Building on the OCU-IPC framework (V3, Zenodo DOI: 10.5281/zenodo.19441390), we demonstrate that a single integer parameter α = 26 — coinciding with the critical dimension of bosonic string theory — determines a cascade of fundamental constants through information-theoretic optimization. The central equation Ṡ = ΔS·Θ/τ (derived as the unique gradient flow from three axioms) yields a communication threshold N_c ≈ 199 via the transcendental equation N_c = α·log₂(N_c+1). From α and N_c alone, we derive: (i) the fine-structure constant, 1/α_em = α·ln(N_c) − γ = 137.007 (0.02% accuracy); (ii) the proton-to-Planck mass ratio, ln(m_P/m_p) = 2(α − 4) = 44 (0.03% on logarithm); (iii) a qualitative hierarchy of all four fundamental forces via α_force = 1/(α·ln(N_eff)); (iv) the third law of thermodynamics from Θ(N=1) = 0 exactly; (v) the baryonic asymmetry η = 1/N_c⁴ = 6.42 × 10⁻¹⁰ (5% accuracy), linking matter-antimatter asymmetry to the dimensionality of spacetime via D = −ln(η)/ln(N_c) = 4.009. Combined with V3 results (4 anomalies resolved, 8σ consilience), the framework yields 19 testable predictions and reduces the 25+ free parameters of the Standard Model to one integer. Version 5 — April 2026 Author: Denis BERNARD Contact: phyborder838@gmail.com Keywords: quantum gravity, fine-structure constant, proton mass, hierarchy problem, gradient flow, computational optimization, information channel capacity, Euler-Mascheroni constant, bosonic string theory, baryonic asymmetry, third law of thermodynamics, consilience
Building on the OCU-IPC framework (V3, Zenodo DOI: 10.5281/zenodo.19441390), we demonstrate that a single integer parameter α = 26 — coinciding with the critical dimension of bosonic string theory — determines a cascade of fundamental constants through information-theoretic optimization. The central equation Ṡ = ΔS·Θ/τ (derived as the unique gradient flow from three axioms) yields a communication threshold N_c ≈ 199 via the transcendental equation N_c = α·log₂(N_c+1). From α and N_c alone, we derive: (i) the fine-structure constant, 1/α_em = α·ln(N_c) − γ = 137.007 (0.02% accuracy); (ii) the proton-to-Planck mass ratio, ln(m_P/m_p) = 2(α − 4) = 44 (0.03% on logarithm); (iii) a qualitative hierarchy of all four fundamental forces via α_force = 1/(α·ln(N_eff)); (iv) the third law of thermodynamics from Θ(N=1) = 0 exactly; (v) the baryonic asymmetry η = 1/N_c⁴ = 6.42 × 10⁻¹⁰ (5% accuracy), linking matter-antimatter asymmetry to the dimensionality of spacetime via D = −ln(η)/ln(N_c) = 4.009. Combined with V3 results (4 anomalies resolved, 8σ consilience), the framework yields 19 testable predictions and reduces the 25+ free parameters of the Standard Model to one integer. Version 5 — April 2026 Author: Denis BERNARD Contact: phyborder838@gmail.com Keywords: quantum gravity, fine-structure constant, proton mass, hierarchy problem, gradient flow, computational optimization, information channel capacity, Euler-Mascheroni constant, bosonic string theory, baryonic asymmetry, third law of thermodynamics, consilience
STATUS (18 October 2026). The research programme this paper belongs to — the finite-QEC substrate ("It from Bit") framework — was concluded in October 2026. The author's review found that the framework's Standard-Model content is assigned rather than derived and that no verified prediction yet distinguishes it from standard physics. The claim of a unified derivation is withdrawn. This paper's results are unaffected except where noted below. Current gravity work: 10.5281/zenodo.23458252. ERRATUM — fine-structure constant (18 October 2026). This paper quotes the framework's value of the fine-structure constant, α−1(0) = 137.035999106904 (or the earlier 137.035999077), as agreeing with experiment. That statement is withdrawn. (1) On 11 August 2026 the value was corrected to 137.0359991069051: the earlier figure came from an extrapolation fitted at the wrong order. Against current determinations the corrected value sits −2.26σ from the caesium-recoil value, +9.01σ from the rubidium-recoil value and +3.94σ from the electron-g−2 route. Those determinations disagree with one another, so no single agreement figure can be quoted [K13]. (2) The second-order coefficient behind the value was computed on a four-dimensional hypercubic lattice that the framework's own geometry does not supply. Recomputed on that geometry under a pre-registered procedure, the same formula gives 137.0359985927, 4.26 parts per billion below CODATA 2022, so the claimed agreement does not survive [G87, G88, 24 September 2026]. The bare count α0 = 1/137 used in the paper is a premise of the framework, not a derived result. NOTE ON SCOPE (18 October 2026). Where this paper says that the Standard Model's matter content, charges or gauge structure are derived from, forced by or emerge from the eight-bit error-correcting