PRM-025 · AX1 — golden unit

Premise

House-drafted note (R81-D15, S327j). R81 registered this premise, splitting it out of PRM-018. No drafting lane wrote this note: the house drafted it from its own reading of the suite TeX — the fourteen AX1 passages it read at R78-c for PRM-018, and every further line of the suite that names AX1, read at S327j. Every quote was matched against the TeX at its locator. No lane has reviewed this note.

Registered from the suite: p0_framework_foundations.tex:521 (PDF p.10), register quality HOUSE_TRANSCRIBED (a house transcription of the TeX, not the PDF's extraction text):

AX1 ρ²−ρ−1 = 0 (the golden unit) — Input (named axiom) — assumed, not derived from nothing.

The TeX at that line: AX1 $\rho^2-\rho-1=0$ (the golden unit) & \status{Input} (named axiom) & assumed, not derived from nothing.

What kind of premise this is

Register kind: POSTULATE. Paper 0 lists AX1 among its declared inputs with the status \status{Input} (named axiom) (p0_framework_foundations.tex:521) and prints it as one of the active operational inputs (p0_framework_foundations.tex:635). Appendix I derives the selection of the golden vacuum modulo this unit: the direction of the defect source and its completion are derived, and the unit magnitude γ = 1 is equivalent to AX1 and is not derived there (appendix_i_dynamics_bounce.tex:94-96). Source status words: the unit magnitude is AX1, not derived from nothing (appendix_i_dynamics_bounce.tex:1042-1043).

Where the suite invokes it

A house census, not a lane draft: every line of the suite TeX that names AX1 (TeX comment lines excluded) falls inside one of the 30 passages below — CONDITIONAL 12, LOAD_BEARING 1, MENTIONED 8, STATED 9. Pages refer to the sealed Rev32.7 page-delimited text. Rows marked “read R78-c” were read at S327i for PRM-018 and moved here by R81-D15; rows marked “read S327j” were read for this note.

House reading notes:

• p0_framework_foundations.tex:521 — The registered statement (PRM-025 PRIMARY). The drafting lane quoted this line in the PRM-018 note (row 2) as the distinct surviving axiom.
• p0_framework_foundations.tex:621 — See the PRM-013 row at this line for the wording check.
• p4_higgs_ewsb.tex:278 — No Registrar record carries this derivation (searched).
• p7_precision_tests_falsification.tex:145 — WORDING CHECK (REV32.8 candidate, minor): the row names AX2, which p3_ckm_pmns_mixing.tex:708 prints as eliminated (D575).
• p8_junkyard.tex:303-305 — LABEL CHECK (register curation): cosh(2 ln phi) = 3/2 is phi^2 + phi^-2 = 3, the equation Appendix E names the DET-7 condition; here it is labelled AX1.
• appendix_h_time_bridge.tex:418-433 — LABEL CHECK (register curation), as at p8_junkyard.tex:303-305: the equation labelled AX1 here is phi^2 + phi^-2 = 3, which Appendix E names the DET-7 condition (PRM-013). For rho > 1 it holds exactly when rho^2 - rho - 1 = 0, so the label states an equivalence, not the printed form of AX1.
• appendix_h_time_bridge.tex:550-551 — LABEL CHECK: as the row above.
• appendix_i_dynamics_bounce.tex:198-200 — No Registrar record carries this reduction (searched for R_d and golden depth).
• appendix_i_dynamics_bounce.tex:318-320 — No Registrar record carries the Appendix I selection results.
• appendix_i_dynamics_bounce.tex:637-641 — The Route B of this passage is Appendix I's grading route (direction K, unit coupling): not the CKM Route B of PRM-017 and not Appendix E's Route B (PRM-024). R81-D14 records the homonyms.

Arguments that rest on it

NO RECORD declared. Under R82-d the PI ruled no edges for PRM-025: no Registrar record carries a result that assumes AX1 — a coverage gap, recorded, not a finding of independence. The suite results above that print a dependence on AX1 and have no Registrar record include the Appendix I selection theorem (derived modulo the AX1 unit), the reduction of the golden depth R_d to AX1, and the natural Yukawa y² = 2/9 of Paper 4. A search of the master for AX1 finds it in one record, and only in a lane note (LIB2-047, whose note says the source row's AX1 wording is not used at that record's locators).

What breaks without it

What the suite prints: without AX1 the golden selection of Appendix I is derived only up to the unit magnitude — the sole viable selector selects golden exactly when the golden axiom holds (appendix_i_dynamics_bounce.tex:281-293) — and whether AX1 is itself forced is printed as an open question (appendix_i_dynamics_bounce.tex:939-943). Paper 4 prints the natural Yukawa as derived from AX1 (p4_higgs_ewsb.tex:278). NOT ASSESSED — the house has not computed what fails in each of these results without AX1; this note records what the suite prints.

Registrar sync

Registrar state after R76, R78 and R82 (S327j, master 0e1418ad6501767d). Declared today: none (UNKNOWN, not INDEPENDENT). R82-d (PI, S327j): no edges for this premise. The R78-c reading found no further record whose result assumes this premise.

Tier and what this does not show

A premise is not a result, and invocation count is not importance. The roles above are house readings, not a lane's and not the PI's. No record or premise is upgraded, downgraded, or edited. Unlocated dependencies remain unknown. Two lines of Appendix H and one of Paper 8 print φ² + φ⁻² = 3 under the label AX1; the label checks are recorded for register curation, not ruled.

Sources

TeX: p0_framework_foundations.tex:210-215; p0_framework_foundations.tex:514-515; p0_framework_foundations.tex:521; p0_framework_foundations.tex:536-537; p0_framework_foundations.tex:538-540; p0_framework_foundations.tex:621; p0_framework_foundations.tex:635; p4_higgs_ewsb.tex:278; p7_precision_tests_falsification.tex:145; p8_junkyard.tex:303-305; appendix_h_time_bridge.tex:418-433; appendix_h_time_bridge.tex:550-551; appendix_i_dynamics_bounce.tex:33; appendix_i_dynamics_bounce.tex:60-61; appendix_i_dynamics_bounce.tex:66-67; appendix_i_dynamics_bounce.tex:94-96; appendix_i_dynamics_bounce.tex:179-180; appendix_i_dynamics_bounce.tex:198-200; appendix_i_dynamics_bounce.tex:281-293; appendix_i_dynamics_bounce.tex:300; appendix_i_dynamics_bounce.tex:318-320; appendix_i_dynamics_bounce.tex:332-335; appendix_i_dynamics_bounce.tex:406-407; appendix_i_dynamics_bounce.tex:637-641; appendix_i_dynamics_bounce.tex:939-943; appendix_i_dynamics_bounce.tex:1022-1027; appendix_i_dynamics_bounce.tex:1032-1034; appendix_i_dynamics_bounce.tex:1042-1043; appendix_n_selector_fences.tex:115-116; appendix_x_zero_parameter_input_ledger.tex:62.

Register: PRM_REGISTER_S312.jsonl row PRM-025 (R81-D15). Ruling: Trackers/RULING_R81_S327_PREMISE_REGISTER.md. R78-c sheet: Trackers/R78C_HOUSE_READ_75_S327.tsv.