This record provides an index and dependency declaration for a one-way trilogy of works: (1) Minimal Ontological Foundation (MOF v3)(2) Phase–Flow Coherence (PFC v4)(3) Alpha Locking (v6) The trilogy establishes a finite-resolution rigidity chain, proceeding strictly in one direction. MOF v3 fixes the minimal ontological conditions for world-formation, from which irreversible internal update order (time), internal projection (measurement), and structural probability follow as necessary consequences. PFC v4 fixes the unique internally coherent representation of dynamics and probability under those conditions, eliminating all alternatives except Schrödinger-type bookkeeping with Born-rule weighting. Alpha Locking v6 completes the chain by showing that finite-resolution update structures cannot terminate arbitrarily. A unique minimal admissible depth is forced under purely discrete accept/reject predicates, leaving the fine-structure constant as a structural residue. No result depends on downstream assumptions.No fitting, tuning, or optimization is introduced at any stage. This overview introduces no new claims and contains no additional results.It serves solely to fix reading order, dependency, and scope.
This record provides an index and dependency declaration for a one-way trilogy of works: (1) Minimal Ontological Foundation (MOF v3)(2) Phase–Flow Coherence (PFC v4)(3) Alpha Locking (v6) The trilogy establishes a finite-resolution rigidity chain, proceeding strictly in one direction. MOF v3 fixes the minimal ontological conditions for world-formation, from which irreversible internal update order (time), internal projection (measurement), and structural probability follow as necessary consequences. PFC v4 fixes the unique internally coherent representation of dynamics and probability under those conditions, eliminating all alternatives except Schrödinger-type bookkeeping with Born-rule weighting. Alpha Locking v6 completes the chain by showing that finite-resolution update structures cannot terminate arbitrarily. A unique minimal admissible depth is forced under purely discrete accept/reject predicates, leaving the fine-structure constant as a structural residue. No result depends on downstream assumptions.No fitting, tuning, or optimization is introduced at any stage. This overview introduces no new claims and contains no additional results.It serves solely to fix reading order, dependency, and scope.
This paper does not propose a new physical model or interpretation.Instead, it records a rigidity chain that emerges when a world is described internallyunder three minimal premises: finite resolution, non-privileged representation,and irreversible internal projection. Under these conditions, structures traditionally treated as axioms or free parameters—the Born probability weighting, Schrödinger-type dynamics, and the fine-structure constant α—do not remain free. Each appears as a unique survivor of eliminative consistency requirements. Disagreement with the conclusions requires explicit rejection of at least one premise,with clearly identifiable conceptual costs.This work serves as a challenge paper and an entry point to a larger trilogy(MOF–PFC–Alpha Locking), directing critical scrutiny toward the choice of premisesrather than interpretive preference.
Archival record. This paper predates the current MOF–SRT–FDC–PFC framework and is retained for historical and priority purposes. Its subject matter has been revised, absorbed, or superseded by the current framework papers. ------------------------------------------------------------------------------------------------------------------------------------ This short theoretical note formulates a bridge between Relative Determination, the Minimal Ontological Foundation (MOF), Finite Distinguishability Closure (FDC), and Phase-Flow Coherence (PFC). The central claim is that probability need not be introduced as primitive global randomness. Instead, when a globally non-random structural realization is read through a finite internal ledger, multiple globally distinct realizations may be mapped to a single internal ledger state. If a later readout partitions this unresolved bundle into possible outcomes, the internal ledger is forced to represent the partition by normalized relative weights. The note first defines a ledger-relative probability representation using a finite ledger map from a structural closure domain to internal ledger states. It then shows that the domain is not a hidden-variable catalogue or an absolute classical value ledger, but a structural closure domain compatible with the relative-determination viewpoint. The second part specializes the abstract ledger-compatible measure to the PFC phase-bundle setting. Under phase invariance, orthogonal-sector additivity, non-negativity, and finite ledger closure, a functional-equation argument shows that the minimal admissible phase-bundle measure is proportional to the squared complex amplitude. This yields the Born-type weight as a specialization of ledger-relative probability. The paper does not claim that all physical probabilities are derived, nor that randomness is fundamental at the global level. Its purpose is to record a structural bridge: finite internal distinguishability forces probability representation, and PFC supplies the phase-measure specialization leading to Born-type weights.
Notice (Updated Framework):This paper presents a constructive formulation of Phase-Flow Coherence (PFC).A newer paper, PFC v4, reformulates the same results in an eliminative (no-go) framework, showing that Born-rule weighting and Schrödinger-type dynamics are internally inevitable under finite resolution and non-privileged representation. Readers interested in the final, assumption-minimal formulation are strongly encouraged to consult:Phase-Flow Coherence (PFC) v4 — DOI: [v4 DOI]10.5281/zenodo.18322699 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ A deterministic phase-fiber formulation of quantum mechanics based on Fisher reduction.This v2.5 version strengthens the previous PFC v2 by:(i) a rigorous derivation of the quantum potential from Fisher information,(ii) explicit handling of the β non-coherence term under θ-periodicity,(iii) entropic coarse-graining for measurement,(iv) an experimentally testable bound on interferometric visibility.All probabilistic features emerge from finite angular resolution on S¹.The theory is self-contained and falsifiable.
