This paper, based on two fundamental physical axioms—Information Conservation (A1) and Computability (A2)—systematically argues for the intrinsic logical structure necessary for describing physical reality. Research shows that in aself-referential universe model constrained by local observations, the truth-valuejudgment logic of physical propositions necessarily deviates from classical Booleanlogic. The core root lies in the “local-global inequivalence” of physical systems: theinformation contained in the global physical state cannot be completely determinedby any finite observational procedure within a finite spacetime region. This leads tothe invalidity of the law of excluded middle within the system, and consequently,the logical structure mathematically manifests as a non-distributive orthomodularlattice, i.e., Birkhoff–von Neumann quantum logic. This structure is proven tocorrespond exactly to the subobject lattice in the ∞-topos TA constructed previously. This theoretical framework finally leads to a testable cosmological prediction:the central value of the non-Gaussianity parameter fNL of the cosmic microwavebackground (CMB) temperature fluctuations is about −3.2. Next-generation CMBexperiments (such as CMB-S4) will be able to test this prediction precisely, andthe results can be used to evaluate whether the quantum logical structure emergingfrom the basic axioms is suitable for describing the real universe.
This paper, based on two fundamental physical axioms—Information Conservation (A1) and Computability (A2)—systematically argues for the intrinsic logical structure necessary for describing physical reality. Research shows that in aself-referential universe model constrained by local observations, the truth-valuejudgment logic of physical propositions necessarily deviates from classical Booleanlogic. The core root lies in the “local-global inequivalence” of physical systems: theinformation contained in the global physical state cannot be completely determinedby any finite observational procedure within a finite spacetime region. This leads tothe invalidity of the law of excluded middle within the system, and consequently,the logical structure mathematically manifests as a non-distributive orthomodularlattice, i.e., Birkhoff–von Neumann quantum logic. This structure is proven tocorrespond exactly to the subobject lattice in the ∞-topos TA constructed previously. This theoretical framework finally leads to a testable cosmological prediction:the central value of the non-Gaussianity parameter fNL of the cosmic microwavebackground (CMB) temperature fluctuations is about −3.2. Next-generation CMBexperiments (such as CMB-S4) will be able to test this prediction precisely, andthe results can be used to evaluate whether the quantum logical structure emergingfrom the basic axioms is suitable for describing the real universe.
This paper proposes and develops a research framework for deriving fundamental mathematical structures from underlying physical axioms. We prove that,starting from two basic principles that a self-referential computational system mustsatisfy Information Conservation (A1) and Computability (A2) the mathematicaldescription of its evolutionary process is necessarily organized into a specific category. The objects of this category correspond to discrete semantic levels of thesystem state, and the morphisms are completely positive trace-preserving (CPTP)maps, which directly embody the constraint of information conservation. The tensor product structure and dagger structure possessed by the category originate,respectively, from the parallel operations permitted by computability and the formal time-reversal symmetry implied by information conservation. Ultimately, wesystematically derive a complete dagger-compact category. Distinct from purelymathematical constructions, the credibility of this framework is rooted in an empirically testable physical prediction: in a quantum processor, the complexity growthdynamics of the system state should exhibit a periodic oscillation pattern related tothe logarithm of the system size (ln N). This explicit prediction provides a crucialfalsification condition for the theory.
This paper starts from two fundamental principles—Information Conservation(A1) and Finite-Step Computability (A2)—to argue the mechanism for the naturalemergence of inherent lower bounds of computational complexity in physically realizable computational processes. Research shows that core concepts of computationalcomplexity (such as polynomial-time upper bounds, circuit depth lower bounds) arenot mere mathematical abstractions but are quantitative laws that must be followedby physical systems when performing information transformations under fundamental constraints such as energy, time, and information conservation. Specifically, thequantum speed limit together with Axiom A2 jointly sets a polynomial-time upperbound for any finite-energy physical system; while the Information Conservationaxiom (A1) combined with the principle of minimal physical realization complexity(A3) ensures that the logical difficulty of a computational task is inevitably reflected in the topological complexity of the spatiotemporal structure of its physicalrealization. This sets a lower bound for the circuit depth determined by topological invariants, and in quantum many-body systems, it directly manifests asvolume-law growth of entanglement entropy, whose coefficient is determined by theunderlying hardware architecture. To test this theoretical framework, this paperdesigns two cross-scale experimental paths: at the microscopic level, using superconducting quantum processors to precisely measure the volume-law coefficient ofentanglement in random quantum circuits; at the macroscopic cosmological level,inferring the “computational complexity” growth information of the early-universeinflationary process by detecting the phase coherence of the primordial gravitationalwave background. These schemes aim to place foundational issues of computationalcomplexity within the domain of empirically testable physical science.
