This project presents a resolution-based framework in which distinguishability emerges from observational projection with finite resolution. The core idea is formalized by a projection operator P_lambda acting on an underlying configuration space, generating observable structure. Zenodo DOI: https://doi.org/10.5281/zenodo.19651731 Updated version (PRX submission): https://doi.org/10.5281/zenodo.19651731
This project presents a resolution-based framework in which distinguishability emerges from observational projection with finite resolution. The core idea is formalized by a projection operator P_lambda acting on an underlying configuration space, generating observable structure. Zenodo DOI: https://doi.org/10.5281/zenodo.19651731 Updated version (PRX submission): https://doi.org/10.5281/zenodo.19651731
This work presents a unified framework for the origin of the Born rule, combining resolution-limited observation and geometric structure. We show that consistency under coarse-graining uniquely selects the quadratic probability rule. In addition, we demonstrate that the mapping from complex amplitudes to observable quantities naturally induces a quadratic structure. This version integrates previous resolution-based and geometric approaches into a single framework. Version: v2 (Unified framework) Related works: - https://doi.org/10.5281/zenodo.19939597 - https://doi.org/10.5281/zenodo.19651731
This work proposes a conceptual framework in which information emerges through the introduction of absence via observation. We introduce a dual structure consisting of a general domain without distinction and a particular domain where differentiation arises. Within this structure, record, consciousness, and time are treated as emergent from transitions involving absence. This work is conceptual and does not provide empirical predictions. It is intended as an interpretational extension related to, but independent from, physics-oriented approaches to resolution and distinguishability. Related work: https://doi.org/10.5281/zenodo.19651731
Papers I and II derived gravitational geometry and second-order dynamics from finite accessibility without invoking measurement, observation protocols, or collapse as primitive notions. This paper extends the operational program to the measurement sector, deriving the structure of record formation and probabilistic weights from the same finite accessibility and compositional constraints. Finite accessibility restricts admissible operations on a subsystem to a proper operator subalgebra. Because bounded certification excludes operators requiring nonlocal coordination or arbitrarily fine phase resolution, the accessible algebra is strictly smaller than the full operator algebra. When a system becomes correlated with orthogonal environment sectors, off-diagonal operators between those sectors fall outside the accessible algebra. The reduced state is therefore indistinguishable, under all admissible operations, from its diagonal ensemble. Definiteness emerges as an algebraic consequence of sector restriction, not as a collapse postulate. The weights of these sectors are fixed uniquely by compositional consistency. Phase invariance, multiplicativity under independent refinement, and stability under record coarse-graining constrain any admissible assignment of sector weights to satisfy a functional equation whose only continuous, non-contextual solution is quadratic in amplitude. The Born rule therefore arises as the unique invariant measure compatible with finite accessibility. Irreversibility follows from action scaling: reversal requires operators outside the admissible tensor algebra and incurs action cost proportional to the number of correlated subsystems. Since admissible operations are bounded by the action gap, macroscopic record reversal is excluded. Measurement introduces no new physical primitives beyond finite accessibility, locality, and compositional stability. Record formation, classical definiteness, and Born probabilities are structural consequences of algebraic restriction under finite accessibility. **This paper is part of the Finite Accessibility series, which reconstructs gravitational geometry, quantum dynamics, gauge structure, cosmological perturbation theory, and the dark sector from a single operational primitive: a finite certification ceiling ω* governing the maximum rate at which physical relations can be maintained across extended domains.