This paper proposes a structural resolution to the persistent failure of quantum mechanics (QM) and general relativity (GR) to unify within a single mathematical framework. Moving beyond technical obstacles, we introduce the Structural Floor Principle: a meta-invariant architecture (n = 1/n) where mature theoretical systems reach stable, self-balancing limits. Key Framework Contributions: The Planck Scale as a Meta-Floor: We demonstrate that the Planck length (sqrt(hbar G / c^3)) is not merely a limit of scale, but a structural balance point between the "Anchor" of quantum uncertainty and the expansion of gravitational collapse. Temporal Complementarity: We frame QM as the description of the Unbounded Future (probabilistic potential) and GR as the Bounded Past (geometric actuality). We argue that these represent opposite temporal directions that cannot be collapsed without loss of information. The Observer as a Normalization Operator: We interpret wavefunction collapse and the measurement problem as Infinite-Depth Root Extraction (where the limit of a^(1/n) as n approaches infinity is 1). This identifies "Particles" as the identical fixed points of normalized identity. Cosmic Acceleration via Sampling Asymmetry: We suggest a structural explanation for dark energy as the "Gap" between configuration-space growth (N^3) and observer-accessible sampling capacity (sqrt(N)). This work connects foundational paradoxes (Zeno, Gödel, Riemann Hypothesis) to physical limits, suggesting that unity exists at the level of invariant architecture rather than through the merging of equations. It frames the "Present" as a mandatory temporal thickness window where complementary descriptions cohere.
This paper proposes a structural resolution to the persistent failure of quantum mechanics (QM) and general relativity (GR) to unify within a single mathematical framework. Moving beyond technical obstacles, we introduce the Structural Floor Principle: a meta-invariant architecture (n = 1/n) where mature theoretical systems reach stable, self-balancing limits. Key Framework Contributions: The Planck Scale as a Meta-Floor: We demonstrate that the Planck length (sqrt(hbar G / c^3)) is not merely a limit of scale, but a structural balance point between the "Anchor" of quantum uncertainty and the expansion of gravitational collapse. Temporal Complementarity: We frame QM as the description of the Unbounded Future (probabilistic potential) and GR as the Bounded Past (geometric actuality). We argue that these represent opposite temporal directions that cannot be collapsed without loss of information. The Observer as a Normalization Operator: We interpret wavefunction collapse and the measurement problem as Infinite-Depth Root Extraction (where the limit of a^(1/n) as n approaches infinity is 1). This identifies "Particles" as the identical fixed points of normalized identity. Cosmic Acceleration via Sampling Asymmetry: We suggest a structural explanation for dark energy as the "Gap" between configuration-space growth (N^3) and observer-accessible sampling capacity (sqrt(N)). This work connects foundational paradoxes (Zeno, Gödel, Riemann Hypothesis) to physical limits, suggesting that unity exists at the level of invariant architecture rather than through the merging of equations. It frames the "Present" as a mandatory temporal thickness window where complementary descriptions cohere.
This paper proposes a structural resolution to the persistent failure of quantum mechanics (QM) and general relativity (GR) to unify within a single mathematical framework. Moving beyond technical obstacles, we introduce the Structural Floor Principle: a meta-invariant architecture (n = 1/n) where mature theoretical systems reach stable, self-balancing limits. Key Framework Contributions: The Planck Scale as a Meta-Floor: We demonstrate that the Planck length (sqrt(hbar G / c^3)) is not merely a limit of scale, but a structural balance point between the "Anchor" of quantum uncertainty and the expansion of gravitational collapse. Temporal Complementarity: We frame QM as the description of the Unbounded Future (probabilistic potential) and GR as the Bounded Past (geometric actuality). We argue that these represent opposite temporal directions that cannot be collapsed without loss of information. The Observer as a Normalization Operator: We interpret wavefunction collapse and the measurement problem as Infinite-Depth Root Extraction (where the limit of a^(1/n) as n approaches infinity is 1). This identifies "Particles" as the identical fixed points of normalized identity. Cosmic Acceleration via Sampling Asymmetry: We suggest a structural explanation for dark energy as the "Gap" between configuration-space growth (N^3) and observer-accessible sampling capacity (sqrt(N)). This work connects foundational paradoxes (Zeno, Gödel, Riemann Hypothesis) to physical limits, suggesting that unity exists at the level of invariant architecture rather than through the merging of equations. It frames the "Present" as a mandatory temporal thickness window where complementary descriptions cohere.
This paper proposes a structural resolution to the persistent failure of quantum mechanics (QM) and general relativity (GR) to unify within a single mathematical framework. Moving beyond technical obstacles, we introduce the Structural Floor Principle: a meta-invariant architecture (n = 1/n) where mature theoretical systems reach stable, self-balancing limits. Key Framework Contributions: The Planck Scale as a Meta-Floor: We demonstrate that the Planck length (sqrt(hbar G / c^3)) is not merely a limit of scale, but a structural balance point between the "Anchor" of quantum uncertainty and the expansion of gravitational collapse. Temporal Complementarity: We frame QM as the description of the Unbounded Future (probabilistic potential) and GR as the Bounded Past (geometric actuality). We argue that these represent opposite temporal directions that cannot be collapsed without loss of information. The Observer as a Normalization Operator: We interpret wavefunction collapse and the measurement problem as Infinite-Depth Root Extraction (where the limit of a^(1/n) as n approaches infinity is 1). This identifies "Particles" as the identical fixed points of normalized identity. Cosmic Acceleration via Sampling Asymmetry: We suggest a structural explanation for dark energy as the "Gap" between configuration-space growth (N^3) and observer-accessible sampling capacity (sqrt(N)). This work connects foundational paradoxes (Zeno, Gödel, Riemann Hypothesis) to physical limits, suggesting that unity exists at the level of invariant architecture rather than through the merging of equations. It frames the "Present" as a mandatory temporal thickness window where complementary descriptions cohere.
