Mentis Umbra

Mentis Umbra: Consciousness, Agency, and Qualia as Admissible Projections This paper establishes a structural classification theorem for systems satisfying irreversibility and redescription stability. It proves that any such system must instantiate a projection structure consisting of (i) transition mediation and (ii) invariant reference. These structures are not introduced as primitives but are derived as necessary consequences of a commutation condition: The argument proceeds in layers. First, for single systems, mediator factorization and invariant reference are shown to be necessary to prevent label-sensitive divergence under admissible redescriptions. Second, the results are extended to interacting systems, yielding joint mediators and jointly invariant references. Third, the framework is lifted to nnn-system contexts, where pairwise restriction and inherited stability are established. Finally, a constructive global mediation theorem is proven: under triple compatibility, all well-typed joint transitions universally factor through a product mediator. Failure of compatibility yields a formally defined obstruction to global coherence. Crucially, renaming richness is not assumed as a primitive condition. It is derived from syntactic fresh-name supply and statewise envelope non-minimality, eliminating dependence on an external structural axiom. The universal factorization result therefore follows from internally defined representational properties rather than stipulation. Terminology such as agency, intentionality, and qualitative interiority is introduced strictly as role-based classification predicates over the derived projection structure. No ontological claims are made. The results are structural and conditional: they characterize what any redescription-stable irreversible system must instantiate. The paper stands independently of broader corpus commitments and provides: Necessity of mediator factorization under redescription stability Necessity of invariant reference structures Necessity of joint mediation in interacting systems A constructive universal global mediation theorem under triple compatibility A formal obstruction criterion when compatibility fails All results are obtained without introducing new primitives beyond admissibility, typing-envelope preservation, and alpha-equivalence–based identity. Highly Recommended reading order to understand the framework as its not practical to reproduce the primitive stack in every downstream paper: Foundational Closure of Admissibility and Standing: Non-Derivability, Minimality, and the Kernel of Non-Degenerate Reasoning — establishes the non-derivable kernel and the transcendental argument structure inherited by the later papers. Foundational Closure of Admissibility and Standing Necessity of Admissibility in Non-Degenerate Compositional Systems: AMetric Boundary, Bivalence, and the Unique Admissible Interior — technical core; derives the forced interface shape from the minimal compositional base. Necessity of Admissibility in Non-Degenerate Compositional Systems The Mathematics of Coherent Reasoning: A Bivalent Trajectory Theory — derives the finite path geometry over the fixed substrate and is the most downstream/mathematically transparent presentation of the internal consequence layer. The Mathematics of Coherent Reasoning: A Bivalent Trajectory Theory