Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

It from Bit, Bit from Fit: Foundational Physics Logically Remastered

Longmire, James (JD)

Published Dec 1, 2025• 0 citations
Publisher

Abstract

Every physical measurement ever conducted has yielded exactly one outcome: self-identical, non-contradictory, determinate. This paper argues that the Three Fundamental Laws of Logic (Identity, Non-Contradiction, and Excluded Middle) are not cognitive conventions but ontological constraints constitutive of physical distinguishability. From this thesis, quantum mechanics emerges as the unique stable structure at the interface between non-Boolean possibility and Boolean actuality. The framework derives rather than postulates: complex Hilbert space structure follows from interface constraints combined with the physical requirement of compositional consistency (local tomography); the Born rule follows from Gleason's theorem; unitary dynamics follows from information preservation requirements. One structural prediction, that quantum mechanics requires complex amplitudes, has been experimentally confirmed (Renou et al., 2021). The framework specifies twelve explicit conditions that would falsify it. Logic Realism Theory provides unified explanation for seventeen quantum phenomena that other interpretations treat as independent postulates, while maintaining realism, locality, and parsimony.

DOI
10.5281/zenodo.17778399

Related papers

Logic Realism Theory: Philosophical Foundations

James (JD) Longmire

Logic Realism Theory (LRT) proposes that the Three Fundamental Laws of Logic (3FLL)—Identity, Non-Contradiction, and Excluded Middle—are not merely rules of reasoning but ontological constraints constitutive of physical distinguishability. The core evidence is an asymmetry: we can conceive of 3FLL violations, yet physical reality never produces them. This asymmetry indicates that 3FLL constrain reality, not merely cognition. This paper develops the philosophical foundations of this claim. We argue that: (1) 3FLL have a dual character, functioning both epistemically and ontologically; (2) quantum mechanics emerges as the unique "interface" structure mediating between non-Boolean possibility and Boolean actuality; (3) this framework resolves longstanding interpretive puzzles while maintaining scientific realism. The result is a form of structural realism grounded in logical necessity rather than contingent physical law.

•Dec 1, 2025•0 citations

The Continuity of Being: An Ontological Derivation of Quantum Mechanics

Guillermo C. Barraza

This work presents a rigorous derivation of quantum mechanics from purely a priori ontological principles, a result not previously achieved within a single self-contained framework. Beginning with the apodictically certain proposition "I am"—immune to all doubt through performative contradiction—we establish through necessary deduction the Principle of Ontological Continuity (POC): Being is continuous and cannot cease or arise ex nihilo. From this single ontological foundation, the complete mathematical structure of quantum mechanics emerges as necessary consequence. We demonstrate that any mathematical representation of ontological continuity must have Hilbert space structure, that ontological conservation necessarily implies unitary evolution, and that the Schrödinger equation follows via Stone's theorem as mathematical necessity, not empirical postulate. The Born rule is derived through three independent converging arguments (Gleason's theorem, direct conservation requirements, and Zurek's envariance), establishing quantum probability as ontological necessity rather than interpretative supplement. Classical foundational problems—wave function collapse, the measurement problem, Bell's non-locality—are resolved without additional assumptions. Collapse emerges as effective description of decoherence; the observer is reconceptualized as self-aware subsystem without ontological dualism; Bell violations confirm ontological unity rather than presenting paradox. Quantum phenomena—superposition as ontological potentiality, tunneling as manifestation of continuity, Pauli exclusion as consequence of ontological structure—are shown to be necessary rather than mysterious. The work establishes quantum mechanics with apodictic certainty mediated through deductive necessity, demonstrating that quantum reality could not have been otherwise. This monograph integrates foundational ontology, mathematical formalism, and resolution of interpretative problems within unified self-contained framework. It deliberately closes at non-relativistic quantum mechanics, establishing stable foundation for future extensions (quantum field theory, general relativity, quantum gravity, normative ethics).

•Jan 27, 2025•0 citations

LRT Constraints on QFT: Deriving Fock Structure and Interpreting Renormalization from Logical Foundations

James (JD) Longmire

Logic Realism Theory (LRT) derives non-relativistic quantum mechanics from the claim that the Three Fundamental Laws of Logic are ontological constraints constitutive of physical distinguishability. This paper extends LRT to quantum field theory through a tiered derivation structure with explicit physical inputs at each level. We establish three principal results: (1) Fock space structure is derived from LRT axioms plus Lorentz invariance and locality; (2) the spin-statistics connection follows from Lorentz invariance and microcausality via the standard Pauli argument; (3) the uniqueness of complex QFT is established. The paper distinguishes derivations from interpretations. Cluster decomposition, vacuum uniqueness, and the spectral gap are physical inputs (Tier 4), not consequences of logical constraints. Renormalization is interpreted as 3FLL-restoration at UV scales, but this does not derive renormalization group equations. Four predictions and six strong falsifiers are identified.

