This paper reconstructs its philosophical foundation of Modal Information Theory (MIT). A complete deductive chain is constructed through Stone duality of Boolean lattices, Alexandroff topology and S4 modal logic correspondence, four modal-probability bridging axioms confining the structure to M3 diamond lattice, two-dimensional Hilbert space quantization, Gleason-Busch theorem and Tsirelson bound. The midpoint of the classical-quantum interval is defined as the mesoscopic order parameter η=1+√2≈2.4142, namely the silver critical value. Serving as the theoretical basis between classical and quantum regimes, it provides fundamental mathematical criterion for Liu Entropy and validates its dedicated mesoscopic information unit mobit. The paper demonstrates the minimality of the axiom system and extremal origin of the critical value, establishes partitioning criteria for classical, mesoscopic and quantum domains from both philosophy of science and quantum logic perspectives, and solidifies the axiomatic system of Modal Information Theory.
This paper reconstructs its philosophical foundation of Modal Information Theory (MIT). A complete deductive chain is constructed through Stone duality of Boolean lattices, Alexandroff topology and S4 modal logic correspondence, four modal-probability bridging axioms confining the structure to M3 diamond lattice, two-dimensional Hilbert space quantization, Gleason-Busch theorem and Tsirelson bound. The midpoint of the classical-quantum interval is defined as the mesoscopic order parameter η=1+√2≈2.4142, namely the silver critical value. Serving as the theoretical basis between classical and quantum regimes, it provides fundamental mathematical criterion for Liu Entropy and validates its dedicated mesoscopic information unit mobit. The paper demonstrates the minimality of the axiom system and extremal origin of the critical value, establishes partitioning criteria for classical, mesoscopic and quantum domains from both philosophy of science and quantum logic perspectives, and solidifies the axiomatic system of Modal Information Theory.
This paper lays out the philosophical foundation of mesoscopic information theory. Taking S4 modal logic and the M₃ diamond modular lattice as its mathematical skeleton, this work puts forward four modal‑probability bridging axioms which form a minimally‑sufficient axiom set: the modal necessity axiom, the modal‑probability consistency axiom, the modal‑probability regularity axiom, and the distributive‑law breaking axiom. This constraint system realizes a controlled transition from the Boolean base of S4 to the non‑Boolean M₃ lattice, embedding modal operators and probability measures within one unified formal framework. Global completeness is not pursued; only internal self‑consistency and traceable reasoning are required. This axiomatic apparatus yields a unified philosophical account of mesoscopic‑level features including modal tension, quasi‑quantum‑like behaviors and informational phase transitions. Empirical adequacy and real‑world case studies are reserved for future versions.
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.
This paper proposes a theoretical framework for topological order emergencebased on three criteria: structural stability (S), emergent entropy (E), and decoherence resilience (D). Through axiomatic definitions of the mathematical formsand physical connotations of each criterion, a phenomenological criterion system fortopological order emergence is established. The article systematically explores thephysical origin and universality challenge of the threshold value 0.5, analyzes thecoupling relationships and independence conditions among the criteria, constructsa specific correspondence bridge with category theory invariants, and designs a setof jointly measurable experimental verification schemes. Furthermore, this framework is placed within the context of quantum information theory, proposing thatthe emergence of topological order may correspond to the fundamental limits ofquantum information processing, thereby providing new theoretical perspectivesand operational tools for the identification, classification, and detection of topological phases.
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.
One can construct a mapping between Hilbert space and the class of all logic if the latter is defined as the set of all well-orderings of some relevant set (or class). That mapping can be further interpreted as a mapping of all states of all quantum systems, on the one hand, and all logic, on the other hand. The collection of all states of all quantum systems is equivalent to the world (the universe) as a whole. Thus that mapping establishes a fundamentally philosophical correspondence between the physical world and universal logic by the meditation of a special and fundamental structure, that of Hilbert space, and therefore, between quantum mechanics and logic by mathematics. Furthermore, Hilbert space can be interpreted as the free variable of "quantum information" and any point in it, as a value of the same variable as "bound" already axiom of choice.
The quantum measurement problem, after nearly a century of exploration, centers on how a macroscopic superposition transitions to a definite classical outcome.Based on two minimal axioms—information conservation and computability—thispaper introduces the information potential difference ∆µ as the unique order parameter for the quantum-classical transition. It is theoretically proven that ∆µhas a minimum quantum of ln2, and completing a ln2 transition corresponds toa ”self-referential closure”, at which point the density matrix diagonalizes and asingle world emerges. When ∆µ is experimentally suppressed below ln2, the system remains in a critical layer, producing observable ”fragmented many-worlds”signals, including a mutual information drop of 0.43–0.46, an entropy production pulse on the order of 10−23J/K, and a chiral current of 17–19 nA without an external field. We design three mesoscopic experiments—superconductingquantum-mechanical oscillator, diamond torsion pendulum-NV center, and topological insulator-Josephson junction—to be implemented in 2025–2028, providing a5σ confidence criterion. This framework transforms the ”Schrödinger’s cat” paradox into an adjustable and readable information potential difference scale in thelaboratory, making the single-world vs. many-worlds debate a testable quantitative problem for the first time, and opening experimental avenues for subsequentexploration of closure time scaling laws, fragmented world manipulation, and themicroscopic origin of information potential difference.