** **Introductory papers** - Geometric Limits to Coherent Timekeeping in Extended Reference Frames — https://doi.org/10.5281/zenodo.18824556 - Accessibility Selection Law (ASL) — https://doi.org/10.5281/zenodo.18824649 - Phase Boundary Gravity — https://doi.org/10.5281/zenodo.18824707 **Pillars (numbered I–IV)** - Paper I: Deriving Gravitational Geometry and Schrödinger Dynamics from Finite Accessibility — https://doi.org/10.5281/zenodo.18601600 - Paper II: Deriving Inertia, Motion, and Wave Propagation from Finite Accessibility — https://doi.org/10.5281/zenodo.18625174 - Paper III: Accessible State Spaces, Record Stability, and the Emergence of Quantum Statistics — https://doi.org/10.5281/zenodo.18625192 - Paper IV: Frame Dissolution, the Certification Ceiling, and Observable Deformations — https://doi.org/10.5281/zenodo.18654458 **Extension papers** - Dark Matter from Finite Accessibility — https://doi.org/10.5281/zenodo.18654433 - Dark Energy from Finite Accessibility — https://doi.org/10.5281/zenodo.18654523 - No-Go Theorems and the Admissibility Corridor — https://doi.org/10.5281/zenodo.18654493 - Gauge Structure from Finite Accessibility — https://doi.org/10.5281/zenodo.18928152 - Perturbation Theory from Finite Accessibility — https://doi.org/10.5281/zenodo.18928213 **Experimental paper** - Experimental Probes of Finite Accessibility: GW Dispersion and Vacuum Path Independence — https://doi.org/10.5281/zenodo.18931126 **Keywords:** Born rule derivation, measurement problem, quantum statistics, finite accessibility, operator subalgebra, record formation, definiteness emergence, wave function collapse, compositional consistency, accessible state spaces, action gap, irreversibility, sector restriction, quantum foundations, algebraic quantum mechanics, decoherence
Abstract This work develops a process-based framework for quantum gravity in which physical space is rigorously described as the topology of a dynamically evolving graph of discrete quantum processes called P-tacts. A P-tact is defined as the primitive unit of quantum evolution, unifying local superposition and entangling operations into a single indivisible process step. Within this formalism, spacetime is not assumed as a pre-existing background but emerges from the connectivity structure of entanglement relations between P-tacts. The present study synthesizes and extends a coherent research program published throughout 2026. The foundational definition of the P-tact as the primitive unit of quantum theory was introduced in: Pavlov, M. (2026). P Tact (П-такт) as the Primitive Unit of Quantum Theory. Zenodo.https://doi.org/10.5281/zenodo.18516711 The emergence of the quantum switch as a process structure and the reconstruction of indefinite causal order were developed in: Pavlov, M. (2026). Quantum Switch as an Emergent Process Structure from Discrete Process Tacts (П-такт).https://doi.org/10.5281/zenodo.18498181 Pavlov, M. (2026). Indefinite Causal Order as Superposition of Process Graphs.https://doi.org/10.5281/zenodo.18519010 Pavlov, M. (2026). From Indefinite Causal Order to Definite Process Order: A Topological Reconstruction of the Quantum Switch via Discrete P-Tacts (П-такт).https://doi.org/10.5281/zenodo.18526959 Pavlov, M. (2026). Quantum Switch as a Minimal P Tact (П-такт) Cycle.https://doi.org/10.5281/zenodo.18607385 The connection between P-tacts, teleportation, and non-classical causal structures was presented in: Pavlov, M. (2026). Quantum Switch and Teleportation.https://doi.org/10.5281/zenodo.18509173 The emergence of time, causality, gravity, and three-dimensional space from discrete P-tact dynamics was developed in: Pavlov, M. (2026). Emergence of Causality, Gravity, Time, and Three-Dimensional Space from Discrete P-Tact (П-такт) Dynamics.https://doi.org/10.5281/zenodo.18504244 Pavlov, M. (2026). Emergence of Time from P Tact Entanglement (Происхождение времени).https://doi.org/10.5281/zenodo.18526015 Pavlov, M. (2026). Causality and Arrow of Time.https://doi.org/10.5281/zenodo.18549931 The Everett interpretation was explicitly formalized within the P-tact graph framework in: Pavlov, M. (2026). Everett Interpretation Formalized via P-Tact (П-такт) Path Graphs.https://doi.org/10.5281/zenodo.18524745 The present work integrates these results into a unified topological model in which space is identified with graph connectivity, curvature corresponds to dynamic restructuring of entanglement relations, and gravitational phenomena emerge as large-scale patterns of connectivity evolution. In this framework, geometry is not fundamental but process-derived. The theory is fully compatible with Everettian quantum mechanics and eliminates the need for wavefunction collapse. Branching structures correspond to graph bifurcations in the P-tact network, providing a structural representation of many-world dynamics. Gravity is thus interpreted not as a fundamental interaction but as an emergent property of quantum process topology. This approach proposes a formally consistent, unitary, and experimentally testable pathway toward quantum gravity grounded entirely in discrete quantum processes. Potential experimental implementations include quantum simulators and BQM platforms capable of modeling evolving entanglement graphs.
