This manuscript introduces a unified theoretical and empirical framework proposing that fundamental physical laws, gauge symmetries, and cosmological dynamics emerge as algorithmic resource-optimization protocols operating on an information-bounded substrate. By bridging quantum information theory, discrete lattice physics, and the Two-State Vector Formalism (TSVF), the paper transitions computational ontologies from speculative metaphysics into mathematically formalized, experimentally falsifiable physics. Key Frameworks & Contributions: Algorithmic Resource Optimization & Substrate Invariants: We map foundational principles to computational conservation laws: the Principle of Stationary Action ($\delta S = 0$) to dynamic programming; invariant light-cone speed ($c$) to distributed causal latency; and quantum superposition to procedural deferred state resolution. We introduce formal substrate calibration parameters, including the information rest-mass invariant ($M_i \approx 2.91 \times 10^{-40}\text{ kg}$ at $300\text{ K}$), holographic spacetime code distance density ($D_{code}$), and multi-fidelity coarse-graining bounds ($\Omega_{MF}$). Algorithmic Quantum Dynamics & State-Space Pruning: We formulate Algorithmic State-Space Pruning, establishing that quantum microstate branching in open systems is biased toward algorithmically compressible states governed by a Solomonoff-Levin distribution, modifying microcanonical equiprobability in non-isolated regimes. Post-Selected Quantum Cosmology (POQCO): Within a unimodular gravity framework, late-time cosmic acceleration is derived directly from a future cosmological boundary constraint (macroscopic post-selection), eliminating the necessity of an ad hoc dark energy fluid or cosmological constant $\Lambda$. We extract explicit cosmographic signatures, predicting an effective phantom divide crossing ($w < -1$ at $z \approx 0.5$) and a characteristic discontinuous jerk parameter ($j \approx 3$). Four Falsifiable Empirical Protocols: To subject the framework to immediate laboratory and observational verification, we detail four experimental designs: • Quantum Computing: A 128-qubit superconducting transmon processor under ergodic Floquet drives to measure low Kolmogorov-complexity bitstring branching excesses across $10^6$ shots. • Optomechanical Metrology: A cryogenic 4-pulse radiation-pressure Fabry-Pérot cavity coupled to a stoichiometric silicon nitride ($\text{Si}_3\text{N}_4$) membrane to detect anomalous geometric phase shifts ($\Delta\Theta$) from minimal-length commutator deformations. • Cold-Atom Interferometry: $^{87}\text{Rb}$ atomic drift tubes utilizing non-destructive weak measurements to isolate terminal boundary-induced peak acceleration ($a_{weak}$). • Observational Cosmography: Testing POQCO kinematic transition regimes against high-redshift datasets from the Nancy Grace Roman Space Telescope, DESI Baryon Acoustic Oscillations (BAO), and Cosmic Chronometers.
This manuscript introduces a unified theoretical and empirical framework proposing that fundamental physical laws, gauge symmetries, and cosmological dynamics emerge as algorithmic resource-optimization protocols operating on an information-bounded substrate. By bridging quantum information theory, discrete lattice physics, and the Two-State Vector Formalism (TSVF), the paper transitions computational ontologies from speculative metaphysics into mathematically formalized, experimentally falsifiable physics. Key Frameworks & Contributions: Algorithmic Resource Optimization & Substrate Invariants: We map foundational principles to computational conservation laws: the Principle of Stationary Action (δS=0) to dynamic programming; invariant light-cone speed (c) to distributed causal latency; and quantum superposition to procedural deferred state resolution. We introduce formal substrate calibration parameters, including the information rest-mass invariant (Mi≈2.91×10−40 kg at 300 K), holographic spacetime code distance density (Dcode), and multi-fidelity coarse-graining bounds (ΩMF). Algorithmic Quantum Dynamics & State-Space Pruning: We formulate Algorithmic State-Space Pruning, establishing that quantum microstate branching in open systems is biased toward algorithmically compressible states governed by a Solomonoff-Levin distribution, modifying microcanonical equiprobability in non-isolated regimes. Post-Selected Quantum Cosmology (POQCO): Within a unimodular gravity framework, late-time cosmic acceleration is derived directly from a future cosmological boundary constraint (macroscopic post-selection), eliminating the necessity of an ad hoc dark energy fluid or cosmological constant Λ. We extract explicit cosmographic signatures, predicting an effective phantom divide crossing (w<−1 at z≈0.5) and a characteristic discontinuous jerk parameter (j≈3). Four Falsifiable Empirical Protocols: To subject the framework to immediate laboratory and observational verification, we detail four experimental designs: • Quantum Computing: A 128-qubit superconducting transmon processor under ergodic Floquet drives to measure low Kolmogorov-complexity bitstring branching excesses across 106 shots. • Optomechanical Metrology: A cryogenic 4-pulse radiation-pressure Fabry-Pérot cavity coupled to a stoichiometric silicon nitride (Si3N4) membrane to detect anomalous geometric phase shifts (ΔΘ) from minimal-length commutator deformations. • Cold-Atom Interferometry: 87Rb atomic drift tubes utilizing non-destructive weak measurements to isolate terminal boundary-induced peak acceleration (aweak). • Observational Cosmography: Testing POQCO kinematic transition regimes against high-redshift datasets from the Nancy Grace Roman Space Telescope, DESI Baryon Acoustic Oscillations (BAO), and Cosmic Chronometers.
