We develop a structural framework in which particle-like localization emerges from interaction-induced redistribution of probability across an ordered hierarchy of microscopic sectors. The frame-work begins with a normalized sector distribution whose weights characterize the degree to whichmicroscopic structure is associated with each sector. Neighboring sectors are coupled locally, andtheir weight differences contribute to a structural functional that determines the cost of reorganizingthe distribution. Interaction therefore does not act as an independent collapse postulate. Instead,its strength controls the extent to which the structural hierarchy can be explored and the degree towhich sector weights are redistributed.We show that finite interactions generically allow partial structural reorganization rather thanautomatic single-sector selection. As the available interaction energy increases, additional structuraltransitions become accessible and the sector distribution can become progressively concentrated. Inthe strong-interaction limit, subject to the stability conditions of the structural flow, the distributionmay approach a single dominant sector. We quantify this process using the sector concentrationand the effective number of occupied sectors.The resulting concentration has a direct representation in the density-operator formalism. For asector decomposition ρ =∑︁ i piPi, structural concentration implies Tr(ρ2) → 1. When the limitingsector is rank one, the state consequently approaches a pure-state representation ρ = |ψ⟩⟨ψ|, withsector probabilities taking the standard form pi = |⟨Si|ψ⟩|2. A minimal ordered four-sector toymodel explicitly demonstrates the continuous redistribution, threshold accessibility, and strong-interaction concentration predicted by the framework. We finally identify interaction-dependentconcentration and purity as experimentally testable signatures of the proposed mechanism
We develop a structural framework in which particle-like localization emerges from interaction-induced redistribution of probability across an ordered hierarchy of microscopic sectors. The frame-work begins with a normalized sector distribution whose weights characterize the degree to whichmicroscopic structure is associated with each sector. Neighboring sectors are coupled locally, andtheir weight differences contribute to a structural functional that determines the cost of reorganizingthe distribution. Interaction therefore does not act as an independent collapse postulate. Instead,its strength controls the extent to which the structural hierarchy can be explored and the degree towhich sector weights are redistributed.We show that finite interactions generically allow partial structural reorganization rather thanautomatic single-sector selection. As the available interaction energy increases, additional structuraltransitions become accessible and the sector distribution can become progressively concentrated. Inthe strong-interaction limit, subject to the stability conditions of the structural flow, the distributionmay approach a single dominant sector. We quantify this process using the sector concentrationand the effective number of occupied sectors.The resulting concentration has a direct representation in the density-operator formalism. For asector decomposition ρ =∑︁ i piPi, structural concentration implies Tr(ρ2) → 1. When the limitingsector is rank one, the state consequently approaches a pure-state representation ρ = |ψ⟩⟨ψ|, withsector probabilities taking the standard form pi = |⟨Si|ψ⟩|2. A minimal ordered four-sector toymodel explicitly demonstrates the continuous redistribution, threshold accessibility, and strong-interaction concentration predicted by the framework. We finally identify interaction-dependentconcentration and purity as experimentally testable signatures of the proposed mechanism
The origin of the Born weighting in quantum measurement is usually formulated as a probabilisticpostulate, while decoherence explains the suppression of interference but does not by itself provide adynamical mechanism for the selection of a single outcome. In this work, we propose a microscopicquantum–structural mechanism in which the squared amplitudes arise first as interaction weightsrather than as outcome probabilities.Starting from a normalized quantum state and a leading-order local quadratic system–apparatusinteraction, we introduce a continuous dissipative structural dynamics with a difference-driven con-stitutive flux. Under an explicit sector-selective interaction condition, the interaction energy associ-ated with sector i is proportional to |ci|2. This interaction contribution deforms the correspondingtransition landscape, leading to an effective barrier reduction proportional to |ci|2. In the near-threshold regime, the resulting structural flux is therefore proportional to the squared amplitude.We then formulate the transition as a conserved flux through an absorbing boundary and showthat, under a sector-independent transmission condition and complete selection, the effective out-come weights satisfyPi = |ci|2.The result is conditional: the derivation does not claim that the sector-selectivity, universalresponse, and transmission conditions are fundamental consequences of standard quantum mechan-ics. Rather, it shows that, when these explicitly stated physical conditions are satisfied, the Bornweighting follows from a continuous microscopic selection dynamics without being introduced as aprobability axiom. The framework therefore provides a concrete dynamical route from quantuminteraction to effective outcome statistics and identifies the microscopic conditions that remain tobe derived in a more complete theory.
