Reading a Fractal Theory from Outside: A Dynamic Bridge for a Recursively Self-Similar Research Programme

Semantic Physics is a research programme that proposes a formal-empirical account of meaning as held difference under cost. Its central claim is not merely that meanings can be represented geometrically, but that meaning-bearing contrast, under explicit admissibility conditions, admits geometric and transport structure from within its own relational organization. This paper addresses a prior question: how can a recursively structured theory be read from outside its own register without being flattened into a slogan or inflated into metaphysics? The answer proposed here is a dynamic pinch-point bridge. A bridge holds when four variables remain above a critical floor along the reader’s trajectory: gradient strength |∇Ψ|, membrane permeability σ, holding capacity h, and addressability A. Unlike a static introduction, the bridge is bidirectional. The reader must not only cross into the Semantic Physics register; the reader must also return to domains such as financial stability, AI safety, active inference, or the philosophy of self-grounding with a structurally faithful translation. This v1.1 formulates the Bridge Viability Proposition: one-way intelligibility is insufficient for structural passage; a bridge becomes viable only when both forward translation and return translation preserve the relevant distinctions of both registers. The paper therefore formulates the intrinsic move without the invalid shortcut from arbitrary relation to metric to curvature; distinguishes recursive self-instantiation from circularity; assigns evidence-status tags to empirical anchors; operationalizes methodological self-consistency as a fifth substrate; defines return criteria for four substrate-specific bridges; and compares Semantic Physics to neighboring traditions without relying on priority rhetoric. The narrow claim that survives is this: Semantic Physics is a candidate formal-empirical programme in which intrinsic derivation, recursive self-instantiation, cross-substrate empirical signatures, and documented methodological auditability are jointly present. The claim is ambitious, but falsifiable at named seams.