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.
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.
ISA v5f (Informational Systemic Actualization, final release) is a mathematically rigorous effective field theory that reconstructs General Relativity (GR) and Quantum Theory (QT) from a single variational principle defined on a statistical manifold of logical states M_ISA. Addressing the ontological fragmentation of standard physics, this framework replaces disjoint primitives (spacetime metrics, wavefunctions, ad hoc measurement postulates) with two operatized quantities: the logical bandwidth W_max(μ) and the density of actualized connections ρ_ISA(x). Reality is modeled as a network of logical correlations whose actualization rate is fundamentally bounded by W_max. When correlation density exceeds a critical threshold Θ, abstract probabilistic potentials transition to actualized relational facts. From the master functional S_ISA, Einstein’s field equations are derived via metric variation, while the Schrödinger equation and canonical commutation relations emerge from constrained geodesic flow under finite W_max. The measurement process is formalized as a nonlinear stochastic Lindblad dynamics, from which the Born rule is rigorously derived via martingale convergence, eliminating ad hoc collapse postulates. The framework resolves several foundational and cosmological tensions: • Hubble tension: Alleviated via a dynamic logarithmic dark energy equation of state w(a), shifting inferred H_0 to 72.8 ± 0.9 km/s/Mpc when fitted to Planck+SH0ES data. • Dark matter: Emerges as a geometric response to background logical density gradients, naturally explaining galactic rotation curves and Bullet Cluster separation without new particle species. • Black hole entropy: Predicts a rigid logarithmic correction α_ISA = −1, distinct from standard quantum gravity estimates. • Baryon asymmetry: Framed as a topological bias during the ρ_ISA → ρ_eq phase transition. All phenomenological deviations scale with W_max^(−2) or the dimensionless factor Z(μ). No free parameters are introduced per phenomenon. Explicit falsifiability thresholds, experimental calibration protocols (based on Margolus–Levitin bounds in superconducting transmons and optical clocks), and a cross-validation matrix are provided. The theory preserves microcausality, ensemble unitarity, and reduces exactly to standard GR and QT in the limits W_max → ∞ and ħ → 0. This release contains the complete theoretical manuscript, supplementary derivations (Appendices A–I), calibration protocols, cross-validation matrices, and numerical implementation details. All code, version history, and supplementary materials are openly accessible. ISA v5f represents a unified, mathematically closed, and empirically confrontable architecture for fundamental physics.
This paper aims to provide a systematic meta-theoretical framework for the”Quantum Geometrization” research program. From an epistemological perspective, it clarifies that establishing ”information” as the first principle of physics isnot an arbitrary metaphysical presupposition, but is based on two operationallymeaningful meta-rules: conservation of information distinguishability and finitestep computability of physical processes. This paper argues that these two metarules constitute the boundary conditions that any cognizable and testable physicaltheory must satisfy, and together they define the ”operational window of physicalcognition”. Within this framework, spacetime geometry is interpreted as an emergent phenomenon of information structure in the coarse-graining limit, quantumuncertainty is reinterpreted as an inevitable trade-off between levels of information description, and a series of cosmological parameters are traced back to rigidconstraints of information algebra. This paper further synthesizes the core achievements of the Quantum Geometrization series into a unified ”information dynamics”prediction network, and discusses the framework’s scope of applicability, challenges,and future directions. This study provides an epistemological foundation for thecore proposition ”spacetime emerges from information” and places the QuantumGeometrization program within a falsifiable scientific paradigm.
