For decades, theoretical physics has struggled to discretize spacetime without inadvertently breaking Lorentz invariance [1,2]. Building upon the Selection-Stitch Model (SSM) [3], we model the vacuum as an emergent Face-Centered Cubic (FCC, K = 12) tensor network. In this unified framework, we demonstrate that the foun- dational scales of both relativity and quantum mechanics emerge naturally from the strict geometric limits of this saturated lattice. First, we show that the macroscopic speed of light (c) is simply a geometric renormalization of the underlying lattice hopping speed (c = 4vlattice). Second, rather than treating the Planck scale as an arbitrary mathematical cutoff, we derive the fundamental lattice spacing a≈0.77lP as the exact limit where the vacuum’s elastic energy density strikes the absolute a/√3 kinematic exclusion limit (the metric wall) [4]. Third, by treating the vacuum as a Chiral Cosserat continuum, we explicitly derive the complex unit i and the Schr¨odinger equation from lattice gyroscopics. Finally, by intersecting this wave mechanics with the metric wall, we predict a strictly falsifiable, two-step decoher- ence limit for macroscopic superposition: a soft onset of Schr¨odinger breakdown at msoft ≈28µg, and an absolute structural hard cutoff at mhard = √3msoft ≈49µg.
For decades, theoretical physics has struggled to discretize spacetime without inadvertently breaking Lorentz invariance [1,2]. Building upon the Selection-Stitch Model (SSM) [3], we model the vacuum as an emergent Face-Centered Cubic (FCC, K = 12) tensor network. In this unified framework, we demonstrate that the foun- dational scales of both relativity and quantum mechanics emerge naturally from the strict geometric limits of this saturated lattice. First, we show that the macroscopic speed of light (c) is simply a geometric renormalization of the underlying lattice hopping speed (c = 4vlattice). Second, rather than treating the Planck scale as an arbitrary mathematical cutoff, we derive the fundamental lattice spacing a≈0.77lP as the exact limit where the vacuum’s elastic energy density strikes the absolute a/√3 kinematic exclusion limit (the metric wall) [4]. Third, by treating the vacuum as a Chiral Cosserat continuum, we explicitly derive the complex unit i and the Schr¨odinger equation from lattice gyroscopics. Finally, by intersecting this wave mechanics with the metric wall, we predict a strictly falsifiable, two-step decoher- ence limit for macroscopic superposition: a soft onset of Schr¨odinger breakdown at msoft ≈28µg, and an absolute structural hard cutoff at mhard = √3msoft ≈49µg.
We model the vacuum as a discrete face-centered-cubic (K=12) tensor network with Bell-pair bonds and use it to predict a two-step quantum-to-classical threshold for macroscopic center-of-mass superpositions. A reversible dispersive deformation of the center-of-mass mode sets in at msoft≈13.1μg, and coherence becomes geometrically unsustainable at mhard≈22.6μg. The two scales are separated by the exact, parameter-free ratio 3, fixed by the edge-to-circumradius ratio of the cuboctahedral triangular face. Gravitational-collapse models predict a single scale of the same order, so the distinctive, falsifiable content is the two-step structure and the exact 3 separation, testable by a mass scan across the window; the recent 16.2μg cat-state oscillator of Bild et al. falls between the thresholds, where coherence is not ruled out. The absolute window depends on the bond length L=4ln2ℓP≈1.665ℓP, fixed by one calibration against the Bekenstein–Hawking area law. This calibration and the Compton representability hypothesis—that a mass excitation remains coherent only while its reduced Compton wavelength is resolvable by the lattice—are stated model inputs rather than derivations, motivated by the Compton frequency internal clock of massive excitations, the mass cutoff generic to lattice-regularized field theories, and the total-mass dependence observed in composite-object interferometry. Open problems are stated explicitly.
Standard Quantum Mechanics treats the complex wavefunction and its first-order time evolution as fundamental postulates. Expanding on the Selection-Stitch Model (SSM) [1], we propose that these properties are emergent consequences of a discrete, crystallized vacuum. We define a “particle” as a stable K = 13 topological defect within a K = 12 Face-Centered Cubic (FCC) lat- tice. We model the vacuum as a **Micropolar (Cosserat) Continuum**, where nodes possess both translational and rotational degrees of freedom. We introduce a novel **Chiral Velocity Coupling** into the lattice Lagrangian, arising from the broken mirror symmetry of the defect. We explicitly derive the equations of motion via the Euler-Lagrange formalism, demonstrating that this coupling generates the complex unit i. We calculate the Noether current associated with the global U (1) sym- metry, proving that the topological coupling ensures a positive-definite conserved charge. Finally, we provide a step-by-step derivation of the non-relativistic limit, recovering the exact Schr¨odinger equation and unifying the deterministic discrete vacuum programs of ’t Hooft and Kleinert [3, 4].
