PRM-004 · AX-MG

Premise

Register corrected — R81 (D3, S327j). The PI ruled this correction to the register row (Trackers/RULING_R81_S327_PREMISE_REGISTER.md). Statement now (PRM-004/r2, appendix_s_selector_ledger.tex:548, quality EXTRACTION_VERBATIM): One unit affine transfer ≡ one complete normalized Fibonacci cap-cup/Jones interface; boundary amplitudes multiply along the unique rooted geodesic.. Two clauses, coefficient-one and degree-one, each proved independent by exact countermodel (p0:276-280). 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: POSTULATE. Located suite statement:

One unit affine transfer $\equiv$ one complete normalized Fibonacci cap-cup/Jones interface; boundary amplitudes multiply along the unique rooted geodesic.

Appendix S · AX-MG — normalized Markov-geodesic boundary coherence · PDF p.294 · appendix_s_selector_ledger.tex:548.

The registered excerpt and/or kind needs the scope clarification below; the registry itself is not edited.

What kind of premise this is

POSTULATE is the register kind. The suite explicitly calls AX-MG an axiom, with two independent clauses: coefficient-one and degree-one. The normalized-interface and geodesic multiplication conventions are not derived by the later scalar-shadow extraction. Paper 7 states what would discharge their price: derive a clause from the banked boundary rows without inserting an edge-functor property. The effective operator remains conditional and awaits a positivity/semigroup test. Source status words: AX-MG (two independent clauses, priced, dated) (appendix_s_selector_ledger.tex:595).

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.

House additions — R78-c (S327i)

The house read the rest of the suite for this premise. The material sent to the drafting lane showed at most twelve passages per premise, so A1634 FINDINGS §7 lists 2 hit lines for PRM-004 that the lane never saw. Under R78-c the house read all 2 in the full suite TeX: 2 passages are added below. Every quote was matched against the TeX at its locator. With the lane's table above, every hit of this premise's search keys is now accounted for.

Arguments that rest on it

NO RECORD — boundary scalar shadow, appendix_s_selector_ledger.tex:595–598: coefficient-one is load-bearing by declaration. NO RECORD — effective boundary operator law, appendix_s_selector_ledger.tex:613–618: the text expressly conditions the law on AX-MG. No carrying record is identified in this material, so no unbound ADD is submitted. NO RECORD — pointed affine export and boundary-state attachment, appendix_x_zero_parameter_input_ledger.tex:690,716–718. These are explicitly priced/conditional uses, without an identified record in the material.

What breaks without it

Boundary scalar shadow: its coefficient-one source is the declaration itself (appendix_s_selector_ledger.tex:597–598). NOT ASSESSED — a replacement coefficient or law without that declaration is not supplied.

Effective law: the printed conditional status cannot be removed; positivity-preservation of the semigroup has not been bank-tested (lines 613–617). The falsifier is the clause-derivation test at p7_precision_tests_falsification.tex:243–247.

Boundary-state/export price: the printed falsifier is a derived edge normalization collapsing the coefficient without the axiom (appendix_x_zero_parameter_input_ledger.tex:716–718). NOT ASSESSED — no replacement export after removing AX-MG is supplied.

Registrar sync

Registrar state after R76, R78 and R82 (S327j, master 0e1418ad6501767d). Declared today: none (UNKNOWN, not INDEPENDENT). The R78-c reading found no further record whose result assumes this premise. 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: none (UNKNOWN, not INDEPENDENT). Draft dispositions — no ADD, CONFIRM or DISPUTE row; there is no declared edge to adjudicate. Unbound NO RECORD arguments are not graph ADDs. No candidate records are supplied. Mentions using AX-MG as an analogy for another coefficient price do not establish a dependency on AX-MG.

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_e_vacuum_selector.tex:423; appendix_s_selector_ledger.tex:548; appendix_s_selector_ledger.tex:595; appendix_s_selector_ledger.tex:595–598; appendix_s_selector_ledger.tex:597; appendix_s_selector_ledger.tex:597–598; appendix_s_selector_ledger.tex:613–618; appendix_s_selector_ledger.tex:616; appendix_t_cartan_observation.tex:471; appendix_x_zero_parameter_input_ledger.tex:675; appendix_x_zero_parameter_input_ledger.tex:689; appendix_x_zero_parameter_input_ledger.tex:690; appendix_x_zero_parameter_input_ledger.tex:716; appendix_x_zero_parameter_input_ledger.tex:716–718; appendix_x_zero_parameter_input_ledger.tex:757; appendix_y_laboratory_notebook.tex:292; appendix_y_laboratory_notebook.tex:293; p7_precision_tests_falsification.tex:243; p7_precision_tests_falsification.tex:243–247. Registrar: no carrying record identified in the supplied material. Premise: PRM-004. Suite-cited kernels: s900.