•Dec 1, 2025•0 citations

Logic Realism Theory: Non-Decomposability, Entanglement, and Bell's Theorem Derived from A_Ω = L₃(I∞)

James (JD) Longmire

This working paper derives quantum non-decomposability, Bell's theorem, and Kochen-Specker contextuality from Logic Realism Theory's single foundational equation A_Ω = L₃(I∞), where I∞ is the Infinite Information Space, L₃ is the Three Fundamental Laws of Logic acting as a selection functional, and A_Ω is the actualized domain. The paper establishes that LRT is a one-equation theory: all results are downstream of the core equation with no independent primitives introduced. Key results: (1) the Unique Necessary Successor (UNS) constraint is derived as a theorem of L₃ via Identity and Excluded Middle, tightened by Leibniz Identity of Indiscernibles; (2) quantum probability is reinterpreted as epistemic underdetermination of state description, with the Born rule as the unique consistent measure over incomplete descriptions via Gleason; (3) the Joint Resolution Condition (JRC) is proved equivalent to Schmidt rank > 1, establishing that entangled states are logically forced by tensor product structure; (4) the Non-Decomposability Theorem shows that decomposing a JRC-satisfying configuration into local sub-descriptions necessarily violates Excluded Middle; (5) Bell's theorem and Kochen-Specker contextuality follow as downstream consequences. LRT is distinguished from hidden variable programs (Bohm, 't Hooft) by its grounding direction: from logic to physics, not from physics to supplemented physics. Three open formalizations for Lean 4 are identified.

•Mar 11, 2026•0 citations

A Rigorous Derivation of All Core Postulates of Quantum Mechanics from the Single Axiom of Binary Distinction

Xiaoqing Ou

This paper provides a rigorous derivation of all core postulates of quantum mechanics from a single axiom: the existence of binary distinction. No prior assumptions—Hilbert space, wave function, probability amplitude, or unitary evolution—are introduced as external inputs. The derivation proceeds in six chapters: Chapter 1 establishes the axiom of binary distinction and proves that the imaginary unit i is the algebraic necessity of iterative distinction operations: Δ applied twice equals a reversal (-1), therefore one distinction corresponds to multiplication by i. Chapter 2 demonstrates that complex probability amplitudes are the unique algebraic carriers of the binary split between confirmed information (real part) and concealed information (imaginary part). Chapter 3 proves the Born rule as the unique solution to information deviation minimization under truncation constraints—the squared modulus is the sole functional form compatible with positivity, normalization, and classical-degenerate compatibility. Chapter 4 derives unitary evolution as the traversal of all indistinguishable paths during the suspension interval between confirmation operations. Schr\"{o}dinger's equation emerges as the differential limit of this traversal under modular flow. Chapter 5 establishes that measurement collapse is not a mysterious nonunitary process but the re-execution of the confirmation operation, projecting the suspended superposition onto a single confirmed eigenstate. The collapse probability is identical to the Born rule derived in Chapter 3. Chapter 6 demonstrates that quantum entanglement is the split-window projection of a shared confirmation projector—two entangled particles share the same confirmation projection in the full-dimensional information field, and spatial separation is merely the appearance of local windows in the observable domain. Bell inequality violation follows directly from the non-homomorphic property of the truncation projection. The entire formalism emerges without fitting parameters, without interpretation debates, and without external physical assumptions. Quantum mechanics is thus revealed not as the fundamental language of the universe, but as the inevitable cognitive structure of any finite observer executing information confirmation and truncation on the full-dimensional information field. All conclusions are strictly demarcated by a "boundary of honesty," distinguishing logically necessary deductions from directional inferences requiring further mathematical hardening.

•May 22, 2026•0 citations

Deriving the Born Rule from Logical Constraint: A Logic Realism Theory Approach

James (JD) Longmire

We present a derivation of the Born rule from the ontological constraints imposed by the Three Fundamental Laws of Logic (L₃) within the Logic Realism Theory (LRT) framework. The central argument proceeds through five stages: (1) L₃ constraints at the vehicle level require that physical systems possess determinate dispositions toward measurement outcomes; (2) these dispositions must satisfy vehicle‑weight invariance—probability assignments cannot depend on the descriptive decomposition chosen; (3) vehicle‑weight invariance, combined with finite additivity, yields the premises of Gleason‑type theorems; (4) Gleason’s theorem then forces the trace form μ(P) = Tr(ρP) for all projectors; (5) for pure states, this reduces to the Born rule p = |⟨φ|ψ⟩|².[Attachment] We provide both an intuitive derivation chain and a formal axiom presentation (A1–A7) suitable for rigorous development. The derivation is non‑circular: L₃ constraints are conceptually and logically prior to the probability measure they entail. We situate this result within the quantum reconstruction literature and discuss implications for foundational physics.