This paper aims to provide a unified physical origin explanation for topological order that transcends the Landau paradigm, starting from principled axioms.Based on two fundamental axioms—Information Conservation (A1) and Finite-StepComputability (A2)—we argue that topological order is not an accidental productof specific models, but rather a macroscopic quantum structure that inevitablyemerges from quantum many-body systems under the joint action of A1 (globalinformation constraints) and A2 (local interaction rules) in order to achieve robustnon-local information storage and processing. This paper systematically demonstrates that core features such as topological degeneracy, anyonic fractional statistics, and topological entanglement entropy can be logically derived from these twoaxioms, and integrates topological order with many-body dynamics from a unifiedspatiotemporal perspective, further proposing numerical and experimental testingschemes. This framework provides a new principled foundation for understandingthe nature, classification, and role of topological order in quantum computing andquantum gravity
Classical information theory and quantum information theory are respectively based on Boolean algebra and Hilbert space projection lattices, lacking a unified logical framework for cross-scale physical propositions covering classical, mesoscopic and quantum domains. Traditional physics attributes the classical-quantum transition to continuous spatial scale variation, which is essentially external parameter determinism and cannot explain the peculiar intermediate characteristics of mesoscopic systems. This paper constructs the philosophical and mathematical foundation of mesoscopic information theory based on the coupling of S4 modal logic and the non-distributive modular lattice M₃. A composite axiom system is proposed, and Axiom 3 (a–g) realizes the consistent embedding of S4 modal operators on non-distributive lattices. The cross-scale evolution of physical systems is reinterpreted as discrete phase transition of propositional lattice types, with an endogenous CHSH-type correlation threshold τ≈2.414 serving as the operational criterion for mesoscopic phase. A Möbius-weighted lattice entropy independent of Shannon and von Neumann entropy is established to characterize structural information of mesoscopic logical systems. Noise and decoherence are redefined as intrinsic signals of lattice structural transition rather than simple information dissipation. This study establishes the independent ontological status of mesoscopic propositional systems, breaks the scale-phenomenological paradigm in traditional cross-scale physics, and provides a new foundational framework for the unification of cross-scale information theory.
Addressing cross-disciplinary fundamental issues including paradigm separation between classical and quantum observation, logical drift in general artificial intelligence probabilistic frameworks, and ambiguous uncertainty tracing in information systems, this study proposes a universal axiomatic framework of the binary excluded middle law and establishes a dual theoretical architecture consisting of ontology entropy and cognitive entropy. Strict logical demonstration verifies that all objective physical systems, regardless of microscopic or macroscopic scale, obey binary exclusive truth-value constraints without inherent superposition states or intrinsic probabilistic uncertainty. Phenomena such as quantum superposition, observational fuzziness, and probabilistic ambiguity are cognitive representations arising from information isolation and insufficient observational coupling, rather than inherent ontological properties of physical systems. This study redefines the essential nature of observation as a threshold-induced phase transition process, in which continuous information aggregation reduces cognitive entropy and eventually drives the system toward a deterministic binary steady state. Under this dual-entropy paradigm, the Schrödinger’s cat superposition paradox is fully and self-consistently resolved, eliminating long-standing logical ambiguities in quantum observation interpretation. This paper further conducts cross-domain adaptability analysis and constructs a unified fundamental logical framework for physical observation, intelligent cognition, information evaluation, and numerical computation, while outlining a phased systematic research roadmap. The results indicate that the binary excluded middle law serves as a universal underlying logical meta-rule for natural and intelligent information systems. The proposed dual ontology–cognitive entropy system fundamentally unifies the paradigms of classical and quantum physics, natural science, and artificial intelligence, possessing significant fundamental theoretical innovative value and broad engineering application prospects.
This paper introduces Axiom 0, a minimal foundational principle for physical reality: the impossibility of any globally closed description of the total correlational structure. Rather than postulating space, time, dynamics, locality, or physical laws as primitive, the framework assumes only: (i) the existence of a correlational structure, (ii) the structural impossibility of complete self-closure, and (iii) consistency under partial comparison. From these ingredients, the paper shows how: physical laws emerge as stabilizing regularities of incomplete descriptions, time, dynamics, and geometry arise as effective, regime-dependent structures, irreversibility follows from projection and information loss, and why no description can be both exact and globally complete. Non-closure is treated as an ontological constraint, not as epistemic ignorance or observer dependence. Physical reality exists precisely because complete closure is impossible, independently of observation or modeling. The paper does not attempt to replace existing physical theories or derive numerical constants. Instead, it provides a structural foundation within which effective physical theories (quantum, classical, relativistic, and open-system regimes) can be consistently understood as emergent and domain-limited. This work is intended as a conceptual and structural foundation for correlational and relational approaches to fundamental physics, clarifying the origin of laws, dynamics, and physical regularity without invoking additional ontological postulates.