cell, read encoded in or assigned to. The finite results themselves stand: the code, its constraints and the anomaly arithmetic are exact. But two things are premises of the framework, not consequences: the identification of codewords with particles, and the choice of the eight-bit [8,4,4] cell. In particular, the step from read/write balance to a single CSS code is not derived [R22]. The author's October 2026 review of the programme concluded that the framework's Standard-Model content is assigned rather than derived. No observation currently distinguishes the framework's account from the Standard Model itself. Noted: as an intuition layer, the paper's readings of Standard-Model content as code structure are assignments (see the note on scope above); its fine-structure value is corrected by the erratum above; and its gravity route is conditional [G89, G99]. This article is the intuition layer for the finite quantum-error-correction (QEC) substrate programme. It is written for a reader who knows some quantum mechanics, special relativity, and the Standard Model vocabulary, but who is new to this framework. The aim is not to replace the equations of quantum theory, quantum field theory, or general relativity. The aim is to supply a coherent picture: physical objects are read as stable quantum records; particles are protected patterns in a finite code; interactions are operations on those records; and the classical world is the part of the quantum world that has become robust enough to remember itself. The paper deliberately separates three levels. First, there is standard physics which this framework uses rather than challenges: Hilbert space, amplitudes, decoherence, gauge fields, and relativistic propagation. Second, there are coding-theoretic and combinatorial claims, especially the emergence of the minimal balanced [8,4,4] record cell. Third, there are speculative or conditional bridges to particle spectra, dark-sector physics, gravity, and cosmology. The closing appendix is a field guide to hard questions: for each one it states what the Standard Model says, why that answer is conceptually incomplete or technically hard, and what this framework offers instead.
Abstract For over a century, theoretical physics has treated General Relativity and Quantum Mechanics as fundamentally incompatible: one posits a continuous, deterministic spacetime manifold; the other, a discrete, probabilistic Hilbert space. The Algorithmic Reality Model (ARM) resolves this schism by identifying a single computational mechanism—the Zeno Threshold (Zα)—as the universal bound governing both quantum collapse and spacetime geometry. ARM treats physical reality as the macroscopic projection of a finite-bandwidth computational substrate operating on a timeless, pre-geometric state (the Singleton). By enforcing Landauer's principle of irreversible erasure, ARM derives the entirety of the gravitational sector from seven pre-geometric, quantum informational axioms. Key Derivations & Unifications Emergent Spacetime: Spatial geometry emerges from the Quantum Fisher Information Metric (QFIM) of the observer's state space, while time emerges from the Tomita-Takesaki modular flow. The Lorentzian signature (-,+,+,+) is algebraically forced by the compact/non-compact structure of their isometry generators. The Holographic Scalar (The 3→1 Unification): Applying the Nyquist-Shannon sampling theorem to the holographic boundary yields the exact Bekenstein-Hawking factor of 1/4 as a universal 2D anti-aliasing limit. This simultaneously fixes the area-law coefficient and structurally derives Newton's constant as G = c3ξmin2 / ℏ. Systematic Boundary Deviations: The framework quantitatively resolves macroscopic anomalies as computational resolution limits. Dark energy emerges as the minimum Landauer maintenance cost of the cosmological event horizon, and the MOND acceleration scale (a0) emerges as a thermodynamic noise floor, algebraically locked by the structural identity a02 = (8πG/3)ρΛ. Thermodynamic State Truncation: Wavefunction collapse, the black hole information paradox, and EPR non-locality are rigorously unified as manifestations of the computational substrate's finite Landauer memory budget. Computational Computability Because ARM is built on discrete informational axioms rather than continuous manifolds, the entire framework is natively computable. The structural derivations in this paper—including emergent geodesic lensing, the Bekenstein-Hawking threshold, and the MOND noise floor—have been explicitly verified via sparse Hermitian lattice simulations. The complete open-source computational validation suite is available at: github.com/srdrymn/algorithmic-reality-model-validations This manuscript represents the master synthesis and culmination of the Algorithmic Theory of Reality (ATR) foundational framework.