Modern quantum measurement theory relies on successful but ontologically incomplete instrumental formalisms, such as decoherence theory, Lindblad dynamics, POVMs, and consistent histories. While these frameworks describe the operational behavior of measurement, they lack a structural account of outcome uniqueness. This paper demonstrates that Boundary-Induced Collapse (BIC), derived from the Theory of Axiomatic Necessity (TNA), provides the foundational ontology from which these formalisms emerge as partial projections. Within this framework, collapse is redefined as a deterministic structural minimization governed by the realizability functional F(psi,B), where B represents the boundary operator encoding experimental and environmental constraints. We establish explicit mathematical correspondences showing that standard quantum formalisms are operational shadows of an underlying boundary-controlled necessity. Quantum randomness is thus characterized as an epistemic consequence of unresolved boundary degrees of freedom, rather than a fundamental stochasticity. Finally, we prove that boundary projections form a complete POVM resolution of identity, naturally recovering the Born rule through boundary ensemble averaging. Diagram https://drive.google.com/file/d/1TxZtBJpwCAzkOGBU3sEpLwhV7DoC3tFA/view?usp=drive_link Boundary engineering: https://zenodo.org/records/18290437 Short explanatory video summarizing the Boundary-Induced Collapse (BIC) framework and its ontological motivation https://vimeo.com/1157778709?share=copy&fl=sv&fe=ci This framework remains physically undecidable until subjected to boundary-engineered experimental collapse, presented in DOI https://zenodo.org/records/18295265 "Technical Note: Empirical Validation of the BIC-TNA Model"DOI https://zenodo.org/records/18306759 "Experimental Predictions of Boundary-Induced Collapse (BIC) in Quantum Devices" Reader’s Guide: Given the high density of the TNA formalization, readers primarily interested in how this framework resolves standard quantum paradoxes (Bell’s non-locality, unitarity, and the Born rule) may find it efficient to first consult the FAQ/Appendix E. This section addresses the most common interpretative frictions by deriving them as structural consequences of the boundary-induced model, providing a clearer context for the technical derivation in the main body. Dedication “To my grandfather, a casino manager, who taught me that roulette cylinders are changed every week.”
This paper has been updated by https://doi.org/10.5281/zenodo.20279031 This paper resolves the measurement problem and the problem of intersubjectivity—two foundational puzzles of quantum mechanics—within the Planck Core Framework, without requiring any additional postulates beyond the three axioms of the framework. I prove that measurement is not a mysterious non-unitary "collapse" of the wavefunction, but a unitary process of entanglement establishment between subsystems of the quantum bit network. The apparent collapse arises from the observer's limited access to the full entanglement structure: what we perceive as a definite measurement outcome is simply our location within a specific entanglement branch. The Born rule is derived, not postulated—the probability of an outcome is proportional to the number of entanglement threads in the corresponding branch. The Wigner's friend paradox is resolved by proving that different observers may occupy different branches, but their descriptions converge when they exchange information via entanglement. I further introduce the concept of the "information eye"—a hypothetical direct entanglement sensor—and prove that any macroscopic biological organism operating at biological temperatures will inevitably perceive a decohered, classicalised representation of reality, not the underlying quantum information network itself. The classical appearance of the macroscopic world is thus derived as a contingent consequence of thermodynamic constraints on biological evolution, not a fundamental feature of reality. This work completes the derivation of quantum mechanics from the Planck Core Framework, establishing that no special measurement postulate is required.