This paper presents a structural derivation of quantum dynamics and probability from a minimal set of pre-physical assumptions: non-privileged phase space, finite resolution, and measure-preserving global dynamics. Rather than postulating quantum axioms, the framework shows how internal probabilistic interpretation (Born rule) and Schrödinger-type dynamics emerge as necessary consequences of finite-resolution internal projections applied to a globally deterministic phase-flow structure. The paper emphasizes a strict separation between global density and internal probability, and includes a structural log clarifying where assumptions are introduced and where they are explicitly excluded. This is Version 1. Subsequent versions may refine appendix structure, notation, and cross-referencing without altering the core theoretical results. Note (2026):A refined and structurally clarified successor to this work is now available as“Phase-Flow Coherence v3: Inevitability of Quantum Dynamics from Finite Resolution and Non-Privileged Phase Space”.The present paper should be regarded as a detailed intermediate derivation, while PFC v3 presents the finalized inevitability result within the MOF framework.
Archival record. This paper predates the current MOF–SRT–FDC–PFC framework and is retained for historical and priority purposes. Its subject matter has been revised, absorbed, or superseded by the current framework papers. ------------------------------------------------------------------------------------------------------------------------------------ This paper is not a theorem paper extending the core claims of MOF, FDC, PFC, or SCR. It is a conceptual note collecting physical reading hypotheses that arise naturally from those frameworks. The hypotheses presented here are therefore not premises of the foundational papers. They are possible physical pictures appearing downstream of the foundational theory. If individual hypotheses are later rejected, the core claims of the foundational papers are not thereby invalidated.The starting point is the conclusion of the companion paper Relative Determination After Bell (RDQ): there is determination in each context, but no absolute ledger for all contexts. The present paper asks the next question: if a ledger is not a static table of values for all contexts, what is a ledger?The central hypothesis is the dynamic ledger hypothesis: a ledger is not a static table storing values, but a dynamic structure that continuously updates contextual readouts. The relative directionality of that updating appears as phase; its sustained coherence is expressed externally as wave-like behaviour.Seven hypotheses are developed: (I) the ledger is not a static value table; (II) phase is the relative directionality of updating; (III) rotation is updating that preserves closure; (IV) the 3×3 six-context grammar is the minimal contextual readout grammar; (V) decoherence is the diffusion of ledger synchronisation; (VI) entanglement is shared constraint rather than shared value; (VII) quantum teleportation is ledger resynchronisation by an update key. Two more speculative hypotheses are added: (A) the action quantum as the pitch of ledger updating; (B) particle species as stable readout solutions at different inventory depths.None of these hypotheses replaces the standard formalism of quantum theory. They offer a structural rereading of the standard formalism from the perspective of ledger, context, finite distinguishability, phase updating, decoherence, and closure.
This preprint develops a discrete, fully relational framework in which spacetime structure, classical dynamics, and quantum-like behavior emerge from three minimal principles: relational existence without background manifold, local deterministic update, and finite per-element update capacity. The central organizing primitive is finite update capacity. At each update step, elements can realise only a bounded number of relational changes. Competition among admissible updates induces “blocked realisations,” which are defined micro-ontologically as energy. Proper time is identified with realised record growth. Spatial distance and effective dimension arise from intrinsic graph structure and shell scaling. Under broad locality conditions, marginal frontier stability constrains viable scaling regimes. Requiring compatibility between flux balance and the observed inverse–square law selects an effective three-dimensional scaling regime among integers. Classical force structure emerges from anisotropies in blocked realisation. A statistical layer appears through coarse-graining of deterministic microhistories. Composition and norm stability require unit-modulus complex weights; refinement invariance and classical coherence fix the phase rule θ=ℏ−1∫Edτ, with the same blocking-defined energy that generates intrinsic force. In decohered regimes, quadratic (Born-type) probability scaling follows from additive consistency under random-phase aggregation. The framework is programmatic: it does not yet derive general relativity or quantum field theory from explicit microscopic rule families. However, it establishes structural coherence linking geometry, inertia, inverse–square interaction, phase accumulation, and probabilistic outcomes under a single finite-capacity relational principle. The work also identifies structural empirical constraints, including compatibility between shell scaling and classical force behavior, stability of inertial response, and the possible appearance of capacity-induced high-energy dispersion within the intrinsic causal-cone bound. Explicit construction and simulation of proposal/selection rule families constitute the next stage of investigation.