A recent axiomatic framework introduced a class of finite informational entities defined by an internal duality, with a proved finite lifetime governed by a dissipative binary recurrence. While mathematically self-consistent, that framework makes no contact with physical observables—its parameters are uninterpreted, its dynamics are posited rather than derived, and its central axiom of "Operational Parity" lacks any realization in the finite-dimensional operator model used to derive its consequences. This paper attempts the translation from axiomatic structure to falsifiable physical theory. We restrict attention to the framework's operational core—a pair of coupled rank-one operators evolving under a symmetric discrete recurrence—and set aside the type-theoretic axiom that resists physical modeling. We assign physical referents to the remaining parameters, derive the discrete recurrence from a continuous-time Lindblad master equation via Suzuki–Trotter decomposition, and provide a concrete experimental protocol for quantum simulation platforms with quantitative predictions. The central finding is negative: the operational core reduces exactly to a standard two-mode damped Rabi oscillator, and the framework's distinctive conceptual claim—that an entity is type-theoretically identical to its internal conjugate pair—does no physical work in the model constructed here. Every falsifiable consequence follows from the Lindblad equation without reference to the original axiomatic structure. The paper's contribution is methodological rather than physical: it provides a worked example of how to extract testable content from an abstract framework and an honest accounting of what gets lost in translation. We conclude that this particular duality axiom is physically inert in the present model, while leaving open whether other axiomatic approaches to foundational physics would similarly reduce to known models upon physicalization.
A recent axiomatic framework introduced a class of finite informational entities defined by an internal duality, with a proved finite lifetime governed by a dissipative binary recurrence. While mathematically self-consistent, that framework makes no contact with physical observables—its parameters are uninterpreted, its dynamics are posited rather than derived, and its central axiom of "Operational Parity" lacks any realization in the finite-dimensional operator model used to derive its consequences. This paper attempts the translation from axiomatic structure to falsifiable physical theory. We restrict attention to the framework's operational core—a pair of coupled rank-one operators evolving under a symmetric discrete recurrence—and set aside the type-theoretic axiom that resists physical modeling. We assign physical referents to the remaining parameters, derive the discrete recurrence from a continuous-time Lindblad master equation via Suzuki–Trotter decomposition, and provide a concrete experimental protocol for quantum simulation platforms with quantitative predictions. The central finding is negative: the operational core reduces exactly to a standard two-mode damped Rabi oscillator, and the framework's distinctive conceptual claim—that an entity is type-theoretically identical to its internal conjugate pair—does no physical work in the model constructed here. Every falsifiable consequence follows from the Lindblad equation without reference to the original axiomatic structure. The paper's contribution is methodological rather than physical: it provides a worked example of how to extract testable content from an abstract framework and an honest accounting of what gets lost in translation. We conclude that this particular duality axiom is physically inert in the present model, while leaving open whether other axiomatic approaches to foundational physics would similarly reduce to known models upon physicalization.
A recent axiomatic framework introduced a class of finite informational entities defined by an internal duality, with a proved finite lifetime governed by a dissipative binary recurrence. While mathematically self-consistent, that framework makes no contact with physical observables—its parameters are uninterpreted, its dynamics are posited rather than derived, and its central axiom of "Operational Parity" lacks any realization in the finite-dimensional operator model used to derive its consequences. This paper attempts the translation from axiomatic structure to falsifiable physical theory. We restrict attention to the framework's operational core—a pair of coupled rank-one operators evolving under a symmetric discrete recurrence—and set aside the type-theoretic axiom that resists physical modeling. We assign physical referents to the remaining parameters, derive the discrete recurrence from a continuous-time Lindblad master equation via Suzuki–Trotter decomposition, and provide a concrete experimental protocol for quantum simulation platforms with quantitative predictions. The central finding is negative: the operational core reduces exactly to a standard two-mode damped Rabi oscillator, and the framework's distinctive conceptual claim—that an entity is type-theoretically identical to its internal conjugate pair—does no physical work in the model constructed here. Every falsifiable consequence follows from the Lindblad equation without reference to the original axiomatic structure. The paper's contribution is methodological rather than physical: it provides a worked example of how to extract testable content from an abstract framework and an honest accounting of what gets lost in translation. We conclude that this particular duality axiom is physically inert in the present model, while leaving open whether other axiomatic approaches to foundational physics would similarly reduce to known models upon physicalization.
