Axiodynamics Formal Kernel – Part II: Formal Realisability, Telotopic Inference, and Falsifiability Architecture

This second part of the Axiodynamics Formal Kernel supplies a jointly realisable formal architecture for the six-axiom constitutional core fixed in Part I. It distinguishes axiological, motivational and telotopic domains; implements the Part I correction from the historical motivational tensor notation to an orthogonal direct-sum geometry; types the mémotional mapping from the archival nine-component source representation to motivational state and telotopic orientation; and specifies eligibility, weighting, bias-corrected circular estimators and a staged telos-resolution gate. A3-KR is realised through an explicit functional non-vacuity criterion while preserving multiple realisability and the non-equivalence between existential witness construction and reference-family selection. The temporal layer supplies family-neutral closure, retained endogenous ingress and constructive regime-transition witnesses. A cumulative carrier establishes joint formal realisability of A1–A6 without implying uniqueness or empirical validation. The final layers distinguish formal falsifiability, observational construction, identifiability and observed failure, and provide the complete FRR-CoDesign architecture. Companion corrigenda preserve historical provenance while prospectively aligning BRC-1 and ICB-1 with the Formal Kernel. Empirical corroboration, cross-cycle identifiability proofs and single-protocol compatibility remain explicitly outside the claims established here.