6, all UNREVIEWED	—

Registrar records cited

Registrar records are IN REVIEW and noindex; their labels are literal as printed in the suite and carry no house tier.

Premises inherited through the records this article cites

Derived, not written: every record cited above was followed to its rests_on_premise edges. This article does not defend these premises and does not adopt them; it inherits them by citing records that rest on them.

Receipt

Registrar master sha256	01d1a5873ede42f5b2c5f4fdcee3a4a74c09a14b99a0deea86a60ebd9c821033
script C04.1_CHECKS.py	dc9afffb4e7a795ddbe98e73f1c4148c75ecc8acf699d096fd05368c0d541492
stdout C04.1_STDOUT.txt	384169f65391ee040078fd3a99417adb58fd869c9cfde531dd4603d3984997db
build	S371a · 2026-09-26 22:53Z

Full digests, never prefixes. Run the script yourself: python3 C04.1_CHECKS.py

What verification these articles have had, and what they have not. Every article here is HOUSE-VERIFIED: re-executed by the house, with complete code, its actual output, input hashes, a declared-sha check, and a §8 prior-art pass labelling each substantive result STANDARD (cited) / PROGRAMME / UNRESOLVED. Several were independently re-derived by a second house code path. They have been read adversarially ONCE, by one lane that did not write them. These articles were drafted by the ChatGPT lane and verified by the house; the Grok lane read all eleven against the contract in dispatch D1263 (intake A1592, S313) and found a stale Registrar basis on 9 of the 11 — the finding that caused textbook_basis_gate.py to be written, which is why this table carries a basis column at all. ★ That is ONE cold read by ONE lane. It is NOT peer review, it is NOT sustained cross-lane review, and no further lane has read the articles since. The Registrar claims they cite are IN REVIEW: 0 of 357 are house-adjudicated. No word on this surface should be read as ‘reviewed’ in any stronger sense than this paragraph states. (PI ruling S312, ACTION A: the house accepts its own verification as the standard here and states it plainly, rather than owing a verifier round indefinitely. Corrected S316 under H58: the previous wording said no second lane had read them, which denied the D1263 read and the gate it produced.)

What this article rests on

Ruling R38: only citations typed use_as_support import a cited record's premise closure. Citing a record in order to criticise or compare it imports nothing.

citations by role	cite 6 · compare 6 · use_as_support 9
premise closure	PRM-013, PRM-023, PRM-024
enumeration state	PARTIAL · UNREVIEWED
held for review	2 citation(s) carry a negation the house has not yet read; they do NOT import until a human does.

An empty closure means UNKNOWN, not INDEPENDENT. It means the records this article supports itself on declare no premises — not that the article rests on none. No record in this corpus has had its dependency enumeration reviewed.