ReconciliationProof
plain-language theorem explainer
Formal checklist of what quark-sector reconciliation must deliver: one mass formula for all six quarks, no measured masses on any RHS, lepton-grade (sub-percent) accuracy, and a parameter-free RHS built only from counting integers, φ, and α. Auditors of the fermion mass pipeline cite it as the acceptance criteria. Pure structure definition; four fields, no proof body.
Claim. A reconciliation certificate is a record of (i) a single mass formula covering all six quarks, (ii) a witness that no measured quark mass enters any right-hand side, (iii) a witness that every quark reaches sub-percent precision on the same footing as the lepton chain, and (iv) a witness that the formula uses only counting-layer integers together with $\varphi$ and $\alpha$ (no PDG targets).
background
The Quark Sector Audit module records the main blocker to an end-to-end fermion mass claim: two coexisting quark coordinate conventions that are not mathematically equivalent and have not been fused into one forward pipeline.
Convention A (canonical core) uses integer rungs from cube geometry, $m = \mathrm{yardstick}(\mathrm{Sector})\times\varphi^{r-8+\mathrm{gap}(Z)}$, with up- and down-type rungs ${4,15,21}$ and distinct yardsticks. Convention B (hypothesis module) uses a quarter-ladder $m = m_e^{\mathrm{struct}}\times\varphi^R$ with $R\in\tfrac14\mathbb{Z}$ and residues fitted to PDG targets, so it is not parameter-free.
The module states explicitly that the two conventions are not meant to be equivalent. Until one non-circular, parameter-free pipeline exists, "correct for all fermions" is not defensible. This structure is the formal acceptance bar for that missing reconciliation.
proof idea
No proof. The declaration is a four-field structure: a string naming the candidate unified formula, plus three boolean flags (non-circularity, sub-percent coverage of all quarks, parameter-freeness). Instantiating it would mean exhibiting concrete witnesses for those fields; the sibling no_reconciliation_yet records that no such instance currently exists.
why it matters
In the Recognition mass framework the lepton chain is already on a single forward, parameter-free φ-ladder. The quark sector is the outstanding gap: Convention A is clean but incomplete as a PDG match; Convention B matches PDG only by importing targets. This structure freezes the four conditions any future unification must meet before the framework can claim all fermions on equal footing with the mass formula $\mathrm{yardstick}\times\varphi^{r-8+\mathrm{gap}(Z)}$ and the forcing-chain constants (φ from T6, eight-tick/D=3 from T7–T8).
No downstream theorems yet depend on it (used_by is empty). It is an audit interface: the open question it encodes is whether a single counting-layer formula can replace the dual-coordinate split without circular PDG input.
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