We present the complete mathematical foundations of New Subquantum Informational Mechanics (NMSI), demonstrating that fundamental physical concepts—mass, energy, gravitational force, spacetime geometry—are not ontological primitives but emergent properties of a deeper informational substrate. Through rigorous construction of the π-indexed Riemann Oscillatory Network (RON) and axiomatic derivation of informational dynamics, we establish that information, not energy, constitutes the fundamental substrate of physical reality. The framework derives the emergence of fundamental constants (ħ, c, G) from RON spectral structure, establishes precise connections to Riemann zeta function zeros ζ(1/2 + itn), and predicts the existence of architectural thresholds at L* ≈ 24 significant digits. NMSI resolves long-standing conceptual paradoxes of modern physics—wave-particle duality, wavefunction collapse, spacetime nature—by reducing them to elementary informational phenomena formulated in rigorous operator-theoretic language. The mathematical framework includes complete proofs for: 1) necessity of informational substrate (no-go theorem for matter-first ontologies), 2) uniqueness of 3 + 1 dimensional spacetime (stability analysis), 3) derivation of Einstein field equations from informational action principle (all steps explicit), 4) emergence of Standard Model gauge structure SU(3) × SU(2) × U(1), and 5) generation mass hierarchy from RON spectral properties. A critical component is the Mathematical Trap construction (Part E)—seven theorems establishing a Point of No Return beyond which NMSI predictions become inevitable, explaining the framework’s multiple discrete falsifiable predictions. Ten falsifiable experimental predictions are presented with explicit timelines (2025-2035), instrumentation requirements, and statistical significance thresholds: hydrogen 1S-2S spectroscopy shifts (Δν = 2.8 ± 1.2 Hz), atomic interferometry phase measurements (δφ ≈ 10−8 rad), cosmological distance-redshift deviations (δ(z) = −0.15z2 for z > 3), stellar mass upper bounds (mstar M☉), CMB phase correlations ( C l phase ~ 10−6 for l H0: 67 vs 73 km/s/Mpc), JWST observations of massive high-redshift galaxies (z > 10), and reinterprets dark matter and dark energy as informational phenomena rather than exotic particle species. All results maintain consistency with established physics (quantum mechanics, general relativity, Standard Model) while predicting novel effects at precision frontiers and extreme scales.
--- VERSION 3.0 MAJOR REVISION UPDATE (JUNE 2026) --- This manuscript has been comprehensively updated to Version 3.0. This major revision transitions the framework from a static dimensional scaling model into a dynamic, non-linear field theory. Key Additions: The Hambardzumian Substrate Equation: A formalized, non-linear Schrödinger-Newton system that scales gravito-electromagnetic self-attraction by 1/α using exclusively fundamental constants. Analytical Soliton Convergence: Direct mathematical derivation showing the collapsed wave substrate naturally stabilizes at the exact spatial radius of the classical electron (re). Temporal Collapse Constant: Derived an instantaneous wave-to-particle localization timeframe (τ≈1.76×10−19 s) that perfectly matches the intrinsic Zitterbewegung frequency of the electron field. Falsifiable Laboratory Target: Establishes a definitive, low-energy vertical boundary condition for wave function collapse at exactly 3,730 eV (soft X-rays), offering a concrete path for terrestrial experimental verification. [The original Version 1.0 abstract follows below] We propose a reframing of the relationship between quantum mechanics and general relativity,and present a parameter-free analytical expression for the hierarchy problem as a consequenceof that reframing. Rather than treating quantum mechanics and general relativity as twoincompatible theories requiring reconciliation, we argue they are two categorical expressions ofa single underlying field — the same fundamental substrate viewed from opposite sides of athreshold. Wave and particle states are not two behaviors of the same object but two entirelydifferent modes of existence separated by a hard binary boundary. A particle is not a wave thathas been measured — it is a concentration of the wave field that has crossed a critical threshold,analogous to the way sufficient spacetime curvature produces a black hole event horizon. Weshow that both thresholds — the quantum-classical boundary and the event horizon — arestructurally identical: both are the unique dimensionless threshold condition available in theirrespective theories, both produce hard binary phase transitions, and both are expressions of thesame substrate at different scales. From the scale separation between the two thresholds wederive the expression: Hierarchy = alpha x (m_P / m_e)^2, which produces the correctelectromagnetic-to-gravitational force ratio of 10^42 with no free parameters, to within 0.015%precision. This result is consistent with the framework being correct and motivates theexperimental test that would constitute proof: a discrete, reproducible collapse of wave behaviorat approximately 3,730 eV of electromagnetic field energy — derived from existing constantswith no free parameters — which standard quantum mechanics does not predict and thethreshold model specifically does.
