We develop a minimal mathematical framework in which physicaldescriptions are characterized by constraints on realizable processesrather than by primitive time evolution. Starting from comparabilityon restricted domains, composability, and stability under refinement,we prove the existence of an additive ordering functional on processes.We show that equilibrium states stable under all cyclic operations nec-essarily take Gibbs form, that regular Euclidean continuation enforcesa universal 2π periodicity in the associated flow parameter, and thatstable interference together with reversibility implies a unitary expo-nential representation. Finally, we demonstrate that in a sector ad-mitting exactly three independent local deformation generators, theassociated boundary redundancy group is Z3. All results are derivedin finite or discrete settings, with explicitly stated assumptions, andwithout assuming spacetime geometry, quantum fields, or microscopicdynamics. The framework isolates structural features that any empir-ical physical theory supporting ordering, equilibrium, and interferencemust possess.
We develop a minimal mathematical framework in which physicaldescriptions are characterized by constraints on realizable processesrather than by primitive time evolution. Starting from comparabilityon restricted domains, composability, and stability under refinement,we prove the existence of an additive ordering functional on processes.We show that equilibrium states stable under all cyclic operations nec-essarily take Gibbs form, that regular Euclidean continuation enforcesa universal 2π periodicity in the associated flow parameter, and thatstable interference together with reversibility implies a unitary expo-nential representation. Finally, we demonstrate that in a sector ad-mitting exactly three independent local deformation generators, theassociated boundary redundancy group is Z3. All results are derivedin finite or discrete settings, with explicitly stated assumptions, andwithout assuming spacetime geometry, quantum fields, or microscopicdynamics. The framework isolates structural features that any empir-ical physical theory supporting ordering, equilibrium, and interferencemust possess.
Aionics is a foundational framework for describing boundary-mediatedphysical structure without presupposing time, dynamics, probability,or spacetime geometry. The theory is formulated on an abstract aioniccoordinate space, from which observable behavior arises solely throughprojection and boundary-induced actions on observables. Within this framework, we identify a minimal structural signature fornon-temporal observable transitions, consisting of three jointlyrequired features: (i) compression of observable noise under increasedstructural order, (ii) realizable reversal of boundary-induced actionswithout temporal inversion, and (iii) path dependence (holonomy) betweenprocedures with identical endpoints. We show that no classicaltime-local, path-independent stochastic or dynamical model can reproduceall three features simultaneously under fixed experimental constraints. Aionics is operationally closed by a minimal experimental protocol thattests for this decisive triad without reference to internal aionicvariables. The framework is logically prior to, but independent of, anyspecific physical realization, and contains existing approachesinvolving informational transitions, conformal boundaries, andobservable-level operators as concrete instantiations.
Recommended reading order Paper I — Core FrameworkStructural Constraints on Realizable Physical Transitions Paper II — Empirical Validation (Ordering)Structural Ordering of Observable Noise in Fixed-Workload Quantum Circuits Paper III — Empirical Validation (Topology & Holonomy)Topology-Dependent Realizability Under Fixed Quantum Dynamics The papers are intended to be read in this sequence. This record contains the complete Aionics trilogy, a coordinated set of three research papers establishing and empirically validating a constraint-based framework for physical realizability. The first paper introduces Aionics, a pre-dynamical framework in which structural constraints delimit which physical transitions are realizable, with time emerging as an ordering of realized transitions rather than as a fundamental substrate. The second paper provides empirical evidence for this framework by demonstrating monotonic ordering of observable noise by structural organization under fixed quantum dynamics, defeating gate-count and workload-based null models. The third paper extends these results by establishing topology-dependent realizability: circuits matched in workload and scalar structure but differing in interaction topology exhibit stable, reproducible differences in observable entropy, demonstrating holonomy and path dependence. Together, these works show that structure is an operationally measurable constraint on physical realizability, supplementing standard dynamical descriptions without modifying existing physical laws.
Modern physics relies on several highly successful mathematical frameworks — quantum theory, gauge theory, general relativity, and thermodynamics. These theories describe nature extremely well, yet their mathematical forms are usually introduced through independent postulates. This work asks a prior question: why do these mathematical structures appear at all? The framework developed here begins from two minimal structural requirements for persistence:coherent return (self-consistency under transformation) and triadic closure (the minimal structure required for such verification). Within clearly stated domain restrictions — independent composability, smooth relational locality, and finite resolution — these postulates impose strong constraints on how physical systems can be represented. From these structural constraints, several familiar elements of modern physics arise as minimal admissible forms: • complex Hilbert space and unitary quantum evolution• quadratic weighting (Born rule)• relational geometry and Einstein-type gravitational response• irreversible temporal ordering from non-invertible return• entropy and the Second Law from indistinguishability growth• compact unitary gauge structure The framework does not attempt to predict parameter values or replace existing physical theories. Instead, it explains why the mathematical forms used by those theories are structurally admissible once coherent persistence under finite resolution is required. As a numerical application, the Koide relation for charged-lepton masses is shown to arise as a geometric consequence of triadic equilibrium in quadratic mass-amplitude space, conditional on the charged-lepton family realizing a coherent triadic structure. The result is a structural program for physics: rather than proposing new dynamical laws, it constrains the mathematical forms that viable physical laws may take.
