ANP-00: Pre-Singularity Causal Relation Domain, Hybrid Continuity, Legality, Phase-Like Transitions, and Causal Interpretation

Pre-Singularity Causal Relation Domain, Hybrid Continuity, Legality, Phase-Like Transitions, and Causal Interpretation

The previous Cycle (III) closed the Type-I reservoir-mechanism classification layer, but revealed a deeper problem: state ancestry plus node-by-node source ancestry does not imply a single compatible causal formation history. What is missing is not another reservoir tax, but a formal causal relation domain. This round therefore defines the semantic, dynamical, numerical, and logical rules every future ancestry edge must satisfy: defines the canonical Causal Atom, covering spacetime, relation, existence, definition, judgment, dynamics, numerics, continuity, discreteness, coupling, legality, phase-like transition, causality, predictability, and interpretability fields; proves basic forward-time/Duhamel causality and a hybrid continuous–discrete legality proposition; defines quantitative edge coordinates and a legality matrix; recompiles the Source-Core Provenance Bridge into fully typed causal obligations. This is a formal research framework, not a proof of chain necessity, finite obstruction, singularity prediction, or Navier–Stokes regularity.