This paper analyzes quantum tunneling and bound states as empirical stress tests for a persistence-based comparison framework. Rather than postulating wave mechanics or operator dynamics, the analysis takes as fixed a small set of structural ingredients: admissible variation, accumulated loss under recomposed change, and a persistence requirement selecting stable continuations. Within this framework, persistence-weighted path amplitudes and an associated quadratic stability operator arise as derived objects. The paper examines what is forced when these objects are applied to barrier penetration and confinement, and which standard quantum-mechanical results are recovered only as correspondence limits under additional conditions. Tunneling is treated as a local suppression problem, while bound states are analyzed in terms of closure and stability rather than operator postulates. Explicit worked examples demonstrate how WKB exponents and discrete spectra emerge in entropy-flat limits, and how controlled deviations arise when admissibility or curvature conditions are relaxed. No new principles are introduced. The results isolate the structural footing of familiar semiclassical constructions and delineate a clear window of falsifiability for persistence-based comparison beyond standard wave-mechanical representations.
This paper analyzes quantum tunneling and bound states as empirical stress tests for a persistence-based comparison framework. Rather than postulating wave mechanics or operator dynamics, the analysis takes as fixed a small set of structural ingredients: admissible variation, accumulated loss under recomposed change, and a persistence requirement selecting stable continuations. Within this framework, persistence-weighted path amplitudes and an associated quadratic stability operator arise as derived objects. The paper examines what is forced when these objects are applied to barrier penetration and confinement, and which standard quantum-mechanical results are recovered only as correspondence limits under additional conditions. Tunneling is treated as a local suppression problem, while bound states are analyzed in terms of closure and stability rather than operator postulates. Explicit worked examples demonstrate how WKB exponents and discrete spectra emerge in entropy-flat limits, and how controlled deviations arise when admissibility or curvature conditions are relaxed. No new principles are introduced. The results isolate the structural footing of familiar semiclassical constructions and delineate a clear window of falsifiability for persistence-based comparison beyond standard wave-mechanical representations.
This paper derives a persistence-weighted path integral from first principles of coherent comparison under composed admissible variation. Rather than postulating probabilistic, geometric, or dynamical structure, the analysis asks which bookkeeping devices are unavoidable if comparison is to remain well defined when admissible variations are recomposed, refined, or reordered. Starting from minimal operational requirements—discernibility, admissible variation, and persistence—the paper shows that path dependence, accumulated loss, stationarity, and quadratic stability classification are structurally forced. An accumulated loss functional emerges as the minimal additive bookkeeping required for coherence, and persistence weighting arises as a monotone representation of the induced ordering on admissible paths. Under additional stability requirements, the exponential weighting appears as a canonical representative compatible with arbitrary recomposition. Second-order variation around persistence-stationary paths yields a quadratic stability form, which can be repackaged as a curvature operator acting on admissible perturbations. Spectral structure then appears as a classification of persistence-relevant deviations, without presupposing geometry, dynamics, or operator postulates. Familiar formalisms—path integrals, entropy-weighted amplitudes, and spectral descriptions—arise only as restricted realizations once further admissibility, locality, and representational constraints are imposed. The entropy-weighted Feynman path integral is recovered explicitly as such a downstream specialization, with all additional assumptions labeled. The result is not a constructive physical model but a boundary-forming derivation: it fixes which structures are forced by coherence of comparison and which questions are deferred to later, more constrained analyses. The paper provides a foundational anchor for subsequent applications that treat persistence-weighted amplitudes and curvature operators as fixed inputs rather than postulates.
A structural derivation of spectral structure and quantization is obtained from minimal requirements on discernibility and persistence under variation. Rather than postulating quantum degrees of freedom, operators, or Hilbert space, the analysis identifies which assumptions are required for eigenstructure to arise as a consequence of stability under irreversible loss. Building on prior results establishing accumulated loss, path dependence, and curvature as necessary consequences of persistence, the paper introduces a clear admissibility ledger. Under explicit conditions—ordered variation, local loss density, and a quadratic stability regime—the second variation of accumulated loss defines a curvature operator that classifies admissible deviations by their susceptibility to persistence loss. Eigenmodes emerge as stability classes selected by persistence filtering, not as fundamental postulates. Discrete spectra appear only when admissibility conditions enforce effective compactness. Additional restrictions concerning closed continuations and phase-valued transport lead to a closure condition under repeated traversal, reproducing Bohr-type quantization as a conditional consequence rather than an axiom. Global spectral weights and regularization are introduced solely as technical bookkeeping devices when persistence comparison is extended to families of modes. The framework deliberately separates structural derivation from physical interpretation. Hilbert space structure, probabilistic interpretation, and standard quantum dynamics arise only under further assumptions and are not required for spectral stability itself. Standard quantum mechanics is recovered as a specialization of the general framework under additional linearity, normalization, and interpretive assumptions. The paper isolates the minimal structural content underlying eigenstructure and quantization, making explicit which assumptions are responsible for each step. It stops short of system-specific applications, but the entropy-weighted variational object derived here serves as the foundation for predictive extensions developed in companion works, including corrections to tunneling behavior, interference suppression, and collapse-like phenomena emerging from resolution instability.
