PRM-003 · AX-COT

Premise

Register corrected — R81 (D2, S327j). The PI ruled this correction to the register row (Trackers/RULING_R81_S327_PREMISE_REGISTER.md). Statement now (PRM-003/r2, appendix_t_cartan_observation.tex:436-438, quality EXTRACTION_VERBATIM): selector/order/depth ≡ transvection/polar/oriented-axial.. On-shell price discharged into AX-MOS (App T:837); off-shell independence stands (App T:602). 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:

selector/order/depth $\equiv$ transvection/polar/oriented-axial.

Appendix T · AX-COT — the Cartan–occupancy transgression · PDF p.306 · appendix_t_cartan_observation.tex:438.

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 names AX-COT an axiom and prices one independent cross-layer typing row with zero continuous moduli. Its sign twist matches two otherwise different occupancy/Cartan characters. The later on-shell discharge is explicitly through log-Hodge naturality absorbed into AX-MOS; it does not overturn off-shell independence. Paper 7 names an isometric universal property tying chamber, Cartan spin factor and occupancy as the off-shell discharge target. Source status words: one independent cross-layer typing row with zero continuous moduli (appendix_t_cartan_observation.tex:470).

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

NO RECORD — occupancy–Cartan character match, appendix_t_cartan_observation.tex:455–460. The sign twist is explicitly the axiom’s content. NO RECORD — ten-coefficient attachment, appendix_t_cartan_observation.tex:491–493. AX-COT is one of three named conditional loads, not the sole hypothesis. Neither argument has an identified carrying record in this material; no unbound graph ADD is submitted.

What breaks without it

Character match: the source says the match is obtained only through the sign twist (appendix_t_cartan_observation.tex:457–460). Ten-coefficient attachment: the stated triple conditional load and underived Stiefel/radial domain remain binding (lines 491–493).

Retirement clause: p7_precision_tests_falsification.tex:248–250 requires the stated isometric universal property to discharge AX-COT off shell. The on-shell discharge at appendix_t_cartan_observation.tex:835–837 is limited to that tier.

Registrar sync

Registrar state after R76, R78 and R82 (S327j, master 0e1418ad6501767d). Declared today: none (UNKNOWN, not INDEPENDENT). 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. The AX-MG countermodel sentence at the register’s first locator belongs to the preceding item, not to AX-COT’s definition.

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:257; appendix_t_cartan_observation.tex:438; appendix_t_cartan_observation.tex:455–460; appendix_t_cartan_observation.tex:457; appendix_t_cartan_observation.tex:457–460; appendix_t_cartan_observation.tex:470; appendix_t_cartan_observation.tex:481; appendix_t_cartan_observation.tex:491; appendix_t_cartan_observation.tex:491–493; appendix_t_cartan_observation.tex:602; appendix_t_cartan_observation.tex:835–837; appendix_t_cartan_observation.tex:837; appendix_x_zero_parameter_input_ledger.tex:723; appendix_x_zero_parameter_input_ledger.tex:758; appendix_y_laboratory_notebook.tex:305; appendix_y_laboratory_notebook.tex:306; appendix_y_laboratory_notebook.tex:310; appendix_y_laboratory_notebook.tex:679; p7_precision_tests_falsification.tex:248–250; p7_precision_tests_falsification.tex:250. Registrar: no carrying record identified in the supplied material. Premise: PRM-003. Suite-cited kernels: s921, s923, s927.