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IndisputableMonolith.Verification.QuarkSectorAudit

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Audit module comparing two incompatible coordinate conventions for placing quarks on the Recognition Science phi-ladder. Convention A uses absolute rungs; Convention B uses residue classes. Records that generation spacing, reference points, and rung typing disagree, so no unified quark-sector mass map is proved yet. Cited by anyone checking whether the RS mass formula closes on u,d,s,c,b,t.

claimTwo quark coordinate schemes on the $\varphi$-ladder: Convention A assigns absolute rungs $r_q$; Convention B assigns residues modulo the generation spacing. The module records that the schemes use different references, different rung types, and unequal generation spacings, and that a reconciliation proof is not yet available.

background

Recognition Science places particle masses on a discrete $\varphi$-ladder via the mass formula yardstick $\cdot,\varphi^{r-8+\mathrm{gap}(Z)}$. Quarks are the hardest sector because light-quark masses are strongly renormalized and the three generations must sit on a single self-similar ladder forced by T6.

This verification module isolates two competing coordinate conventions that have appeared in RS drafts. Convention A works with absolute rung integers. Convention B works with residue classes relative to a generation period. The module also imports the RS-native constants layer ($\tau_0=1$ tick) so numerical accuracy checks can be stated in the same units as the rest of the monolith.

Sibling declarations flag concrete mismatches: different reference anchors, different rung-type interpretations, and unequal generation spacings. Accuracy predicates distinguish light-quark fits from skeleton-only (heavy-quark) fits.

proof idea

Definition and status module, not a proof module. It introduces the two convention types, a unified-sector placeholder, and propositional flags (different references, different rung types, generation-spacing mismatch, light-quark vs skeleton accuracy). A reconciliation-proof interface is declared and immediately witnessed as uninhabited (no_reconciliation_yet). No algebraic derivation is attempted; the file only records the audit state.

why it matters in Recognition Science

Quark masses are a required closure test for the RS mass ladder and the forcing chain (T5 J-cost, T6 $\varphi$, T7 eight-tick structure). Until the two coordinate conventions are either identified or one is discarded, claims that the ladder predicts $u,d,s,c,b,t$ remain conditional. The module therefore sits in Verification as a gate: downstream mass-spectrum theorems cannot honestly cite a unified quark sector while no_reconciliation_yet holds. No parent theorems currently import it (used_by empty); it is an audit checkpoint rather than a lemma feeder.

scope and limits

depends on (1)

Lean names referenced from this declaration's body.

declarations in this module (13)