Abstract: Quantum tunneling is conventionally described through semiclassical WKB methods and imaginary-time formulations of the Feynman Path Integral, which successfully reproduce transmission probabilities but leave the local kinematic structure of the barrier transition largely implicit. In this work, we introduce a finite-rate temporal integration framework in which localized quantum states evolve through successive stochastic re-integrations over a characteristic interval . Within this picture, a macroscopic potential barrier acts as an open fluctuating electromagnetic environment rather than a rigid static boundary. As a localized state partially penetrates the barrier, transient geometric interlocking suppresses forward integration and prolongs the effective interaction window. The under-barrier configuration is modeled not as a single coherent leap across the forbidden region, but as a metastable sequence of stochastic local re-integrations continuously driven by environmental fluctuations. Transmission through thick barriers therefore emerges as a rare cumulative process requiring repeated successful geometric alignments across many finite integration intervals, naturally producing exponential suppression with barrier thickness. To formalize this mechanism, the tunneling process is represented as a coupled stochastic escape problem governed by bipartite Langevin dynamics and an associated Fokker–Planck description. The transition probability acquires a bilinear structure arising from simultaneous compatibility conditions between particle-side and environment-side fluctuations. In the self-consistent limit, this naturally produces the quadratic probability weighting characteristic of the Born measure, while remaining compatible with normalized Hilbert-space amplitudes. Within this framework, the Euclidean-time contribution appearing in standard tunneling theory admits a local kinematic interpretation as the extended stochastic integration interval required for compatible transition geometries to accumulate across the barrier. The formalism further predicts enhanced sensitivity of tunneling dynamics to high-frequency external probing, potentially relevant to attoclock tunneling-delay experiments and strong-field manifestations of the Quantum Zeno effect.
What are the physical conditions required for agency? Recent work has rigorously shown that purely unitary, coherence-preserving quantum dynamics are insufficient to support deliberation, comparison of counterfactual actions, and reliable action selection. These results establish a genuine no-go theorem for agency in a strictly quantum-coherent regime. This paper provides a structural completion of that no-go result. Rather than challenging its correctness, the analysis identifies the underlying assumption on which it rests: that unitarity alone is sufficient as an admissibility criterion for decision endpoints. We show that this assumption is incomplete. Working within the Tier-0 closure framework, physical lawfulness is characterized by closure-stable fixed points selected by structural constraints rather than by unconstrained dynamical evolution. Within this framework, coherent quantum states may function as intermediate computational or representational states but are excluded as lawful endpoints for records, decisions, and control. Applying closure stability to quantum systems yields a classical decision subspace without introducing new dynamics, observer-dependent postulates, or interpretation-specific assumptions. The paper further shows that agency requires a closure-stable internal selection process capable of consistent expected-utility comparison. Imposing closure compatibility rigidly fixes the standard quadratic Born probability rule as the only weighting compatible with stability, representation-independence, and admissibility-preserving re-expression. Together, these results integrate agency into the same structural framework that accounts for quantum measurement and probability. The absence of agency in purely quantum-coherent models is shown to reflect an under-constrained admissibility regime rather than a fundamental limitation of quantum theory. Lawful agency emerges as a closure-stable property of coupled agent–world dynamics, fully consistent with standard quantum mechanics. This work clarifies the physical limits of purely quantum models of decision, sharpens existing no-go arguments, and provides a mathematically explicit foundation for agency grounded in structural admissibility rather than interpretation.
