PhiGeneral: Universal Causal Geometry, Membrane Admissibility, and Global Audit Integration in Φ5 Space

This work introduces PhiGeneral, a universal geometric admissibility operator within the Causal Theory (CT) framework, designed to enforce global coherence constraints on structured states prior to local certification. In the CT architecture, Start-1 transforms raw input into a normalized causal representation in Φ5 space, while Start-2 performs discrete slot-based certification across a finite set of 118 structural attractors. However, local slot proximity alone is insufficient to guarantee validity, as geometrically inconsistent states may still appear close to valid attractors. PhiGeneral resolves this limitation by acting as a global audit layer positioned between projection and slot evaluation. It ensures that every Φ5 state satisfies a set of universal constraints before entering the certification process. The Φ5 state space is formalized as a normalized 4-simplex (affine-constrained manifold with ∑Φᵢ = 1), defining a bounded geometric domain of admissible causal configurations. The paper introduces: A membrane of admissibility separating valid and invalid configurations A reality band defined by constrained SU(2)-like / SU(3)-like coupling (κ constraint) A phase balance law governing expansion and dissipation (Δ dynamics) A closure horizon defined by π-axis saturation A finite resolution limit induced by the 118-slot attractor structure PhiGeneral is defined as a deterministic operator performing classification via constraint satisfaction over invariant geometric structures. It partitions states into: VALID (globally admissible and stable) UNSTABLE (admissible but outside stability bounds) INVALID (outside admissible manifold) The integration into Start-2 is fully specified, including: insertion point in the processing pipeline constraint-aware modification of slot ranking enforcement of admissibility during slot audit persistence of global metrics in the causal ledger trajectory re-validation during state evolution explicit exposure in final system outputs A key contribution is the introduction of a non-interference principle, ensuring that multiple slot candidates cannot be simultaneously certified within resolution limits, preventing ambiguity and structural contamination. Unlike probabilistic or semantic approaches, this framework is fully deterministic and invariant-driven. It unifies signal extraction (phonetic layer), dynamic validation (symphonic layer), and global admissibility (PhiGeneral) into a coherent causal certification system. The result is a mathematically constrained, implementation-ready architecture where global geometry governs local truth, preventing invalid state certification and enforcing structural coherence across all system layers.