Quantum Mechanics as Reversible Closure Representation and the Emergence of Relativistic Structure (Paper 2) Abstract This work develops a representation-theoretic extension of the closure-first discrete gravity framework established in Reality is What Misspoken Language Cannot Deliver (Rev17). Starting from finite primitive state spaces and reversible closure algebra, we construct a unitary representation of the closure group on a complex Hilbert space. Quantum evolution arises naturally as the continuous representation of discrete reversible transitions, with phase structure determined by restoration periods. Defect transport within the closure algebra yields dispersion relations that recover relativistic propagation in the macroscopic limit. Local flatness emerges as the tangent limit of the discrete curvature substrate, giving Special Relativity as a local geometric approximation of the underlying simplicial structure. General Relativity appears as the coarse-grained curvature density of defect-labelled simplicial geometry, preserving the Einstein field equations within their established effective domain of validity. Quantum mechanics is therefore not postulated independently, but arises as the representation layer of reversible finite closure, while relativistic structure emerges from geometric coarse-graining of the same primitive algebra. No new macroscopic gravitational equations are introduced; the present work concerns the structural origin of existing relativistic frameworks rather than their modification. Introduction In the preceding work (Rev17), finite entropy bounds were shown to exclude primitive continuum ontology and to imply a finite state space for bounded physical regions. Under assumptions of deterministic closure, no primitive erasure, and inverse realisability, the reversible sector of primitive transitions forms a group. Defect labels associated with group elements define discrete curvature quanta, which embed naturally into a Regge-type geometric framework. A minimal continuum-limit argument yields the Einstein–Hilbert action under refinement. Importantly, this construction does not alter the Einstein field equations at macroscopic scales. General Relativity remains valid within its established regime as an effective continuum description. The prior work addresses the structural substrate from which that continuum description emerges. The present work extends this foundation by addressing two remaining structural questions: How does quantum mechanics arise from finite reversible closure? How does relativistic kinematics emerge from the same primitive structure? Rather than introducing Hilbert space or Lorentz symmetry axiomatically, we derive them as representation and coarse-graining layers of the previously established closure algebra. The guiding principle is minimal structural extension: no new primitive entities are introduced. All additional structure follows from representation consistency and macroscopic limit coherence. Quantum theory appears as the unitary representation of reversible closure; relativistic structure emerges as the geometric compression of defect-labelled algebra under scale separation. References[1] J. Bloggs, Aligning GR with Reality – Fully and Finally, Zenodo (2026). DOI: 10.5281/zenodo.18673556.[2] T. Regge, General relativity without coordinates, Nuovo Cimento 19 (1961) 558–571. DOI:10.1007/BF02733251.[3] J. W. Barrett, D. Oriti, and R. M. Williams, Tullio Regge’s legacy: Regge calculus and discrete gravity, arXiv:1812.06193 (2018). DOI: 10.48550/arXiv.1812.06193.[4] R. Loll, Discrete approaches to quantum gravity in four dimensions, Living Rev. Relativ. 1 (1998) 13. DOI: 10.12942/lrr-1998-13.[5] B. Dittrich and S. Steinhaus, Path integral measure and triangulation independence in discrete gravity, Phys. Rev. D 85 (2012) 044032. DOI: 10.1103/PhysRevD.85.044032.
Modern theoretical physics faces an abundance of mathematically consistent frameworks and a scarcity of decisive empirical constraints. This work proposes a principled response to that situation by identifying stability under intervention as a primary selection criterion for viable physical theories. Adopting an explicitly operational perspective, the paper formulates stability as the non-amplification of operational distinguishability under physical processes, a requirement motivated by the finite precision and reproducibility of experimental practice. When combined with compositional consistency, purification, and reversible symmetry, this principle strongly constrains admissible statistical frameworks. Within this setting, quantum theory emerges not as a fundamental ontology or a historically contingent choice, but as the uniquely stable non-classical fixed point compatible with reproducible physical control by finite agents embedded within the systems they study. The defining structural features of quantum mechanics, including convex state spaces, affine dynamics, state–effect duality, and a Born-type probability rule, arise as consequences rather than postulates. The framework further suggests that spacetime locality and geometry need not be assumed a priori, but can be understood as constraints on the propagation of distinguishability in composite systems. Potential deviations from quantum theory are predicted to manifest as failures of stability, such as breakdown of dilation, violation of distinguishability monotonicity, or loss of local tomography. This repository contains the final submission-ready manuscript together with its LaTeX source and bibliography, deposited on Zenodo prior to journal submission.This version (v1.1) incorporates clarifications on scope, logical dependencies between principles, worked examples within the Jordan-algebra classification, strengthened hedging of speculative material, and refined statements of falsifiability, in response to detailed referee feedback.
This work presents a minimal structural framework for interpreting quantum discreteness and coherence as emergent properties of recursive ordering, rather than as primitive features of microscopic degrees of freedom. Motivated by recent experimental results demonstrating enhanced coherence under quasiperiodic (e.g., Fibonacci) driving, the paper explores how stability can arise from structured, non-repeating dynamical constraints imposed on system evolution. We introduce a conservative formalization in which discrete quantum states correspond to states that remain stable under recursive domain cycling (up to global phase), while incompatible modes fail to accumulate coherently and are naturally expelled toward boundaries. This perspective is expressed through three complementary layers: a minimal conceptual statement, an extended dynamical formulation compatible with standard quantum mechanics, and a purely algorithmic pseudocode representation suitable for simulation and toy-model exploration. The framework does not propose new physical primitives, nor does it replace existing quantum formalisms. Instead, it provides an interpretive and organizational lens through which familiar features—such as half-factors, coherence plateaus, boundary effects, and quasiperiodic stabilization—may be understood as signatures of relational and recursive structure. The presentation intentionally emphasizes clarity, restraint, and reproducibility, leaving room for independent rediscovery, reinterpretation, and future extension by others. This work builds on a year-long exploration of structured recursive geometry, toy models, and quasiperiodic dynamics, and is intended as a conceptual bridge between abstract stability principles and concrete quantum behavior.