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.
Quantum mechanics and quantum field theory (QM/QFT) offer precise mathematical tools for describing microscopic systems, but remain ambiguous with regard to the precise nature of collapse, measurement, and causal structure. This work introduces a structural reinterpretation of quantum evolution grounded in a conserved, Lorentz-compatible coherence substrate. Within this framework, wavefunctions are understood as phase-supported structures that evolve over finite causal intervals bounded by collapse events. We propose that Planck’s constant encodes structural thresholds of the substrate’s capacity to support coherent evolution. These limits define a minimum spatial and temporal envelope—referred to as the coherence tick—during which standard QM/QFT behavior is valid. Collapse is not introduced as a measurement postulate, but emerges as a necessary structural re-lock at the end of each coherence interval. The Collapse Boundary is thus a physically meaningful event horizon, and if energy or configuration offload is required, a Quantum Emission Opportunity (QEO) occurs. This framework preserves all predictive results of QM/QFT while offering a physically causal explanation for collapse timing, wavefunction termination, and entanglement. It resolves the quantum time asymmetry paradox by distinguishing between internal evolution (experienced in +t) and external observation (reconstructed in −t). By reinterpreting Planck constants as causal boundary conditions rather than universal abstractions, this model provides a substrate-based foundation beneath conventional quantum dynamics—one in which measurement, correlation, and irreversibility arise from finite structural support, not observer-induced discontinuity.
Quantum mechanics and quantum field theory (QM/QFT) offer precise mathematical tools for describing microscopic systems, but remain ambiguous with regard to the precise nature of collapse, measurement, and causal structure. This work introduces a structural reinterpretation of quantum evolution grounded in a conserved, Lorentz-compatible coherence substrate. Within this framework, wavefunctions are understood as phase-supported structures that evolve over finite causal intervals bounded by collapse events. We propose that Planck’s constant encodes structural thresholds of the substrate’s capacity to support coherent evolution. These limits define a minimum spatial and temporal envelope—referred to as the coherence tick—during which standard QM/QFT behavior is valid. Collapse is not introduced as a measurement postulate, but emerges as a necessary structural re-lock at the end of each coherence interval. The Collapse Boundary is thus a physically meaningful event horizon, and if energy or configuration offload is required, a Quantum Emission Opportunity (QEO) occurs. This framework preserves all predictive results of QM/QFT while offering a physically causal explanation for collapse timing, wavefunction termination, and entanglement. It resolves the quantum time asymmetry paradox by distinguishing between internal evolution (experienced in +t) and external observation (reconstructed in −t). By reinterpreting Planck constants as causal boundary conditions rather than universal abstractions, this model provides a substrate-based foundation beneath conventional quantum dynamics—one in which measurement, correlation, and irreversibility arise from finite structural support, not observer-induced discontinuity.
The Problem of Time — the apparent incompatibility between quantum mechanics' time parameter t and general relativity's proper time τ — has been treated as a fundamental obstacle to quantum gravity. I argue that this is a level-confusion: both theories define time within their own entity-theoretic frameworks, generating an apparent opposition that disappears when time is relocated to a meta-structural layer. Drawing on the meta-level temporal structure T_SDT := (V_G, ≺) (Zeng 2026), the paper formalizes QM and GR time as two projections of a single Universal Time Formula, parameterized by entity-theoretic tokens. Four token specializations recover the corresponding time concepts. A Bridge Theorem establishes mutual compatibility of all token projections. A bidirectional QM-GR channel is constructed (forward: GR geometry → QM phase; reverse: discrete chain-pair → Lorentzian spacetime), composing into a self-consistent closed loop. Three further results move beyond dissolution toward unification. First, a Madelung-bridge construction derives the Schrödinger equation — Hilbert space, unitarity, Hamiltonian, quantum potential, Born rule — from the determination-graph axioms together with the continuum embedding (CL1), with no independent QM input; the derivation extends to Klein-Gordon. Second, a Planck-scale token μ = t_P / |A_{v'}| is constructed on the discrete 𝒢_D, where |A_{v'}| is the admissibility cardinality; under CL1, this single step-measure recovers QM (|A| ≫ 1) and GR (|A| = 1) as its two continuum limits, with Einstein's equation proved in the classical regime (|A| = 1) via a two-stage argument (Benincasa-Dowker action convergence + standard scalar-tensor variation). The exact quantum-gravitational correction is derived as a scalar-tensor equation with φ = 1/|A|. Third, the discrete determination graph without continuum embedding constitutes a self-contained Planck-scale quantum gravity theory: it has a well-defined path integral, a finite-dimensional S-matrix (unitary in the κ = 0 sector, isometric in the κ > 0 sector; no UV divergences), preserves information across black hole horizons, resolves singularities, derives the Past Hypothesis, and provides structural origins for gauge symmetry, Hawking radiation, spectral dimensionality, and the spin-statistics connection. The Problem of Time is not merely dissolved — it is replaced by a constructive framework in which QM and GR are unified as two limits of a single discrete structure.