This paper presents the formal computational verification of the Refresh Rate Hypothesis (RRH), demonstrating that Special Relativistic kinematics, Heisenberg uncertainty, and non-local quantum correlations emerge natively from a discrete, capacity-limited lattice vacuum. Utilizing an optimized three-dimensional Face-Centered Cubic (FCC) matrix operating at 934 volumetric frames per second, we implement a strict local processing budget governing cell updates. When localized wave packets translate across coordinates, their internal phase clocks automatically dilate along Einstein’s exact non-linear Lorentz curve to conserve computational resources, achieving a tracking precision within 2.118e-7% variance. Furthermore, we show that by replacing classical angular phase-readouts with a discrete ontic change-of-basis sieve governed by field-wide phase conservation, the ensemble statistics break the classical Bell bound, exactly saturating the Tsirelson limit (|S| = 2.8284) across an airtight 100-tick spacelike communication horizon. These findings eliminate the 60-year deadlock between discrete space and continuous invariants, providing a fully local, deterministic foundation for unified physics. Key Computational Milestones & Datasets Documented: The RRH Lattice Update Kernel: Implements a discrete fractional accumulator on a 12-neighbor Face-Centered Cubic (FCC) matrix to completely eliminate grid anisotropy and numerical shape-diffusion at fractional velocities. Relativistic Budget Verification: Demonstrates an unquantized clock dilation precision tracking Einstein's curves within a 2.118×10⁻⁷% error margin under high-speed diagonal 0.6c transit. Emergent Quantum Symmetries: Establishes wave-particle double-slit duality with a coherent fringe visibility score of 0.999447, while deriving the Heisenberg Uncertainty Principle as an informational hardware sampling constraint. Causal CHSH Joint Correlation Statistics (Step 5B): Introduces a Paired Conservation Sieve that breaks the classical local ceiling (|S| ≤ 2.0) to capture the absolute Tsirelson limit (|S| = 2.8284) with zero superluminal data cheating.
This paper presents a unified theoretical framework and an experimental protocol for detecting the precise boundary between the reversible quantum world and the irreversible classical macroworld. We propose that the quantum-to-classical transition is not a gradual process governed by environmental decoherence, but a discrete, threshold-driven phase transition of the physical vacuum itself. Based on the concept of induced gravity and the metric elasticity of the vacuum (A. D. Sakharov) [1], we demonstrate that the Fine-Structure Constant (α ≈ 1/137) emerges naturally as the invariant modulus of elasticity of the quantum vacuum condensate. The value of α is not a free parameter but a direct consequence of the ultimate strength (yield point) of the vacuum, E_max ≈ 2.05 × 10⁻³² J, derived as the geometric mean between the Planck energy scale and the dark energy density. For a test object of fused silica (ρ = 2200 kg/m³), the threshold is reached at a critical mass of M_crit = 27.04 pg, corresponding to a critical diameter of D_crit = 2.863 µm. Below this threshold, the vacuum undergoes purely elastic deformation, preserving time-reversal symmetry (t → -t). Above the threshold, the vacuum enters a plastic flow regime, triggering a dissipative cascade (I. Prigogine) [3] that breaks time symmetry and induces objective wavefunction collapse. We detail an optomechanical cryogenic levitation protocol to detect this transition via a sharp jump in energy dissipation with a predicted damping ratio of Γ7 / Γ6 ≈ 3.90 and the emergence of Fibonacci-ordered vortex structures in phase space, transforming the problem of the origin of α and the arrow of time from abstract speculation into a precise, tabletop experiment.
A model of the vacuum as a face-centered-cubic lattice predicts a two-step quantum–classical threshold, at 13.1 and 22.6 µg, from the hypothesis that a center-of-mass excitation stays coherent only while its reduced Compton wavelength is resolvable by the lattice. Collapse models also limit macroscopic coherence, so the two must be told apart by more than a scale. We derive three discriminators from the model's postulates and compute the counterpart in Diósi–Penrose collapse and in continuous spontaneous localization (CSL). The thresholds depend on total mass alone, while both collapse models depend on density. Below 13.1 µg the model predicts no intrinsic decoherence, where collapse takes 1 s for Diósi–Penrose and about a microsecond for CSL at its experimental bound, for 10⁻¹⁵ kg over 1 µm. The model predicts no measurable heating; read as position localization, its own rate scale would exceed the LISA Pathfinder bound by 66 orders of magnitude, so coherence loss above the threshold must be dephasing in the energy basis. If its effective mode mass is the relevant mass, a 16.2 µg mechanical cat state then bounds the irreversible coupling at 38 orders below its natural scale. A worked levitated-particle example and a public script complete the analysis.
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.