This work introduces a falsifiable symbolic field framework for modeling quantum-like behaviors under explicit structural constraints. Rather than modifying the formalism of quantum mechanics or proposing a new physical ontology, the paper investigates which behaviors associated with quantum systems persist within a restricted class of admissible dynamics—defined as bounded, well-posed, and stable under perturbation. At the core of the framework is a bounded nonlinear stabilizing function, KN, which constrains symbolic field evolution within a modular phase space. Within this constrained regime, phenomena commonly associated with quantum mechanics—interference, collapse-like transitions, entanglement, memory persistence, and decoherence—emerge as structural consequences of resonance, phase alignment, and admissibility filtering rather than as observer-dependent postulates. Using four simulation-based tests, the paper demonstrates that: Linear superposition fails under KN modulation, producing bounded asymmetry rather than cancellation. Symbolic memory decays without active modular reinforcement and persists only under feedback. Collapse-like transitions propagate synchronously across phase-aligned symbolic fields. Decoherence emerges from stochastic phase drift without invoking measurement or observation. The framework reframes collapse as resonance locking, entanglement as modular phase alignment, and decoherence as admissibility failure induced by phase instability. These mechanisms do not alter the empirical predictions of quantum mechanics, but instead clarify the structural conditions under which quantum-like behavior survives. This work is intended as a structural and methodological contribution, providing a constrained symbolic model that complements existing quantum theory and connects ideas from nonlinear dynamics, decoherence, and constructive field theory. It forms part of a broader research program exploring admissibility as a unifying principle across physical, symbolic, and informational systems.
Eigenstate Engineering as Admissibility Architecture: Constraint-History Retention, Recursive Eigenspace Sculpting, and the Experimental Emergence of Persistent Quantum Accessibility This work introduces Eigenstate Engineering as Admissibility Architecture (EEAA), an admissibility-first framework for understanding how recursively structured quantum interactions reshape the practical accessibility of eigenstate manifolds under standard quantum mechanics. Rather than treating eigenstates solely as static operator solutions, the paper proposes that bounded, path-dependent, non-commuting control sequences can bias future coherent reachability by sculpting admissible eigenspace accessibility over time. Anchored in orthodox Hamiltonian dynamics, Floquet engineering, decoherence theory, and coherent control, the framework introduces no new particles, forces, or departures from established physics. Instead, it reorganizes known quantum formalisms under an admissibility-first interpretation in which persistence, orderability, and bounded continuation govern experimentally realizable state accessibility. The paper formalizes operators and diagnostics for: admissible eigenspace deformation, history-retentive accessibility, potency-conditioned state volume, recursive control sequencing, and constraint-history retention in coherent quantum systems. A central empirical motivation is the recent trapped-ion quadsqueezing breakthrough achieved through staged non-commuting interactions, demonstrating that recursively admissible sequencing can unlock higher-order eigensectors dramatically faster than conventional direct-driving approaches. The work interprets such results as evidence that practical eigenspace accessibility can be systematically reshaped through bounded interaction history. The EEAA framework further develops falsifiable predictions across: trapped-ion systems, superconducting qubits, Floquet-engineered lattices, topological materials, quantum sensing architectures, and coherent quantum memory systems. Conceptually, the work extends a broader admissibility-first research program in which persistence under constraint, orderability, and bounded continuation are treated as minimal structural preconditions for experimentally resolvable physical systems. Related foundations include admissible continuation geometry, recursive accessibility deformation, χ-based stability diagnostics, potency-conditioned continuation volume, and deterministic boundary projection under exhausted admissible continuation. The paper is intended as a falsifiable interpretive and engineering framework for coherent quantum accessibility rather than a replacement for standard quantum mechanics. Its central claim is operational: recursively staged admissible control sequences can sculpt the practical geometry of eigenstate accessibility and thereby function as effectively programmable accessibility structures for persistent coherent quantum behavior. All claims are formulated within experimentally testable control-theoretic and dynamical regimes compatible with standard quantum mechanics. Keywords Quantum Physics Quantum Mechanics; Eigenstate Engineering; Quantum Control; Coherent Control; Quantum Accessibility; Quantum Memory; Trapped Ions; Quadsqueezing; Floquet Engineering; Quantum Dynamics; Quantum Information; Quantum Architecture; Hamiltonian Dynamics; Non-Commuting Operators; Eigenspace Accessibility; Quantum State Accessibility; Coherent State Reachability Admissibility-First Framework Admissibility Architecture; Admissible Continuation; Constraint-First Physics; Constraint-History Retention; Recursive Accessibility; Bounded Continuation; Persistence Under Constraint; Orderability; Potency; χ-Diagnostics; Boundary Projection; Recursive Eigenspace Sculpting Mathematical / Theoretical Physics State-Space Geometry; Accessibility Manifolds; Operator Theory; Stability Geometry; Constraint Topology; Recursive State Reachability; Nonlinear Quantum Accessibility; Phase-Space Structure; Dynamical Constraints; Admissible Projection Operators; Quantum Control Geometry Experimental / Applied Systems Superconducting Qubits; Quantum Sensing; Topological Quantum Systems; Coherent State Engineering; Quantum Hardware Architecture; Experimental Quantum Control; Recursive Control Sequences; Higher-Order Squeezing; Quantum Coherence Engineering Philosophy / Foundations of Physics Interpretations of Quantum Mechanics; Emergent Accessibility; Constraint Geometry; Physical Continuation; Geometry of Quantum Reachability