We propose a structural criterion for macroscopic classicality formulated within a hierarchical graph framework. Physical systems are modeled as finite graphs endowed with nested rigid substructures generated through successive coarse-graining. Two structural parameters are introduced: the fraction of hierarchically rigid matter fcf_cfc and the hierarchical depth D(G). We show that when fc and D(G) exceed critical thresholds, boundary-spanning structurally transmitting clusters cease to exist and the dynamically admissible macroscopic configuration space reduces to a single connected component. In this regime, macroscopic non-superposition emerges not from a modification of quantum dynamics, but from structural closure of configuration space. The framework combines combinatorial rigidity theory with percolation arguments and yields critical scaling behavior for the lifetime of macroscopic configuration branching near closure. Classicality is thereby interpreted as trivial dynamic connectivity of configuration space rather than dynamical suppression of quantum superposition. This structural perspective provides a topological mechanism for the quantum-to-classical transition while preserving microscopic quantum validity, and offers falsifiable predictions through threshold behavior and scaling relations in hierarchical matter systems.
We propose a structural criterion for macroscopic classicality formulated within a hierarchical graph framework. Physical systems are modeled as finite graphs endowed with nested rigid substructures generated through successive coarse-graining. Two structural parameters are introduced: the fraction of hierarchically rigid matter fcf_cfc and the hierarchical depth D(G). We show that when fc and D(G) exceed critical thresholds, boundary-spanning structurally transmitting clusters cease to exist and the dynamically admissible macroscopic configuration space reduces to a single connected component. In this regime, macroscopic non-superposition emerges not from a modification of quantum dynamics, but from structural closure of configuration space. The framework combines combinatorial rigidity theory with percolation arguments and yields critical scaling behavior for the lifetime of macroscopic configuration branching near closure. Classicality is thereby interpreted as trivial dynamic connectivity of configuration space rather than dynamical suppression of quantum superposition. This structural perspective provides a topological mechanism for the quantum-to-classical transition while preserving microscopic quantum validity, and offers falsifiable predictions through threshold behavior and scaling relations in hierarchical matter systems.
The macroscopic manifestation of quantum coherence in complex many-body systems remains one of the most profound and challenging frontiers in modern physics. While traditional percolation theory successfully describes classical connectivity phase transitions in disordered media, and quantum phase transitions typically focus on zero-temperature Hamiltonian parameter variations, the interplay between network topology and quantum coherence propagation lacks a unifying macroscopic framework. In this paper, we propose the theory of Quantum Coherence Percolation Threshold (QCPT), introducing the concept that quantum coherence can undergo a sudden, non-analytic macroscopic percolation transition across complex networks. We formally define the coherence connection probability, denoted as p_C, and demonstrate that when p_C exceeds a critical threshold p_C*, a global coherent cluster abruptly emerges, characterized by a non-zero macroscopic global coherence measure C_global > 0. By formulating the density matrix evolution, local coherence sharing, and topological constraints over complex graph structures, we establish the analytical foundation for this network-mediated quantum phase transition. This framework bridges quantum information theory, statistical mechanics, and network science, offering a foundational blueprint for understanding macroscopic quantum states in complex environments.
Abstract: The transition from quantum to classical behavior remains one of the central open problems in fundamental physics. Decoherence theory describes the dynamical process by which quantum superpositions become effectively classical, but does not identify a sharp structural threshold. We present an algebraic criterion for the quantum-classical boundary derived from a single-parameter (N = 3) framework called Trichiral Theory (TT). The framework produces a palindromic degeneracy spectrum whose values — 1, 2, 4, 8, 12, 20, 54 and their mirror — each reduce to closed-form expressions in N (respectively: 1, c, N+1, N2 −1, N(N+1), (N+1)(N+2), 2N3). At the first stable state of this spectrum (degeneracy g = 4 = N+1), the four known forces admit a natural partition into two pairs: the Strong and Weak forces, which are capable of forming new bound states via a three-edge closure mechanism, and the electromagnetic and gravitational forces, which interact with existing states but do not produce new bound configurations. Notably, the gravitational coupling derives as VG = 2VEM 2, linking the hierarchy problem to the quantum-classical boundary through a common algebraic origin. We argue that this 2+2 partition at g = 4 constitutes a precise, falsifiable criterion for the onset of classical behavior, and present three experimentally relevant predictions.
Dynamic Harmony Structural Stress-Test Series. This paper evaluates the problem of unifying microscopic quantum dynamics with macroscopic classical behavior. The analysis examines whether proposed mechanisms linking these scales satisfy the structural conditions required for genuine emergence within the Dynamic Harmony framework. Using the Phase Non-Substitutability Test introduced in Paper 0 and the architectural boundary criterion developed in Paper 0B, the paper analyzes whether the transition from microscopic quantum dynamics to macroscopic classical systems represents a true architectural redefinition or remains a configurational rearrangement within an existing state space. The analysis clarifies the structural conditions under which unified dynamical descriptions can account for the emergence of stable macroscopic organization. This paper forms part of the Dynamic Harmony Structural Stress-Test Series, a research program that evaluates major theories of emergence across physics, biology, and complex systems through adversarial structural analysis.
