TRISDUCTION: A Three-Axis Verification Methodology. Pre-Bayesian Structural Audit for Multi-Source Convergence.

This paper develops a pre-Bayesian structural audit for multi-source-convergence claims. The primary contribution is the Convergence Dissolution Test (CDT), an operational procedure that subtracts a candidate latent common cause from the convergence-supporting evidence streams via orthogonal projection and returns a discrete Heaviside verdict on whether the residual evidence architecture remains non-degenerate. Where convergence survives subtraction with non-zero residue, the architecture issues a Geometric Orthogonal Lock (GOL); where convergence dissolves into a single shared upstream factor, the architecture returns broken geometry. The verdict is logically prior to Bayesian credence: it audits whether the evidence architecture is non-degenerate at the structural-admissibility layer before Bayesian update on the architecture's content proceeds. The methodology is demonstrated retrospectively on the BICEP2 detection of primordial gravitational waves (March 2014) and its dissolution under the joint BICEP2/Keck/Planck analysis (January 2015). CDT applied to the March 2014 evidence configuration identifies the shared foreground-dust modeling assumption as the latent common factor across every internal cross-check and returns broken geometry at the cascade's Minimum Population gate via Convergence Hallucination. The cascade's verdict on March 2014 matches the eventual scientific verdict on January 2015 without requiring the September 2014 Planck independent dust measurement. The same procedure applies to any multi-source-convergence claim whose convergence may be conditional on a shared upstream assumption. The cascade operates over three orthogonal verification axes (formal-structural V_F, empirical-thermodynamic V_E, epistemic-registration V_ER) anchored on the Friedrichs-Hodge decomposition L²Ω^k(M) = im(d) ⊕ im(δ) ⊕ ℋ^k(M) and on a Root Axiom that links existence to kinetic-thermodynamic content via Landauer's bound, Heisenberg uncertainty, set-theoretic distinguishability, and Hadamard-regularized smeared field operator variance. A twelve-gate cascade specifies the structural-admissibility tests; a substrate-portable execution protocol (Appendix E) permits reproducible verdicts across verification substrates; a Linguistic Isolation Test operationalizes axis-independence at the vocabulary layer where Bayesian conditional-independence testing does not apply. A failure-mode taxonomy classifying structural defects of substrate-floor proposals and an optional foundational-ontology commitment to a trilayer substrate model are provided as supporting material. The chain is sealed at honest per-layer typing. Theorem-grade on the underlying mathematics and physics. Methodological warrant on the Hodge-to-verification correspondence, the GOL truth function specification, the T_4 closure stipulation, and the gate taxonomy. Conditional warrant on the Bridge Axioms typed per-axiom (T/C/S). The architecture's distinctness from Bayesian inference, Mayo error-statistics, Pearl-Hernán causal inference, falsificationism, abduction, and consilience is anchored on the BICEP2 worked example plus the Linguistic Isolation Test specification.