kappaLeptonCandidate_ne_zero

Item 8 is the open quark sub-leading mass correction in the Recognition Science mass ladder. This module builds the smallest precise theorem framework that would close that item and make the all-sector generalization falsifiable: a refined residual family with coefficients $(c,\eta)$ fitted to observed generation residuals.

The lepton coupling candidate is the RS electromagnetic seed reciprocal $\kappa_{\mathrm{lep}} = 1/\alpha_{\mathrm{seed}} = 1/(4\pi\cdot 11)$. Refined-family solvability for a sector requires a nonzero coupling on the signature; positivity of this candidate was already proved by unfolding the seed and applying a positivity tactic.

Local setting: the module already has unique solvability for any negative-sign sector once the residual pair has nonzero gen12 step, non-degenerate cross-difference, distinct steps, and nonzero coupling. The lepton sector is the first concrete freeze of that abstract $\exists!$ package.

One-line term proof: apply ne_of_gt to the already-proved strict positivity theorem kappaLeptonCandidate_pos (itself an unfold of the seed definition plus positivity). No further algebraic work.

Feeds leptonSectorClosure, the concrete $\exists!$ package for the lepton negative-sign sector at $\kappa_{\mathrm{lep}} = 1/(4\pi\cdot 11)$. That parent freezes the active pair $(c_{\mathrm{Neg}},\eta)$ independently of quark data, which is the first sector-level closure step toward Item 8.

In the Recognition framework the electromagnetic seed $\alpha_{\mathrm{seed}} = 4\pi\cdot 11$ sits upstream of the fine-structure band and the mass-ladder yardstick. Non-vanishing of its reciprocal is the elementary gate that lets the refined-family uniqueness lemmas apply to leptons without importing quark residuals. Without this fact the lepton signature would fail the nonzero-coupling hypothesis of the constructive solvability theorems already proved in the module.