•Feb 24, 2026•0 citations
Every physical measurement ever conducted has yielded exactly one outcome: self-identical, non-contradictory, determinate. This paper argues that the Three Fundamental Laws of Logic (Identity, Non-Contradiction, and Excluded Middle) are not cognitive conventions but ontological constraints constitutive of physical distinguishability. From this thesis, quantum mechanics emerges as the unique stable structure at the interface between non-Boolean possibility and Boolean actuality. The framework derives rather than postulates: complex Hilbert space structure follows from interface constraints combined with the physical requirement of compositional consistency (local tomography); the Born rule follows from Gleason's theorem; unitary dynamics follows from information preservation requirements. One structural prediction, that quantum mechanics requires complex amplitudes, has been experimentally confirmed (Renou et al., 2021). The framework specifies twelve explicit conditions that would falsify it. Logic Realism Theory provides unified explanation for seventeen quantum phenomena that other interpretations treat as independent postulates, while maintaining realism, locality, and parsimony.
Logic Realism Theory (LRT) proposes that the Three Fundamental Laws of Logic (3FLL)—Identity, Non-Contradiction, and Excluded Middle—are not merely rules of reasoning but ontological constraints constitutive of physical distinguishability. The core evidence is an asymmetry: we can conceive of 3FLL violations, yet physical reality never produces them. This asymmetry indicates that 3FLL constrain reality, not merely cognition. This paper develops the philosophical foundations of this claim. We argue that: (1) 3FLL have a dual character, functioning both epistemically and ontologically; (2) quantum mechanics emerges as the unique "interface" structure mediating between non-Boolean possibility and Boolean actuality; (3) this framework resolves longstanding interpretive puzzles while maintaining scientific realism. The result is a form of structural realism grounded in logical necessity rather than contingent physical law.
This work presents a rigorous derivation of quantum mechanics from purely a priori ontological principles, a result not previously achieved within a single self-contained framework. Beginning with the apodictically certain proposition "I am"—immune to all doubt through performative contradiction—we establish through necessary deduction the Principle of Ontological Continuity (POC): Being is continuous and cannot cease or arise ex nihilo. From this single ontological foundation, the complete mathematical structure of quantum mechanics emerges as necessary consequence. We demonstrate that any mathematical representation of ontological continuity must have Hilbert space structure, that ontological conservation necessarily implies unitary evolution, and that the Schrödinger equation follows via Stone's theorem as mathematical necessity, not empirical postulate. The Born rule is derived through three independent converging arguments (Gleason's theorem, direct conservation requirements, and Zurek's envariance), establishing quantum probability as ontological necessity rather than interpretative supplement. Classical foundational problems—wave function collapse, the measurement problem, Bell's non-locality—are resolved without additional assumptions. Collapse emerges as effective description of decoherence; the observer is reconceptualized as self-aware subsystem without ontological dualism; Bell violations confirm ontological unity rather than presenting paradox. Quantum phenomena—superposition as ontological potentiality, tunneling as manifestation of continuity, Pauli exclusion as consequence of ontological structure—are shown to be necessary rather than mysterious. The work establishes quantum mechanics with apodictic certainty mediated through deductive necessity, demonstrating that quantum reality could not have been otherwise. This monograph integrates foundational ontology, mathematical formalism, and resolution of interpretative problems within unified self-contained framework. It deliberately closes at non-relativistic quantum mechanics, establishing stable foundation for future extensions (quantum field theory, general relativity, quantum gravity, normative ethics).
Logic Realism Theory (LRT) derives non-relativistic quantum mechanics from the claim that the Three Fundamental Laws of Logic are ontological constraints constitutive of physical distinguishability. This paper extends LRT to quantum field theory through a tiered derivation structure with explicit physical inputs at each level. We establish three principal results: (1) Fock space structure is derived from LRT axioms plus Lorentz invariance and locality; (2) the spin-statistics connection follows from Lorentz invariance and microcausality via the standard Pauli argument; (3) the uniqueness of complex QFT is established. The paper distinguishes derivations from interpretations. Cluster decomposition, vacuum uniqueness, and the spectral gap are physical inputs (Tier 4), not consequences of logical constraints. Renormalization is interpreted as 3FLL-restoration at UV scales, but this does not derive renormalization group equations. Four predictions and six strong falsifiers are identified.
