PRM-005 · AX-MOS

Premise

Register corrected — R81 (D4, S327j). The PI ruled this correction to the register row (Trackers/RULING_R81_S327_PREMISE_REGISTER.md). Statement now (PRM-005/r2, appendix_t_cartan_observation.tex:715-722, quality EXTRACTION_VERBATIM): Given the active c3 /c2 branch, (1, 0, −1) is the unique assignment by enumeration … AX-MOS carries no new bit inside the loaded branch — honest compression, not unconditional derivation.. 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:

Given the active $c_3/c_2$ branch, $(1,0,-1)$ is the unique assignment by enumeration; the shell reversal gives $SJ_+S=J_-$ and $SD_\phg S=-D_\phg$ exactly, so the arrow \emph{is} the standing OS/time $\mathbb Z_2$; the relative entropies are exactly equal both ways ($\log\phg/\phg$, via $1-\phg^{-2}=\phg^{-1}$) and the spectra coincide, so no inversion-symmetric scalar orients.

Appendix T · AX-MOS, compressed · PDF p.309 · appendix_t_cartan_observation.tex:716.

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

What kind of premise this is

The register kind is POSTULATE. Appendix T presents compressed AX-MOS as the active branch plus the standing time-orientation bit. The score assignment is conditional on that branch; compression does not turn physical realization into a theorem. The log leg is discharged as a separately priced clause and absorbed into AX-MOS. Appendix X leaves the ordered experiment and minimal UCP/OS readout conditional on a microscopic derivation. Source status words: no new bit inside the loaded branch (appendix_t_cartan_observation.tex:721).

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

LIB2-173 — CONFIRM. Confirm only the registered ordered-pair/branch assignment used for the score. The text makes that assignment conditional on the active branch; it does not derive the physical experiment from microscopic dynamics. Step locator: appendix_t_cartan_observation.tex:716 (CONDITIONAL).

LIB2-174 — CONFIRM. The minimal modular-OS observation is expressly conditional in the premise ledger. This supports the loaded readout package in the record, while its uniqueness-under-conditions statement does not select the microscopic realization. Step locator: appendix_x_zero_parameter_input_ledger.tex:939 (CONDITIONAL).

LIB2-182 — DISPUTE. The supplied passage distinguishes existence of the record-quotient channel family from selecting O_MOS. No read passage establishes that the family-existence/endpoint-bound predicate requires the physical AX-MOS attachment. Hold this declared edge for PI review; this is not a proof of independence. Step locator: appendix_t_cartan_observation.tex:711 (MENTIONED).

NO RECORD — conditional relative-modular-log export, appendix_x_zero_parameter_input_ledger.tex:940; no separate carrier is identified beyond the registered score/readout records.

What breaks without it

LIB2-173: the assignment is expressly given the active branch (appendix_t_cartan_observation.tex:716); no source for an unconditionally selected branch is supplied. The time arrow remains the standing OS/time bit (lines 718–720).

LIB2-174: appendix_x_zero_parameter_input_ledger.tex:939 requires deriving the ordered golden/inverse experiment and its minimal readout from microscopic parent dynamics. NOT ASSESSED — the text does not specify a replacement uniqueness theorem after deleting individual AX-MOS conditions. The relative-log export is likewise explicitly a microscopic state/readout derivation target at line 940.

LIB2-182 is disputed as a dependency, not refuted as a channel theorem. No counterfactual failure is claimed for that family.

Registrar sync

Registrar state after R76, R78 and R82 (S327j, master 0e1418ad6501767d). Declared today: LIB2-173. Retired, each recorded in full in the record's version history: LIB2-174 (R82-b) — A uniqueness construction for O_MOS under its own seven premises plus a status sentence ("the microscopic theory has not selected it"); it does not assume that O_MOS is the physical observation. As R78-b LIB2-182; LIB2-182 (R78-b) — The record asserts that the record-quotient channel family exists for |lambda| <= sqrt2; that construction does not assume AX-MOS (App T:711 "that fold does not select O_MOS either"). 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: LIB2-173, LIB2-174, LIB2-182. Supplied transitive-only closure: LIB2-176, LIB2-183. It is not itself a new direct-edge declaration. Draft dispositions — CONFIRM: LIB2-173, LIB2-174; DISPUTE: LIB2-182. LIB2-176 and LIB2-183 are in the supplied transitive closure. Their record-process and score-solder predicates are not automatically made new direct edges. The channel pointer at appendix_t_cartan_observation.tex:709–711 mentions the readout but expressly does not select it; mention is insufficient for this physical-attachment dependency.

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_t_cartan_observation.tex:605; appendix_t_cartan_observation.tex:709–711; appendix_t_cartan_observation.tex:711; appendix_t_cartan_observation.tex:716; appendix_t_cartan_observation.tex:718; appendix_t_cartan_observation.tex:721; appendix_t_cartan_observation.tex:837; appendix_t_cartan_observation.tex:838; appendix_x_zero_parameter_input_ledger.tex:723; appendix_x_zero_parameter_input_ledger.tex:779; appendix_x_zero_parameter_input_ledger.tex:821; appendix_x_zero_parameter_input_ledger.tex:939; appendix_x_zero_parameter_input_ledger.tex:940; appendix_y_laboratory_notebook.tex:313. Registrar: LIB2-173, LIB2-174, LIB2-176, LIB2-182, LIB2-183. Premise: PRM-005. Suite-cited kernels: s927.