We present a self-contained axiomatic framework in which a fundamental entity is defined not by intrinsic materiality but as a finite, quantized information node governed by an internal duality. The central postulate—the Axiom of Operational Parity—asserts that an individual entity is mathematically identical to an interacting pair of itself and its conjugate: S≡S×SˉS≡S×Sˉ. Working in a finite-dimensional Hilbert space H=CdH=Cd with d≥3d≥3, we introduce a strictly positive quantization operator QQ encoding geometric bounds, an antiunitary conjugation CC, and a command vector ∣v⟩∣v⟩ satisfying two orthogonality conditions. From these we construct a pair of positive rank-one entity operators (S,Sˉ)(S,Sˉ) with equal trace ττ and orthogonal support. The entity's global state is postulated to be the maximally entangled Bell state of the active and conjugate sectors. Temporal persistence is governed by a dissipative binary recurrence—a deterministic discrete-time linear evolution coupling S(n)S(n) and Sˉ(n)Sˉ(n). We prove that positivity is preserved if and only if the coupling parameters satisfy ∣A−B∣≤1−γ∣A−B∣≤1−γ, and that the trace decays as Tr(S(n))=τ(1−γ)nTr(S(n))=τ(1−γ)n. An intrinsic collapse criterion based on trace threshold is introduced. The main result, the Finite Lifetime Theorem, establishes that every entity returns to the zero state in a finite number of steps, with the explicit formula Nmax=⌈logα/log(1−γ)⌉Nmax=⌈logα/log(1−γ)⌉, depending only on the dissipation constant γγ and the collapse threshold αα. We provide a categorical framing via dagger compact closed categories, distinguish rigorously between proved results and postulates, and identify open problems including the dimensional obstruction to realizing the type axiom in finite-dimensional operator models.
This work introduces the foundations of an observer-dependent informational theory of physics.Rather than proposing a closed or final model, the paper establishes the conceptual and methodological architecture of a unified research program in which physical phenomena are described through observer-accessible informational states. The theory treats the observer as an integral component of physical description, rather than as an external disturbance or purely abstract entity.Information is defined operationally, as a relational construct linking observation, structure, and temporal coherence. The paper does not present new mathematical derivations.Instead, it provides a stable foundational framework that unifies a set of modular technical works, each addressing specific physical, cognitive, or interpretative problems. Mathematical formulations, empirical models, and testable predictions are delegated to the corresponding modular papers, allowing the theory to evolve through falsification and refinement without requiring repeated foundational revision. This contribution is intended as a foundational reference for an evolving observer-centered informational approach to physics.
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.
Scientific understanding proceeds through experiments that reveal how systems behave and through abstract models constructed to account for those behaviors. Persistent conceptual and philosophical confusions arise, however, when the distinction between empirical reality and its abstract representations is left implicit. This issue is particularly evident in the study of light, where multiple, mutually non-equivalent models coexist, each successful within specific limits, yet none capable of exhausting all observed phenomena. In this work, light is analyzed as a case study using the empirical–axiomatic self framework. Light is treated first as an empirical self: a system that exists and behaves in reality and constrains observation through experimental interaction. Experimental outcomes are taken as empirical facts, understood not as explanations but as constraints imposed by reality on representation. From these constraints, multiple axiomatic selves ray, wave, classical electromagnetic, particle, quantum, and quantum field models are constructed as abstract, internally coherent structures, each defined by assumptions and restricted domains of validity. The analysis shows that domains of validity are determined directly by experimental results and indirectly by comparison with more general axiomatic selves, though experimental constraint remains the ultimate authority. More general models clarify, but do not replace, earlier ones, explaining their success within restricted regimes. No axiomatic self, regardless of generality, is identified with the empirical self itself. By maintaining a strict distinction between empirical reality and abstract representation, the framework dissolves several long-standing philosophical confusions, including realism versus instrumentalism, wave–particle duality, theory replacement, determinism versus probability, and the measurement problem. These issues are shown to arise from category mistakes rather than from deep features of nature. Although light serves as the central example, the principles extracted are not specific to optical phenomena. The empirical–axiomatic distinction applies broadly across physical systems and extends naturally to complex systems. The work thus offers a clarified account of scientific understanding: to understand a system is to know the empirical constraints it imposes, the axiomatic structures used to represent it, the domains in which those structures apply, and the limits beyond which they fail.
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.