The Algorithmic Reality Model: Unifying Quantum Mechanics and General Relativity via the Zeno Threshold and Thermodynamic Graph Routing

The Algorithmic Reality Model: Unifying Quantum Mechanics and General Relativity via the Zeno Threshold and Thermodynamic Graph Routing Author: Serdar YamanKeywords: Algorithmic Reality, Zeno Threshold, J-field, Emergent Spacetime, Emergent Gravity, Landauer's Principle, Quantum Information Geometry, Tomita-Takesaki Theory, Nyquist-Shannon Theorem, Dark Energy, MOND, Quantum Gravity Abstract & Overview For over a century, theoretical physics has treated General Relativity and Quantum Mechanics as fundamentally incompatible frameworks. One posits a continuous, deterministic spacetime manifold, while the other relies on a discrete, probabilistic Hilbert space. The Algorithmic Reality Model (ARM) addresses this schism by identifying a single computational mechanism — the Zeno Threshold (Zα) — as the universal bound governing both quantum state reduction and macroscopic spacetime geometry. ARM models physical reality as the macroscopic projection of a finite-bandwidth computational substrate operating on a timeless, pre-geometric state (the Singleton). By applying the Bennett-Landauer thermodynamic bound of irreversible erasure to physical states, ARM argues that the universe is constrained by a finite processing budget. From three foundational axioms, one empirical input, and zero free parameters, the framework derives a unified informational account of quantum mechanics, spacetime, gravity, and several major physical anomalies. Key Theoretical Derivations & Resolutions Emergent Lorentzian Spacetime: Spatial geometry emerges from the Quantum Fisher Information Metric (QFIM), while temporal evolution emerges from the Tomita-Takesaki modular flow. The Lorentzian signature (-,+,+,+) is derived from the algebraic coexistence of compact and non-compact generators. Wavefunction Collapse & the Born Rule: Measurement is reinterpreted as a finite-budget truncation process. When local entanglement entropy breaches the Zeno Threshold, the substrate executes a non-unitary Born-rule update as the thermodynamically optimal, Kullback-Leibler-minimizing compression step. The EPR Paradox & Entanglement: Entanglement is reframed as backend memory aliasing: multiple apparent subsystems share a common informational address in the pre-geometric Singleton, explaining Bell-type correlations without superluminal signaling. Dark Energy & the MOND Anomaly: The vacuum catastrophe is addressed by deriving the irreducible Bennett-Landauer cost of maintaining the cosmological event horizon. The MOND scale similarly emerges as an algorithmic noise floor when the local Unruh temperature falls below the ambient Gibbons-Hawking temperature. Why Complex Numbers? ARM derives complex Hilbert space as the unique state-space architecture that preserves local tomography while minimizing Landauer processing cost. The Gravitational Sector & the J-field: Macroscopic gravity is recast as a scalar clock-rate field J(x), replacing much of the effective weak-field gravitational description with a resource-allocation law on the informational substrate. Computational & Cross-Paper Validation ARM is a synthesis paper, but its central claims are supported by companion computational validation papers across the broader ATR/ARM framework. These include explicit demonstrations of: double-slit interference and which-path erasure emerging from discrete lattice dynamics and Zeno-threshold-triggered truncation, the spectral-gap → area-law → gravity chain in explicit computational form, and multi-body data-condensation dynamics within the broader ARM validation programme. This upload contains the comprehensive synthesis paper presenting the full mathematical architecture and thermodynamic unification of the Algorithmic Reality Model. Version 3 Update (April 2026) §2: Clarified the observer clock update by defining the continuous tick interval Δtα explicitly. §8.1: Updated the superconducting-qubit falsifier to match the new ATR first-principles clocked-observer computation. Falsification: Added the quantitative 199.50σ / 106.73σ discrimination result and the off-resonant control excluding simple aliasing.