PRM-023 · Route A inversion symmetry (palindromic spectrum)

Premise

Register kind: ADOPTED_PREMISE. Located suite statement:

\textbf{Inversion symmetry (palindromic spectrum):} the characteristic polynomial of $\vac$ is palindromic, i.e.\ $\vac$ is isospectral to its Jordan adjoint $\vac^{\#}$.

Appendix E · Setup and hypotheses — H1 · PDF p.163 · appendix_e_vacuum_selector.tex:43.

What kind of premise this is

ADOPTED_PREMISE is the register kind. Appendix E calls H1 a structural hypothesis and states its isospectral meaning. Under unit determinant the Jordan adjoint equals the inverse. This is the residual assumption of the field-free Route A, not a physical CKM route selection. The arithmetic Route B uses a different residual field hypothesis. The note preserves the source’s palindromic terminology without substituting a textbook convention. Source status words: structural hypotheses (appendix_e_vacuum_selector.tex:94).

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-023 that the lane never saw. Under R78-c the house read all 9 in the full suite TeX: 2 passages are added below, 7 are not this premise. 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.

Hit lines that are not this premise:

• appendix_m_order5_clock_occupation.tex:383 — Key Route[ -]?A matched "route above" (case-insensitive).
• appendix_x_zero_parameter_input_ledger.tex:587 — Key Route[ -]?A matched "route are" (case-insensitive): "the KV-flow route are dead".
• p1_peirce_gauge_group.tex:154 — The legacy CKM/flavour Route A (the pair PRM-017 belongs to), not Appendix E's inversion-symmetry route.
• p3_ckm_pmns_mixing.tex:81 — Paper 3's CKM first-row Route A (compared with kaon data), not Appendix E's Route A.
• p3_ckm_pmns_mixing.tex:676 — Paper 3's CKM first-row Route A ("Route~A gave 0.22749").
• p3_ckm_pmns_mixing.tex:893 — Key Route[ -]?A matched "route A654" (an assessment serial).
• p8_junkyard.tex:70 — Key Route[ -]?A matched "route and" (case-insensitive).

Arguments that rest on it

LIB2-019 — CONFIRM. The field-free theorem explicitly takes H1 with H0 and DET-7; its lemma uses H1 to reduce the spectrum to a reciprocal pair and a unit eigenvalue. It selects the multiset, not an ordered physical frame. Step locator: appendix_e_vacuum_selector.tex:94 (CONDITIONAL).

NO RECORD — the separate invariant-selector presentation on the inversion family, appendix_i_dynamics_bounce.tex:593–595. No further record beyond the supplied symmetry-form selector is identified for a new graph edge.

What breaks without it

LIB2-019: the lemma explicitly uses H1 to reach the reciprocal-pair spectrum before DET-7 fixes its positive parameter (appendix_e_vacuum_selector.tex:71,94). Without H1, this printed Route-A reduction has no stated source. NOT ASSESSED — no replacement field-free reduction is supplied. Appendix I likewise restricts to the inversion family before evaluating the invariant (lines 593–595); no unrestricted replacement is supplied.

The conclusion is a spectral orbit: the ordered physical Peirce frame remains loaded (appendix_e_vacuum_selector.tex:509). The existence of the alternative arithmetic route is not a derivation or discharge of H1 within Route A.

Registrar sync

Registrar state after R76, R78 and R82 (S327j, master 0e1418ad6501767d). Declared today: LIB2-019. 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: LIB2-019. Draft dispositions — CONFIRM: LIB2-019. LIB2-020 uses the different arithmetic hypothesis, not H1 as an explicit premise. LIB2-239 is a deprecated Cabibbo-route account; a shared Route-A label is insufficient.

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:111; appendix_e_vacuum_selector.tex:144; appendix_e_vacuum_selector.tex:34; appendix_e_vacuum_selector.tex:43; appendix_e_vacuum_selector.tex:509; appendix_e_vacuum_selector.tex:71; appendix_e_vacuum_selector.tex:94; appendix_i_dynamics_bounce.tex:593; appendix_i_dynamics_bounce.tex:593–595; appendix_i_dynamics_bounce.tex:637. Registrar: LIB2-019, LIB2-020, LIB2-239. Premise: PRM-023. Suite-cited kernels: s978, s981.