We propose a minimal dynamical framework in which a quantum state physically drives structuralselection during measurement. Rather than treating the quantum amplitudes as specifying outcomeprobabilities only at the end of the measurement process, we introduce a quantum–structural inter-action energy that generates a sector-dependent structural response. This response defines nonneg-ative structural weights wi, which subsequently drive structural transition fluxes and the completionof measurement outcomes. The resulting general outcome law isPi = Wiwi∑︁j Wj wj,where Wi characterizes the integrated transmission of the structural response into a completedtransition. In the sector-selective regime of the proposed interaction, wi ∝ |ci|2. Consequently,when the structural transmission is universal, Wi = W , the outcome law reduces to the Bornweighting Pi = |ci|2. The Born form is therefore obtained as the universal-response limit of the pro-posed quantum-driven structural selection dynamics rather than being introduced as a microscopicprobability postulate. The framework also predicts three experimentally distinguishable effects:apparatus-dependent deviations from Born statistics, nonlinear corrections in the strong-responseregime, and a finite-time structural precursor preceding the completed outcome. The constructiondoes not claim a complete first-principles theory of wave-function collapse or a unique microscopicontology for the structural field; instead, it provides a minimal dynamical route linking quantumamplitudes to physical structural selection
The present work investigates collective evaluation under accessibility-constrained non-factorizable latent distinction persistence. Previous PoD analyses established that distinct transformation pathways may remain compositionally distinguishable despite sharing identical reduced endpoint representation [5]. The present work investigates the structural consequences that arise once such latent distinctions remain globally persistent beyond local recoverability. The analysis begins from the observation that transformation distinction persistence may become distributed across focal structures, interacting structures, interaction consequences, and subsequent compositional organization. Under such conditions, globally persistent distinction structure no longer factorizes completely into independently reconstructible local sectors. The present framework therefore investigates situations in which: latent distinction persistence remains non-factorizable, only reduced sectors remain operationally accessible, and no accessibility-compatible reconstruction remains available. Under these conditions, independently recoverable transformation structure ceases to remain locally closed. Independently decomposed evaluation consequently becomes structurally incomplete. To investigate the resulting collectively dependent structure, the present work introduces a collectively dependent evaluation hierarchy: where independent evaluation appears as the lowest-order approximation and jointly dependent corrections emerge progressively at higher orders. Within this hierarchy, pairwise quadratic organization appears naturally as the leading nontrivial collectively dependent approximation, while higher-order jointly dependent structures remain structurally admissible whenever multiple transformation pathways remain jointly influential simultaneously. The resulting framework establishes the following structural progression: non-factorizable persistencerecoverability collapsecollective evaluationcollectively dependent hierarchy The present analysis further clarifies the structural relation between the current framework and existing approaches including decoherence, consistent histories, and generalized probabilistic frameworks. In particular, the present work investigates recoverability collapse prior to probabilistic assignment itself, thereby suggesting that probability-like collective organization may emerge from accessibility-constrained distributed latent distinction persistence rather than from primitive stochastic assumptions.
We investigate the nature of probability and the possibility of prediction within the framework of Universal Modular Dynamics (UMD), where physical structure is defined in terms of the density operator ρ, its modular generator K = −log ρ, and the associated spectral distribution p(k). In contrast to conventional approaches, where probability is introduced as a primary concept, we develop a structural interpretation in which probability emerges as a derived property of the underlying organization. We show that the probability of a state is determined by the interplay of three factors: its structural weight within p(k), its accessibility to the observer, and its dynamical stability. This leads to the interpretation of probability as a measure of structural realizability. Within this framework, prediction is not understood as the determination of specific future events. Instead, it corresponds to the analysis of the spectrum of possible states and their relative stability under structural evolution. We demonstrate that observed outcomes arise from the competition between structurally allowed configurations, constrained by accessibility and stabilized by dynamics. This provides a unified description of probability, transitions, and observable behavior without introducing probability as an independent postulate. The results establish a consistent framework in which probability and prediction are derived from structure, and suggest that complex systems may be analyzed in terms of their accessible and stable configurations, rather than through direct event-based forecasting.
Abstract This paper develops Distributed Presence (DP) as a discrete ontological framework for the structural reconstruction of core features usually represented within nonrelativistic quantum mechanics. Rather than taking the wave function, Hilbert space, or collapse postulates as fundamental, DP begins from the claim that a physical object possesses ontological presence distributed over a context-dependent set of admissible channels. Actualization is treated as a primitive stochastic event through which one admissible channel becomes manifest. Within this framework, a quantum particle and a die are structurally comparable as objects of manifestation: in both cases, the object’s identity is not exhausted by any single realized outcome, even though the quantum case requires a richer representational structure. On this basis, the paper argues that complex Hilbert space functions as a minimal manifestation-level encoding of distributed presence together with retained relational structure. The Born rule is reconstructed as a cross-layer identity between phenomenal probability and normalized structural presence fraction, while the Schrödinger form is interpreted as an effective law of pre-actualization redistribution. Measurement is correspondingly reframed as context-driven actualization followed by record stabilization. For composite systems, DP understands entanglement as the nonfactorizability of joint distributed presence, while operational no-signaling is expressed through invariance of local marginal presence fractions under remote contextual variation. The contribution of the paper is therefore ontological and reconstructive, not the proposal of a new empirical formalism. DP offers a single-world realist framework for understanding why central quantum structures take the form they do, while leaving the formalization of actualization, composite dynamics, and the derivation of physical constants for future research.
We investigate the origin of boundaries within the framework of Universal Modular Dynamics (UMD), where physical structure is defined in terms of the density operator ρ, its modular generator K = −log ρ, and the associated spectral distribution p(k). While all observable systems exhibit finite extent and well-defined limits, it remains unclear whether such boundaries are fundamental properties of the underlying structure or emergent features of its organization. We show that within UMD, boundaries need not be imposed a priori. Even in the absence of intrinsic spectral bounds, effective finiteness arises naturally through three mechanisms: localization of the spectral distribution, suppression of contributions outside its dominant region, and limited accessibility of structure. In this framework, observable systems correspond to localized regions of p(k), giving rise to effective boundaries without requiring fundamental cutoffs. We further demonstrate that the appearance of boundaries is inherently linked to the role of the observer, understood as a localized structural configuration with restricted access to the full organization. These results provide a unified structural interpretation of finiteness, scale, and stability, and suggest that boundaries are emergent features arising from the interplay of structure, dynamics, and observation. This work extends the structural program developed in previous studies and motivates further investigation of observation, measurement, and accessibility as fundamental components of physical reality.