The Zeno Threshold: Wavefunction Collapse and the Emergence of Time via Landauer Erasure Limits

Note on Version 2: This paper was originally drafted under the title "Wavefunction Collapse as Algorithmic Garbage Collection" (ATR-WC). Version 2 represents a major theoretical upgrade. We formally introduce the Zeno Threshold (Z-Scale) as the active, observer-dependent limit of actualization, and we restructure the framework to explicitly derive the flow of Time as the thermodynamic exhaust of this non-unitary truncation. The core KL-divergence mechanics remain, but the conceptual foundation has been finalized as a purely relational quantum information theory. Abstract: We propose a resolution to the quantum measurement problem by introducing an observer-dependent processing limit: the Zeno Threshold (Zα). Within the Algorithmic Theory of Reality (ATR), observers are modeled as finite-bandwidth rendering channels operating on a timeless, pure quantum state. When a microscopic superposition entangles with a macroscopic apparatus, the entanglement entropy grows. We prove that when the Bennett-Landauer processing cost of this superposition exceeds the observer's specific Zα capacity, the rendering engine is forced to execute a non-unitary state truncation to prevent a logic crash. We derive a quantitative collapse timescale that matches environmental decoherence, and we demonstrate that the irreversible heat generated by this Landauer erasure is the physical mechanism generating the forward flow of Time. Furthermore, we prove that given pointer-state orthogonality, the Born Rule (pi = |ci|2) is the unique thermodynamically optimal truncation (minimizing the Kullback-Leibler divergence). By defining the observer purely as a finite epistemic horizon, this framework determines when collapse must occur, with what statistics, and how the discrete ticks of time emerge from a timeless quantum backend. Key Contributions: The Z-Scale: Re-defines wavefunction collapse as an automated algorithmic "garbage collection" forced by finite thermodynamic bandwidth limits. The Emergence of Time: Identifies the forward flow of time as the sequential, thermodynamic exhaust generated by Landauer erasure events. Born Rule Derivation: Proves mathematically that the Born Rule is the optimal truncation protocol to minimize algorithmic information loss. Relational Ontology: Resolves Wigner's Friend paradoxes by demonstrating via simulation that collapse is an observer-relative rendering artifact. All quantitative claims in this paper are computationally verified via the companion Python suite available at github.com/srdrymn/atr-wavefunction-collapse.