Dual-Layer Light v4.0: Necessary and Sufficient Conditions for the Existence of Ma — A Deductive Completion

This paper completes the deductive program of the Dual-Layer Light framework by formally establishing both necessary and sufficient conditions for the existence of Ma (間, φ₂) as the structural origin of light speed invariance. Two critical adversarial objections (Miki-kun simulation) are resolved: (1) NECESSARY CONDITION — "Empty vacuum" alternative eliminated: The Casimir effect (Casimir 1948; Lamoreaux 1997; Decca et al. 2003) provides direct empirical proof that the quantum vacuum is not empty. The choice is not between "a field exists" and "nothing exists" — the vacuum contains quantum fields in their ground states. This eliminates the objection that "empty vacuum also produces invariant c." (2) SUFFICIENT CONDITION — Existing field candidates eliminated: Three uniform field candidates are systematically evaluated against four necessary criteria (uniform, universal, dynamic, photon-coupled): - Higgs field: coupling to photon = 0 in Standard Model (L_Higgs-photon = 0). No physical pathway to influence c. - Zero-point energy: spatially non-uniform (Casimir effect demonstrates boundary dependence) + cosmological constant problem (10^120 discrepancy). - Cosmological constant Λ: not dynamic (no degrees of freedom), couples to g_μν not F_μν. φ₂ (Ma) is the only field candidate satisfying all four necessary conditions simultaneously. The logical structure is identical to the dark matter hypothesis: existing known fields cannot explain the observation → new field required. The sufficient condition: L_int = λ·φ₂·F_μνF^μν with uniform φ₂ = φ₀ produces constant renormalization of the photon Lagrangian → invariant c. Perturbations δφ₂ (KOKU Interval events) produce local transient δc. A fourth falsifiable prediction is added: Casimir force measurement variance during IceCube GOLD windows vs. non-GOLD windows — the most direct φ₂ detection pathway proposed. Residual limitation acknowledged: unknown fields other than φ₂ satisfying the four conditions cannot be logically excluded.

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