A Falsification-First Validation Harness for Discretized Spectral Operators on Compact Product Manifolds (v0.1.16 Pre-Review Draft)

GeoSpectra Falsification Ladder methodology paper. Presents a falsification-first validation workflow for discretized spectral operators on compact toy manifolds, validated through the v0. 1. 15 case study (S²×S¹ product-discretized full diagnostic, 6615+6615+1349 cases). Ring/alpha=0 caveat resolved via targeted follow-up (s1ₛize≥64 empirical guideline). Pre-review manuscript ready for external domain expert feedback (Track A: lattice field theory, differential geometry, numerical analysis). This is a METHODOLOGY paper, NOT a physical compactification proof. All validation on finite-lattice toy operators (s1ₛize≤96). Eight scientific non-claims explicitly stated: no continuum compactification, no S⁶/S³×S⁶, no Standard Model, no physical chirality, no Witten/Lichnerowicz bypass, no physical extra dimensions, no hierarchy solution, no observable predictions. Baseline: v0. 1. 15-s2-s1-product-discretized-full (computational validation completed 2026-05-16).