Expositions · Registrar · Pasture

C02.1 — The cubic norm, characteristic identity and the real multiplication operator

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: 6 standard · 3 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-C02.1.source-basis-status`	PROSE	269	—	—
Prerequisites · `E-C02.1.prerequisites`	PROSE	39	—	—
Claims used · `E-C02.1.claims-used`	CLAIMS_USED	107	—	—
Definitions/conventions · `E-C02.1.definitions-conventions`	PROSE	138	—	—
Derivation · `E-C02.1.derivation`	DERIVATION	583	—	From the product to the cubic identity, The trace form is not a positive Euclide, An element cubic is not an operator cubi, A split-Hermitian element with nonreal r
Computations · `E-C02.1.computations`	COMPUTATION	813	—	—
Interpretation · `E-C02.1.interpretation`	PROSE	111	—	—
What this does not show · `E-C02.1.what-this-does-not-show`	PROSE	59	—	—
Prior art · `E-C02.1.prior-art`	PRIOR_ART	563	—	—
Sources/receipt · `E-C02.1.sources-receipt`	RECEIPT	155	—	—

Premises inherited through the records this article cites

★ None. Not because this article rests on nothing — because none of the records it cites declares a premise. An empty inheritance means UNDECLARED, not INDEPENDENT. Across the surface this is the usual case, and it is printed rather than left blank so that a reader can tell an empty result from an absent check.

Receipt

Registrar master sha256	01d1a5873ede42f5b2c5f4fdcee3a4a74c09a14b99a0deea86a60ebd9c821033
script C02.1_CHECKS.py	69fb7790811e19318e0850e0d2cb9704f54f4e3c18948b8704bef70cf72efed1
stdout C02.1_STDOUT.txt	7e376baeb9b9b709f742d4d432b985d5889d2c27294cade75170e292c4529ef5
build	S371a · 2026-09-26 22:53Z

Full digests, never prefixes. Run the script yourself: python3 C02.1_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.)