PRM-007 · Action shape (the adopted principle Φ_diag)

Premise

Register corrected — R81 (D6, S327j). The PI ruled this correction to the register row (Trackers/RULING_R81_S327_PREMISE_REGISTER.md). Statement now (PRM-007/r2, appendix_s_selector_ledger.tex:776-784, quality EXTRACTION_VERBATIM): The clause Φdiag : {v = 0, w = 0, u = t, 27z = t} — four coefficient relations — isolates exactly the Fchar orbit and is minimal in codimension (dropping any one relation restores a projective one-parameter family). It is not intrinsic: it identifies the units of three inequivalent primitive generator lines (inequivalent by Theorem 9.3’s Casimir separation), and independent generator rescaling moves the selected action. It is adopted here as a declared structural principle — the named form of the previously implicit choice that nature’s action is Fchar -shaped.. Name now Action shape (the adopted principle Φ_diag) (was Action shape). The register row the drafting lane quotes below is the row as it was supplied to the lane, before R81; it is kept in the register's history (R29: nothing is overwritten).

Register kind: ADOPTED_PREMISE. Located suite statement:

The clause $\Phi_{\rm diag}:\ \{v=0,\ w=0,\ u=t,\ 27z=t\}$ --- four coefficient relations --- isolates exactly the $F_{\rm char}$ orbit

Appendix S · Priced axiom Phi-diag · PDF p.297 · appendix_s_selector_ledger.tex:778.

What kind of premise this is

The register kind is ADOPTED_PREMISE. The suite calls Phi-diag a declared structural principle, not an intrinsic selection. It equates units on inequivalent primitive generator lines; independent rescaling moves the selected action. This adopts the nonlinear shape after the variational representation is established. The class restriction is part of the premise: enlarging the word class needs a further coefficient relation. Source status words: declared structural principle (appendix_s_selector_ledger.tex:783).

Where the suite invokes it

Located invocations in the read excerpts, not an exhaustive full-source-tree census. Pages refer to saved Rev32.7 page-delimited text, not PDF-image authentication.

Arguments that rest on it

LIB2-026 — DISPUTE. The record asserts a Hessian identity for the displayed Fchar, whereas this premise chooses that action as nature’s action. The source separates variational representation from unselected nonlinear shape. Computing the given functional is not conditioned on adopting its physical selection; retain an explanatory association, not this proof-dependency edge. Step locator: appendix_s_selector_ledger.tex:662 (MENTIONED).

LIB2-028 — ADD. The record is exactly the in-class isolation result under the four adopted coefficient relations. It is the action-selection argument, unlike the preceding representation identity. Step locator: appendix_s_selector_ledger.tex:778 (CONDITIONAL).

NO RECORD — the stated one-word enlargement at appendix_s_selector_ledger.tex:786–789 is a separate class-scope argument. No additional carrying record was supplied for a graph ADD.

What breaks without it

LIB2-028: the printed deletion test says dropping any one diagonal relation restores a projective one-parameter family (appendix_s_selector_ledger.tex:779–780). Under one-word enlargement the printed moduli increase and a further relation is required (lines 786–789). These are class-specific losses of selection, not a universal impossibility claim.

LIB2-026 is disputed only as an edge. Its Hessian identity is not recomputed or demoted here.

Registrar sync

Registrar state after R76, R78 and R82 (S327j, master 0e1418ad6501767d). Declared today: none (UNKNOWN, not INDEPENDENT). Retired, each recorded in full in the record's version history: LIB2-026 (R78-b) — A Hessian identity of the displayed F_char is unconditional; the action-shape premise concerns adopting F_char as the action of nature (App S:662-667 separates the two). Proposed ADDs not declared: LIB2-028 — declined under R78-a — the record states the adoption status of Φ_diag; it is about the premise, and its result does not assume it. The lane's lines below describe the master as it was supplied to the lane (d0aa26db154ff43f), before these changes.

Declared today in the supplied material, Registrar master d0aa26db154ff43f: LIB2-026. Draft dispositions — ADD: LIB2-028; DISPUTE: LIB2-026. LIB2-026 contains a representation theorem and cites a fence saying microscopic selection is absent. It should not be made dependent merely because its functional is later adopted. LIB2-028 carries the conditional selecting-relations argument.

Tier and what this does not show

A premise is not a result, and invocation count is not importance. An ADD remains a proposal until house verification under R76; a DISPUTE goes to the PI. No record or premise is upgraded, downgraded, or edited. Unlocated dependencies remain unknown.

Sources

TeX: appendix_s_selector_ledger.tex:662; appendix_s_selector_ledger.tex:778; appendix_s_selector_ledger.tex:779; appendix_s_selector_ledger.tex:779–780; appendix_s_selector_ledger.tex:783; appendix_s_selector_ledger.tex:786–789; appendix_s_selector_ledger.tex:787; p0_framework_foundations.tex:238. Registrar: LIB2-026, LIB2-028. Premise: PRM-007. Suite-cited kernels: s1055.