PRM-006 · AX6_pol — polarisation postulate (weak-angle orbit selector)

Premise

Register corrected — R81 (D5, S327j). The PI ruled this correction to the register row (Trackers/RULING_R81_S327_PREMISE_REGISTER.md). Statement now (PRM-006/r2, p4_higgs_ewsb.tex:348-352, quality EXTRACTION_VERBATIM): AX6pol is the polarisation postulate Λ⋆ = 3P/Q(Y ) = 6ϕ − 1 on the exact-colour I4 = ϕ3 orbit. Name now AX6_pol — polarisation postulate (weak-angle orbit selector) (was AX6pol). The Det² object that shared the label is registered separately as PRM-026 (historical). 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:

AX6$_{\rm pol}$: $\Lambda_\star=3P/Q(Y)=6\phi-1$ on the exact-colour orbit; readout $\sin^2\theta_W=3/(4+\Lambda_\star)=\phi^{-3}$ exactly.

Appendix X · Fit-free-interior ledger — Weak-angle selector · PDF p.323 · appendix_x_zero_parameter_input_ledger.tex:90.

What kind of premise this is

POSTULATE is the register kind. The ledger calls this an independent orbit-selector postulate. It fixes the polarization branch; the algebraic readout then has the displayed value. The present Coleman–Weinberg framework does not select it. The Det-squared angle and AX6pol are explicitly different objects: retiring the former as a selector does not retire the latter premise. Source status words: Independent orbit-selector postulate (appendix_x_zero_parameter_input_ledger.tex:90).

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 9 hit lines for PRM-006 that the lane never saw. Under R78-c the house read all 9 in the full suite TeX: 6 passages are added below (3 further hit lines fall inside them). 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.

House reading notes:

• p4_higgs_ewsb.tex:342-347 — The suite itself records the conflation the register row carries (R78-d).
• p4_higgs_ewsb.tex:358-360 — LIB2-200 carries this argument; the house refused its ADD at A1634 until the PRM-006 register repair (R78-d). LIB2-199 (the value phi^-3 as a structural target) is NOT proposed: p4_higgs_ewsb.tex:344 prints phi^-3 as a constant identity in the Peirce eigenvalues, not a function of any orbit angle.
• p6_rg_thresholds.tex:211-212 — PRINT DEFECT (REV32.8 candidate): the clause "decoupled from the value phi^-3." is printed twice (tex lines 211-212; also in the sealed Rev32.7 text). The label is the unsubscripted AX6.
• p6_rg_thresholds.tex:1187-1188 — STALE PRINT (REV32.8 candidate): the box prints sin^2 theta_W = 3/13 as the target under AX6, while p6_rg_thresholds.tex:166 marks 3/13 superseded by phi^-3 and p4_higgs_ewsb.tex:293 closes the 3/13 trace-ratio estimate; the operative readout is phi^-3 under AX6_pol (p4_higgs_ewsb.tex:348-360).

Arguments that rest on it

LIB2-200 — ADD. The ledger places the exact weak-angle readout after the independently postulated Lambda-star value on the exact-colour orbit. The record carries precisely this conditional identity, not a derivation of the polarization selector. Step locator: appendix_x_zero_parameter_input_ledger.tex:90 (CONDITIONAL).

What breaks without it

LIB2-200: without the postulated orbit value, this passage does not supply the selected Lambda-star for the registered readout. Appendix A states that the present CW framework does not supply that selector (appendix_a_lagrangian_derivation.tex:382). NOT ASSESSED — no replacement physical weak angle is printed for dropping AX6pol. The group-level passages condition only the weak-angle branch, not selection of the gauge group (p1_peirce_gauge_group.tex:51,352).

Registrar sync

Registrar state after R76, R78 and R82 (S327j, master 0e1418ad6501767d). Declared today: LIB2-200. Declared at S327j under R82-c, after R81-D5 made this row AX6_pol alone and the house re-read the passage: LIB2-200. 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 — ADD: LIB2-200. LIB2-249 concerns the former Det-squared selector account, explicitly retired for this task. LIB2-289 and LIB2-292 are archived targets/proof prompts, not present conditional derivations. No dependency is added to them.

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_a_lagrangian_derivation.tex:373; appendix_a_lagrangian_derivation.tex:382; appendix_x_zero_parameter_input_ledger.tex:90; appendix_y_laboratory_notebook.tex:567; p0_framework_foundations.tex:1075; p0_framework_foundations.tex:177; p0_framework_foundations.tex:78; p0_framework_foundations.tex:99; p1_peirce_gauge_group.tex:352; p1_peirce_gauge_group.tex:51; p2_mass_hierarchy_resolvent_quintics.tex:725; p4_higgs_ewsb.tex:367. Registrar: LIB2-200, LIB2-249, LIB2-289, LIB2-292. Premise: PRM-006. Suite-cited kernels: s1135.