This working paper derives quantum non-decomposability, Bell's theorem, and Kochen-Specker contextuality from Logic Realism Theory's single foundational equation A_Ω = L₃(I∞), where I∞ is the Infinite Information Space, L₃ is the Three Fundamental Laws of Logic acting as a selection functional, and A_Ω is the actualized domain. The paper establishes that LRT is a one-equation theory: all results are downstream of the core equation with no independent primitives introduced. Key results: (1) the Unique Necessary Successor (UNS) constraint is derived as a theorem of L₃ via Identity and Excluded Middle, tightened by Leibniz Identity of Indiscernibles; (2) quantum probability is reinterpreted as epistemic underdetermination of state description, with the Born rule as the unique consistent measure over incomplete descriptions via Gleason; (3) the Joint Resolution Condition (JRC) is proved equivalent to Schmidt rank > 1, establishing that entangled states are logically forced by tensor product structure; (4) the Non-Decomposability Theorem shows that decomposing a JRC-satisfying configuration into local sub-descriptions necessarily violates Excluded Middle; (5) Bell's theorem and Kochen-Specker contextuality follow as downstream consequences. LRT is distinguished from hidden variable programs (Bohm, 't Hooft) by its grounding direction: from logic to physics, not from physics to supplemented physics. Three open formalizations for Lean 4 are identified.
This paper provides a rigorous derivation of all core postulates of quantum mechanics from a single axiom: the existence of binary distinction. No prior assumptions—Hilbert space, wave function, probability amplitude, or unitary evolution—are introduced as external inputs. The derivation proceeds in six chapters: Chapter 1 establishes the axiom of binary distinction and proves that the imaginary unit i is the algebraic necessity of iterative distinction operations: Δ applied twice equals a reversal (-1), therefore one distinction corresponds to multiplication by i. Chapter 2 demonstrates that complex probability amplitudes are the unique algebraic carriers of the binary split between confirmed information (real part) and concealed information (imaginary part). Chapter 3 proves the Born rule as the unique solution to information deviation minimization under truncation constraints—the squared modulus is the sole functional form compatible with positivity, normalization, and classical-degenerate compatibility. Chapter 4 derives unitary evolution as the traversal of all indistinguishable paths during the suspension interval between confirmation operations. Schr\"{o}dinger's equation emerges as the differential limit of this traversal under modular flow. Chapter 5 establishes that measurement collapse is not a mysterious nonunitary process but the re-execution of the confirmation operation, projecting the suspended superposition onto a single confirmed eigenstate. The collapse probability is identical to the Born rule derived in Chapter 3. Chapter 6 demonstrates that quantum entanglement is the split-window projection of a shared confirmation projector—two entangled particles share the same confirmation projection in the full-dimensional information field, and spatial separation is merely the appearance of local windows in the observable domain. Bell inequality violation follows directly from the non-homomorphic property of the truncation projection. The entire formalism emerges without fitting parameters, without interpretation debates, and without external physical assumptions. Quantum mechanics is thus revealed not as the fundamental language of the universe, but as the inevitable cognitive structure of any finite observer executing information confirmation and truncation on the full-dimensional information field. All conclusions are strictly demarcated by a "boundary of honesty," distinguishing logically necessary deductions from directional inferences requiring further mathematical hardening.
We present a derivation of the Born rule from the ontological constraints imposed by the Three Fundamental Laws of Logic (L₃) within the Logic Realism Theory (LRT) framework. The central argument proceeds through five stages: (1) L₃ constraints at the vehicle level require that physical systems possess determinate dispositions toward measurement outcomes; (2) these dispositions must satisfy vehicle‑weight invariance—probability assignments cannot depend on the descriptive decomposition chosen; (3) vehicle‑weight invariance, combined with finite additivity, yields the premises of Gleason‑type theorems; (4) Gleason’s theorem then forces the trace form μ(P) = Tr(ρP) for all projectors; (5) for pure states, this reduces to the Born rule p = |⟨φ|ψ⟩|².[Attachment] We provide both an intuitive derivation chain and a formal axiom presentation (A1–A7) suitable for rigorous development. The derivation is non‑circular: L₃ constraints are conceptually and logically prior to the probability measure they entail. We situate this result within the quantum reconstruction literature and discuss implications for foundational physics.