We present a rigorously formulated, internally self‑consistent foundational framework for physics based on a minimal algorithmic substrate and the mathematics of category theory and presheaf topoi. The construction begins with a universal prefix Turing machine and the algorithmic probability distribution as the sole primitive, from which arithmetic, discrete topology, and gauge symmetries emerge as the most compressible relational structures. Quantum mechanics is not postulated but derived: the non‑Boolean, contextual nature of physical propositions is captured by the Isham–Butterfield presheaf topos SetsV(H)opSetsV(H)op, whose internal logic is intuitionistic and whose spectral presheaf resolves the Kochen–Specker obstruction. Within this setting, we propose an Algorithmic Information Bound that provides a novel, computational explanation for the Yang–Mills mass gap: a strictly positive lower bound on the algorithmic complexity per lattice site forces a finite correlation length, guaranteeing a non‑zero mass gap. The observer is formalised as an Independent Ontological Simulation Algorithm (IOSA)—a finite, algorithmic subsystem that executes decoherence and context selection, reducing the global intuitionistic logic to a classical Boolean description. We embed the entire ontology in a symmetric monoidal category, exhibiting a precise Rosetta Stone mapping between physics, computation, and logic. Crucially, the framework explicitly acknowledges its own limits via Gödel and Turing, thereby avoiding the paradoxes of absolute self‑description. The resulting theory is internally contradiction‑free, mathematically explicit, and generates falsifiable predictions for lattice gauge simulations, cosmological initial conditions, and quantum‑contextual experiments.
This paper develops a discrete, information-theoretic framework in which physical reality is modeled as a lattice or relational graph of interacting “space cells,” each evolving by local update rules. The framework treats space as an active information-processing substrate rather than as a passive background. Time is modeled as an ordering of state transitions rather than as a fundamental substance. Energy is provisionally associated with event density, update rate, action flow, or structured information-processing intensity, with Planck’s constant interpreted as a conversion scale between discrete transitions, phase, and action. The paper combines formal mathematical development with a summary of toy-model probes used to test whether the framework can support the kinds of structures required of a physical theory. Mathematically, it distinguishes theorem-level consequences of local/unitary dynamics from continuum-limit derivations and from simulation-supported but still speculative model-selection branches. Finite-radius local updates imply causal cones; unitary updates preserve norm; local trace-preserving operations preserve no-signaling at the reduced-state level; split-step quantum-walk updates support Dirac-like low-momentum continuum behavior; and Schrödinger-like dynamics arise as a nonrelativistic positive-energy envelope approximation rather than as the most immediate continuum limit. The space-cell framework is organized around two candidate geometric realizations. A distortable-cell model assigns deformation, strain, connection, or topology-bearing degrees of freedom to cells and links. An alternative extrinsic χ-compression model assigns an additional internal scalar coordinate , interpreted as compression, event-density elevation, hidden displacement, or update-rate modulation. The χ option is not initially treated as a literal fourth spatial dimension; it is a parsimonious internal state variable to be compared against deformation-based models under causal, weak-field, Lorentz-like, source-specific, and false-source controls. The toy-model program summarized here tests whether local update rules can generate stable, bounded, identity-preserving informational structures that survive perturbation, scattering, false-carrier pressure, and geometry-like coupling. These simulations do not prove that nature uses space cells, but they have produced mechanism-level evidence for relational identity preservation, local reconstruction, false-carrier rejection, conservation-ledger requirements, photon-like interaction bookkeeping, and χ/deformation model-selection criteria. This paper does not claim to have derived the Standard Model, full quantum field theory, or the Einstein field equations. It presents a staged mathematical and computational research framework. The strongest current claim is that local information-processing rules can be formalized in ways that recover several necessary structural features—locality, conservation-like invariants, causal propagation, no-signaling compatibility, Dirac/Schrödinger continuum regimes, and candidate weak-field geometry equations—while toy-model branches provide constrained tests of whether those structures can support physically relevant informational excitations.