Axiodynamics Formal Kernel – Part I: Canonical Constitution and Verified Issues Register

This document is Part I of the Axiodynamics Formal Kernel. Its function is constitutional rather than expository: it fixes what the programme's six constitutive axioms commit to, records the status of every non-canonical claim attached to them, and corrects a small number of formal and classificatory errors accumulated across the corpus (v5.7 through v5.12 and associated addenda). For each of the six axioms, a register separates the minimal semantic commitment – binding on every future realisation – from its historical glosses and formal realisations, and states explicitly which formal commitments the axiom does not make; this last stratum is the structural safeguard against the retro-projection and modal-strengthening drifts documented in the corpus. Three results are established independently of the still-unspecified formal morphism and are therefore fixed here: the motivational tension space is corrected from a tensor product to an orthogonal direct sum; the hard core is restored to Axioms 1–6, with Axioms 7–9 as positive heuristic; and the historical telos-existence gate is shown, by elementary derivation, to be mismatched to the axial object it tests. A dated normative clarification (A3-KR) resolves a documented underdetermination in the status of the telos. A preregistration firewall governs the interaction between these consolidated definitions and studies already in progress. Part I is deliberately incomplete: the formal spaces, the morphism, the estimators, and the falsifiability charter are reserved for Part II, which is bound by a Formal Realizability Obligation to exhibit at least one realisation jointly satisfying the axioms' commitments and the corrigenda stated here.