The Semantic VIN Framework: Value-Invariant Network Analysis of Physical Theories as Representation Systems (v3.0)

AbstractWe introduce the Semantic VIN (Value-Invariant Network) framework, a formal apparatus foranalysing physical theories as representation systems R = ⟨X, E, T, I, C, O, Δ, Υ⟩. The frameworkmodels how a theory encodes world structure (E), its admissible transformations (T), theinvariants preserved (I), compression efficiency (partitioned into descriptive Cdesc and generativeCgen), residual distortion (Δ), observer coupling (O), and computational tractability (Υ). We provea Compression-Invariance Theorem linking invariant constraints to maximal compression viaKolmogorov complexity bounds, and a Parameter Relocation Principle demonstrating thatreducing explicit parameters inflates implicit representational load unless constrained byinvariants. A category-theoretic formulation of equivalence closure (Q) counts isomorphismclasses of invariant-preserving functors, enabling rigorous comparison of representation systems.Applying the framework to General Relativity and the Standard Model formalises theirincompatibility as the absence of natural isomorphisms across representational strata. Theframework demonstrates that structural preservation is insufficient withoutinformation-theoretic constraints, offering a diagnostic tool for foundational physics and theevaluation of quantum gravity candidates including the amplituhedron programme.