A Formal Semantics for the Φ Generative Architecture: Dependency Control, Provenance, Admissibility, Countermodels, and the Boundary of Current Formal Claims

Holophase proposes a dependency-controlled generative architecture in which downstream scientific targets are not permitted to license their own prerequisites. This paper isolates the formal burden of that proposal before any physical recovery is considered. The current Revision E canon separates a mute Absolute Φ boundary from Differential Φ, defines a relational trunk from co-articulation through exact Difference, introduces Unity Without Erasure with a separate retained-provenance channel, and expresses lawful continuation by a set-valued operator S′ ∈ GΦ(S). The leading mechanism hypothesis, Retentive Differential Articulation (RDA), states that earned consequential Difference can be retained, generate prospective constraints, change admissibility, and thereby condition later articulation. We formalise the core interfaces required to make this architecture criticisable and retain the strongest results of the internal red-team programme: static admissibility filters implemented only by set intersection commute; provenance that differs within a generated identity class cannot in general factor through quotient identity; generic composable Path does not require cyclicity; relational Difference does not require a global phase-position potential; quotient identity does not license representative-sensitive operations without congruence; pairwise compatibility does not imply global compatibility; and local consistency does not guarantee global gluing. Two finite prototype implementations previously returned true on thirty selected witness predicates, but an adversarial code audit showed that these do not constitute complete satisfaction of the thirty mechanism passports and do not establish carrier neutrality. The central unresolved formal problem is therefore sharpened rather than hidden: derive the prospective constraint package ΓΦ(S) from already-earned structure without outcome-dependent target leakage, and show that the resulting admissibility field is non-vacuous, restrictive, and stable across materially distinct faithful realisations. The paper defines the current claim ceiling, falsification routes, and an independent-review programme for theorem proving, model search, deletion/substitution analysis, and rival comparison.