A central open problem at the intersection of quantum information theory, quantum thermodynamics, and many-body physics is determining the exact mathematical conditions under which the information-geometric distance d_g(ρ, σ) between two quantum states coincides with the minimum physical resource and thermodynamic cost 𝒱(ρ → σ) required to transform one into the other. In this paper, we establish the Extended Quantum Information Geometry System (EQIGS), a unified deductive framework synthesizing Petz monotone Riemannian metrics, quantum resource theories, finite-time thermodynamic length bounds, and tensor-network submanifold geometry, anchored directly in our 71-page ZFC Master Reference Monograph (Lee, 2026, DOI: 10.5281/zenodo.23486681) [1]. All foundational spaces and universal constants 𝔘 = (𝒯_0x8A2C, C_UPTC, η_friction, ε_SHID) follow Proposition 1.5, Theorem 2.9, Lemma 4.5, Lemma 4.6, Lemma 5.2, Lemma 6.3, Lemma 8.4, Lemma 8.6, Theorem 8.7, and Theorem 9.5 of [1]. Regularizing the quantum state space 𝒮(ℬ) on the Takesaki Type II_1 ground factor (𝓜_ground, τ_ground) and the Fractional Sobolev–Colombeau Quotient Algebra 𝓖^α(𝒮), we formulate six core axioms (EQIGS-1 through EQIGS-6) and prove six fundamental theorems: (1) Complete Chentsov–Petz Monotone Metric Classification regularized at pure-state boundaries via ε(α) = exp(-1/(1-α)); (2) Exact Necessary and Sufficient Conditions for Information Distance–Physical Cost Equivalence and Tight Finite-Time Control Bounds governed by Planck-BCH arithmetic friction η_friction ≥ 10^-22; (3) Quantum Cauchy–Schwarz Thermodynamic Length Lower Bounds (Σ_na ≥ ℓ_g^2 / (2τ)); (4) Multipartite Entanglement Witnessing via Quantum Fisher Information Curvature Thresholds (ℱ_Q(ρ, H) > 4(Δh)^2 N); (5) Natural Choi–Bures Information Metrics on the Quantum Channel Space Chan(ℬ) and Isometric Reversibility; and (6) Exact Curvature–Volume Formulas for Bond-Dimension-D Tensor Network Manifolds and Area-to-Volume Law Phase Transitions at C_UPTC. Complete Python numerical verification is provided in Appendix A.
A central challenge at the frontier of theoretical physics is transforming qualitative analogies connecting quantum information, spacetime geometry, non-equilibrium thermodynamics, and quantum measurement into exact, falsifiable dynamical equations with proven domains of validity. In this paper, we establish Unified Information–Geometry–Dynamics Physics (UIGDP), a deductive physical framework anchored in our 71-page ZFC Master Reference Monograph (Lee, 2026, DOI: 10.5281/zenodo.23486681) [1] and synthesized with the Extended Quantum Information Geometry System (EQIGS, DOI: 10.5281/zenodo.23557698) [6], the High-Dimensional Geometric Probability System (HDGPS, DOI: 10.5281/zenodo.23557360) [4], and the Dynamic Topological Critical Transition System (DTCTS, DOI: 10.5281/zenodo.23557507) [5]. Condensing local Type III₁ quantum field algebras onto the Takesaki Type II₁ ground factor (ℳ_ground, τ_ground) governed by the universal quadruple 𝔘 = (𝒯_0x8A2C, 𝐂_UPTC, η_friction, ϵ_SHID), we formulate six core axioms (UIGDP-1 through UIGDP-6) and prove six fundamental theorems: (1) Necessary and Sufficient Curvature–Entanglement Conditions for reconstructing spacetime metric tensors g_μν^spacetime from Petz quantum Fisher information Hessians; (2) The Exact Unified IGD Master Cost Identity and Optimal Finite-Time Control Horizon τ⋆ = √((d_g² + Δ_ctrl²)/(2η_friction)); (3) Emergent Einstein–Cartan–Information Field Equations from modular entanglement equilibrium and Area-to-Volume phase transitions at D_crit = e^(𝐂_UPTC); (4) Dynamical Resolution of Quantum Measurement Projection via the URRHC Idempotent Monad 𝕄_URRHC (T² = T) with a testable dephasing floor; (5) Universal State Classification for Far-from-Equilibrium and Active Matter via Thermodynamic Length and Topological Persistence Dissipation; and (6) Quantum Simulator Advantage Thresholds under noise and control deficits. Complete Python numerical verification is provided in Appendix A.