This paper proposes a quantum measurement framework based on structuralstability theory, aiming to resolve the logical dilemma of the quantum–classicaltransition in Schrödinger’s cat paradox. Traditional quantum mechanics relies onexternal mechanisms such as “observer introduction” or “decoherence” to explainmacroscopic reality, leading to vague ontological commitments. We argue that thefundamental reason macroscopic quantum states cannot maintain coherent superpositions lies in the self-organizing critical behavior constrained by the system’sinternal structural stability. The core mechanism is: when a quantum system couples with a classical measuring device, its Hilbert space representation is forced toproject from a high-dimensional unitary representation onto a low-dimensional classical representation, a process driven by the extremization of a structural stabilityfunctional, not by external observation. We rigorously prove that when the system’sstructural information density exceeds a critical threshold, the quantum superposition state cannot satisfy self-consistency constraints mathematically; the systemmust select a classical eigenstate through an “algebraic filtration” mechanism. Thetheory yields three testable predictions: (1) a microscopic entropy production pulseat the moment of coupling between the measuring device and the quantum system,of order 10−21 J/K; (2) a deviation of the quantum Zeno suppression factor fromstandard quantum mechanical predictions on microsecond scales; (3) a scaling-lawdivergence of the decoherence time of macroscopic superpositions at critical parameters. These effects can be tested in coupled superconductor qubit–mechanicalresonator systems. The framework does not modify unitary evolution, does not relyon many-worlds assumptions, and does not introduce collapse postulates; instead,it transforms the measurement problem into a question of compatibility betweenquantum information structure and geometric–topological constraints.
Stability Geometry of Branch Structures in Open Quantum Systems. DOI: https://doi.org/10.17605/OSF.IO/RKPTQ. Main paper PDF: tability_Geometry_of_Branch_Structures_in_Open_Quantum_Systems.pdf. Causal–Continuity Stabilization Theory (CCST) characterizes macroscopic causal persistence as a physical stability property of finite substrates, rather than as an ontological feature of the universal wavefunction. In its original formulation, CCST formalized descriptive admissibility: a coarse-grained macroscopic causal history remains well-posed only when thermodynamic dissipation stays below a substrate-dependent bound and when coarse-grained dynamical sensitivity preserves closure. This work extends CCST by addressing a logically distinct question: not only whether a macroscopic description remains admissible within a branch, but whether a branch structure itself can remain dynamically coherent as an organized physical entity under sustained environmental coupling. Although unitary quantum mechanics preserves all components of the global quantum state, organized branch structure may dynamically disperse into microscopic degrees of freedom in open-system dynamics, thereby losing the correlation patterns required for macroscopic organization. We distinguish structural dispersion (loss of branch-level organizational coherence) from Causal Exit (loss of description-level definability on a finite physical substrate), emphasizing that these correspond to stability failures at distinct physical layers and should not be conflated. Using standard open-system effective-action and influence-functional formalisms, we motivate a dynamical weighting over coarse-grained path ensembles: microscopic dynamics induces a non-uniform stability geometry in path space through irreversible dynamical suppression rather than probabilistic selection, without introducing collapse, selection rules, or inter-branch transport. Finally, we introduce a minimal toy model to visualize the qualitative sensitivity of branch-structural persistence under controlled stability thresholds. The model is strictly illustrative and is accompanied by transparent parameter definitions and a reproducible numerical implementation in the appendix.
This work formulates classical physics as a stable residual-rigid macroscopic phase of quantum dynamics. The central thesis is not that classical mechanics is an independent fundamental theory, nor that decoherence alone solves the measurement problem, but rather that classical behavior arises conditionally when quantum states belong to a protected small-residual basin around a regular classical stratum. Let ρ denote a quantum state and let Mcl denote a regular classical stratum in the quantum state space. The non-classicality residual is defined as the multi-component map Rcl(ρ) = (Roff(ρ), Rloc(ρ), REhr(ρ), Rdyn(ρ), Rred(ρ)), where the components measure, respectively, off-diagonal coherence in a pointer decomposition, failure of semiclassical localization, Ehrenfest defect, transverse dynamical instability, and lack of redundant environmental records. The associated residual energy is ηcl(ρ) = woff ‖Roff‖² + wloc ‖Rloc‖² + wEhr ‖REhr‖² + wdyn ‖Rdyn‖² + wred ‖Rred‖², with positive weights determined by the macroscopic resolution scale of the physical model. The mathematical structure is residual-quadratic. If R(u*) = 0, η(u) = ‖R(u)‖², and L = DR(u*), then the canonical second variation satisfies D²η(u*)[h,h] = 2 ‖Lh‖², and the associated stability operator is A = L∗L. Applied to the classicality residual, this gives the transverse stability operator Acl = DRcl∗ DRcl. The principal rigidity statement is conditional: if the linearized residual has a coercive transverse spectral gap and if small residual energy cannot occur far from the classical stratum, then ηcl(ρ) ≤ ε* implies dist(ρ,Mcl)² ≤ C ηcl(ρ). Thus classical physics is interpreted as a protected low-residual basin in quantum state space: a stable macroscopic regime in which decoherence, semiclassical localization, Ehrenfest control, dynamical invariance, and environmental redundancy jointly enforce rigidity of classical behavior. The framework also identifies the main failure modes of classicality: closing of the transverse spectral gap, absence of decoherence, loss of localization, failure of redundant records, tunneling, revivals, mesoscopic superpositions, and concentration-like escape channels. Consequently, the classical regime is not asserted as a universal limit of all quantum states, but as a gapped residual-rigid phase valid under explicit stability and anti-concentration hypotheses.