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.
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.
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.
We present an empirical study of observable noise behavior in quantum circuits under fixedworkload constraints. Using publicly available circuit archives and measurement data, we showthat observable dispersion metrics are monotonically ordered by pre-measurement interactionstructure derived solely from circuit topology, and not by gate count or circuit depth alone.Structure is quantified using topology-derived interaction matrices constructed prior to measurement, while noise is quantified using observable-level statistics such as measurement distribution entropy and fidelity proxies. The observed ordering persists across multiple system sizesand hardware-inspired datasets. These results indicate that circuit-level noise cannot be fullycharacterized by workload-local or gate-independent models, and suggest that pre-measurementstructural organization plays a decisive role in shaping observable noise.
This repository contains the source files for the paper: Irreversibility and Ordering in Classical Observability of Quantum Structure The paper develops a formal framework explaining when and why classical statistics extracted from noisy quantum systems retain architecture-dependent information, and when they inevitably lose it. Building on a trilogy of earlier empirical and operational studies, the work introduces the diagnostic pipeline as a fundamental object of analysis: a fixed composition of a noise channel, a measurement choice, and a deterministic classical feature map. Such pipelines are shown to form a preorder under information-degrading transformations, induced by standard monotonicity principles. Within this framework, several phenomena observed empirically are shown to be structural necessities rather than numerical accidents: Feature-dependent collapse arises from deterministic feature post-processing below the identity (full-distribution) pipeline. Basis-dependent diagnostic blindness corresponds to incomparability between pipelines using different fixed measurement bases. Irreversible loss of distinguishability follows from genuine noise degradation and cannot be undone by downstream measurement or feature choices. The paper proves general monotonicity results, establishes generic incomparability of measurement bases, and derives falsifiable predictions linking noise–basis alignment to collapse thresholds for population-encoded distinctions. Minimal empirical consistency checks against the companion trilogy datasets are provided. The framework yields practical design principles for lightweight diagnostics in NISQ-era experiments, clarifying fundamental limits on classical access to quantum structure under realistic constraints. Contents Irreversibility_and_Ordering_in_Classical_Observability_of_Quantum_Structure.pdfFinal compiled manuscript. Irreversibility_and_Ordering_in_Classical_Observability_of_Quantum_Structure.texLaTeX source (self-contained; bibliography and figures embedded). Relation to Other Work This paper provides the formal, structural foundation for a companion trilogy on architecture-sensitive classical fingerprints under noise, including: Feature-dependent collapse under fixed pipelines Basis-dependent diagnostic blindness Selective transcription as an operational principle The present work unifies and explains these results within a single information-theoretic preorder framework. Status Submission-ready manuscript.Intended for submission to a peer-reviewed journal in quantum information theory. Licence See LICENSE.
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.
This work reports experimental evidence that physical outcomes in quantum hardware depend on the interaction structure realized during execution rather than solely on the intended logical circuit description. Using four-qubit experiments on superconducting quantum processors, we demonstrate that nominally equivalent circuits may be compiled into distinct physical interaction graphs, leading to markedly different correlation patterns in measurement outcomes. The results support a structure-dependent realization perspective, in which global system constraints select admissible physical outcomes from a space of formally defined possibilities. The findings provide empirical grounding for realization-based theoretical frameworks and complement independent evidence obtained from temporal-coherence studies and gravitational systems. This work is not intended as a performance or optimization study, but as an experimental investigation of structural selection in physical systems.
This record presents a review and synthesis of a five-part research series devoted to clarifying the domain of validity of quantum descriptions. The work introduces an explicit process–event framework, distinguishing between continuous quantum processes described by the formalism and their irreversible realization as physical events. Rather than proposing new dynamics or modifying quantum theory, the synthesis operates at a meta-level, making explicit the conditions under which standard quantum concepts—such as Planck’s relation, Born’s rule, conservation laws, entanglement, and Bell-type constraints—acquire physical meaning. A minimal realization criterion, expressed schematically as a resonant event threshold, delineates when a quantum description corresponds to an empirically accessible event rather than a purely formal process. By consistently maintaining the process–event distinction, the framework resolves longstanding conceptual tensions surrounding measurement, nonlocality, conservation laws, and information without altering the mathematical structure or empirical predictions of quantum mechanics.