TSKR-04: Two-Sided Mismatch Stress, Second-Order Zero-Base Recovery, Harmonic-Pressure Tail Rigidity, Adjoint Compatibility, Amplitude Tax, and Cycle-X Closure Audit

Two-Sided Mismatch Stress, Second-Order Zero-Base Recovery, Harmonic-Pressure Tail Rigidity, Adjoint Compatibility, Amplitude Tax, and Cycle-X Closure Audit

TSKR-03 reduced the surviving tangential residual singular kernel to LHF∨HPR∨ZQD∨TSM∨ASC∨AMP. This paper runs the Cycle X closure audit, determining which are genuine primitive residuals. Linearizing the exact quadratic tangency constraint at a reproduced zero-covariance nonzero basis, it proves the energy-invisible two-sided mismatch stress has the special traceless hyperbolic form H = u⊗w+w⊗u (w ⊥ u); its nonzero eigenvalues are exactly ±|u||w|. Flux-invisibility further forces w ⊥ Su, so at a generic three-dimensional point where u and Su are linearly independent, the entire two-sided mismatch kernel is at most one-dimensional, w ∥ u×Su. It proves that zero-base quadratic degeneracy is only a first-order failure: under the natural second-order blow-up, the exact tangency geometry re-enters the rank-one decay theorem, and second-order covariance–energy invisibility forces H = 0, b = ±a. It proves an interior harmonic-pressure tail estimate, routing tangential recurrence supported on nontrivial harmonic pressure into the explicit harmonic-tail ledger already preserved by the finite-window recursive audit. Cycle X thereby reduces TRSK to a "two-sided residual phantom" (TSRP).