Entropy, Information, and the Limits of Unification: Register Discipline in Foundational Physics

Abstract Three persistent confusions in foundational physics — the origin of thermodynamic asymmetry, the ontological status of information, and the stalling of unification programmes — share a common source: the compression of distinct explanatory registers into a single formal framework. This paper applies the register discipline developed across the Triaxial Existential Field (TEF) programme to show that each confusion dissolves once the orthogonality between constraint structure (R-register) and evental actualisation (P-register) is consistently enforced. Entropy is reframed as constraint accumulation through record formation. Each P-actualisation incurs structural cost, that is, non-refundable remainder that enters the R-register as constraint on subsequent admissibility. The arrow of time is this accumulation, not a dynamical tendency. The past hypothesis is derived rather than posited: three convergent arguments, from record-formation conditions, from the cost structure of admissible persistence, and from the ItoE exclusion of null-equivalence, establish that any admissible cosmological origin must be far from equilibrium, since equilibrium cannot initiate ordered history. Information is shown to require the coincidence of coherence, reflexivity, and participation (C ∧ R ∧ P), resolving longstanding disputes between information-first and information-as-epistemic positions. The black hole information paradox dissolves once global unitarity (R-constraint) is distinguished from local retrievability (P-accessibility): the S-matrix remains unitary while operationally accessible information is lost at the evaporation boundary. Unification programmes are diagnosed through operational signatures of register collapse, namely constraint discretisation, constraint encoding as exchange, and the absence of explicit register separation, with specific predictions for gravity-mediated entanglement experiments. The framework predicts that gravity can mediate entanglement between massive quantum systems while exhibiting no superposition signatures of its own, distinguishing it from standard quantum gravity expectations. Explicit falsification conditions are stated for each claim. The framework is advanced as a disciplined research programme whose central wager, that constraint and event are irreducible explanatory roles, is staked against determinate empirical and conceptual outcomes.