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. https://doi.org/10.5281/zenodo.18028427
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. https://doi.org/10.5281/zenodo.18028427
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 version has been superceeded, see v.3) Contemporary approaches to physical unification typically emphasize dynamical laws, interpretive frameworks, or information-theoretic reconstructions. Less attention is given to the structural constraints that determine which physical descriptions can remain coherent and stable under interaction, scale transition, and aggregation. This paper develops a constraint-first analysis of coherence, arguing that persistence and unification require restrictions on admissible physical continuations that are not reducible to dynamics alone. Within the framework referred to here as Quantum Coherence Theory (QCT), coherence is treated not as a fragile quantum resource but as a structural property governed by interaction geometry and constraint density. On this view, classical behavior emerges when accumulated constraints sufficiently narrow admissible evolution, while quantum behavior re-emerges when constraints are relaxed. The account does not introduce new dynamics, collapse mechanisms, or modifications of quantum formalism, but instead clarifies the conditions under which existing formalisms yield stable, unified descriptions. The resulting constraints distinguish QCT from observer-centric, intrinsic-collapse, and purely descriptive decoherence accounts, while remaining compatible with globally unitary dynamics. Formal analysis in later sections develops operational redundancy conditions, admissibility constraints on joint states, and rigidity-style arguments linking redundant record structure to the stability of classical descriptions. These results do not constitute a complete theory of unification, but they narrow the space of physically admissible descriptions and clarify the structural role of coherence in bridging quantum and classical regimes.
This work provides a structural derivation of the quadratic form of the Born rule in quantum mechanics. Rather than postulating the probability rule as a foundational axiom, the paper proves that the exponent governing quantum probabilities is uniquely fixed by stability, contractivity, and duality requirements imposed on admissible physical laws. The analysis is carried out within a general operator-theoretic and law-space framework, in which physical laws are treated as fixed points of recursive generative dynamics. By combining strict contractive flow (Kappa Law), topological rigidity (Law of Endogenous Constraint), and algebra–geometry duality (Monad Duality), the paper demonstrates that only the Hilbert–Schmidt geometry is compatible with global stability of law evolution. As a consequence, the quadratic probability rule emerges as a rigid structural invariant rather than a free modeling choice. The result implies that any hypothetical modification of quantum theory based on non-quadratic probability rules would necessarily violate at least one of the fundamental structural requirements of admissible physical law, such as uniform contractivity, spectral stability, or duality consistency. Relation to Tier-1 dynamical formulation: This work develops a law-level (structural) resolution of the Born exponent. A complementary Tier-1 dynamical realization, formulated entirely within a constrained operator framework and independent of law-level recursion language, is developed in: J. Rodgers, Saturation Geometry and the Structural Emergence of Measurement and the Born Rule in a Capacity-Constrained Dirac–Λ System, Zenodo (2026).https://doi.org/10.5281/zenodo.18704783 The Tier-1 formulation may be read independently and derives the quadratic Born rule as a consequence of modular implementability and saturation geometry within the coupled Dirac–Λ system.
This work provides a structural derivation of the quadratic form of the Born rule in quantum mechanics. Rather than postulating the probability rule as a foundational axiom, the paper proves that the exponent governing quantum probabilities is uniquely fixed by stability, contractivity, and duality requirements imposed on admissible physical laws.The analysis is carried out within a general operator-theoretic and law-space framework, in which physical laws are treated as fixed points of recursive generative dynamics. By combining strict contractive flow (Kappa Law), topological rigidity (Law of Endogenous Constraint), and algebra–geometry duality (Monad Duality), the paper demonstrates that only the Hilbert–Schmidt geometry is compatible with global stability of law evolution. As a consequence, the quadratic probability rule emerges as a rigid structural invariant rather than a free modeling choice.The result implies that any hypothetical modification of quantum theory based on non-quadratic probability rules would necessarily violate at least one of the fundamental structural requirements of admissible physical law, such as uniform contractivity, spectral stability, or duality consistency.This work builds directly on the operator-theoretic resolution of quantum measurement: “A Complete Operator-Theoretic Resolution of the Quantum Measurement Problem” (DOI: 10.5281/zenodo.17823241), and on the generative law framework introduced in: “The Tier-0 Framework and the Everything Equation: A Universal Recursion Law for Physics, Mathematics, and Information” (DOI: 10.5281/zenodo.17813117).See also: The Tier–Omega Monad: Trans-Recursive Completion of the Everything Equation (DOI: 10.5281/zenodo.17859631), which establishes the unique trans-recursive invariant that terminates all possible meta-law recursion and completes the Everything Equation. This work provides the structural boundary underlying the entire framework developed in the associated papers. https://doi.org/10.5281/zenodo.17864384
Foundational problems in physics—including quantum measurement, spacetime emergence, gravitational dynamics, nonlocality, the arrow of time, and the status of physical existence—are typically addressed in isolation, via model-dependent extensions or interpretive assumptions. This work proposes a different approach. We introduce a constraint-based framework, the Closure Admissibility Principle (CAP), which specifies minimal structural conditions any physical description must satisfy in order to be globally consistent. CAP is formulated in operational terms, using admissibility of states, recoverability under refinement, and stability of closed records, without assuming spacetime, dynamics, or ontology a priori. We show that enforcing these constraints induces a unifying closure structure on law-space, from which several persistent foundational puzzles are resolved as structural consequences rather than postulates. In particular, collapse is reclassified as record selection, spacetime and gravity emerge only in compressible regimes, General Relativity appears as an infrared universality class rather than a fundamental law, singularities correspond to failures of admissible description, and null (“nothing”) models are excluded as inadmissible fixed points. The framework is explicitly falsifiable via operational and weak-field tests, and its scope and limits are stated precisely. The results suggest that many foundational paradoxes arise not from incomplete dynamics, but from admitting globally incoherent physical descriptions.
Modern theoretical physics faces an abundance of mathematically consistent frameworks and a scarcity of decisive empirical constraints. This work proposes a principled response to that situation by identifying stability under intervention as a primary selection criterion for viable physical theories. Adopting an explicitly operational perspective, the paper formulates stability as the non-amplification of operational distinguishability under physical processes, a requirement motivated by the finite precision and reproducibility of experimental practice. When combined with compositional consistency, purification, and reversible symmetry, this principle strongly constrains admissible statistical frameworks. Within this setting, quantum theory emerges not as a fundamental ontology or a historically contingent choice, but as the uniquely stable non-classical fixed point compatible with reproducible physical control by finite agents embedded within the systems they study. The defining structural features of quantum mechanics, including convex state spaces, affine dynamics, state–effect duality, and a Born-type probability rule, arise as consequences rather than postulates. The framework further suggests that spacetime locality and geometry need not be assumed a priori, but can be understood as constraints on the propagation of distinguishability in composite systems. Potential deviations from quantum theory are predicted to manifest as failures of stability, such as breakdown of dilation, violation of distinguishability monotonicity, or loss of local tomography. This repository contains the final submission-ready manuscript together with its LaTeX source and bibliography, deposited on Zenodo prior to journal submission.This version (v1.1) incorporates clarifications on scope, logical dependencies between principles, worked examples within the Jordan-algebra classification, strengthened hedging of speculative material, and refined statements of falsifiability, in response to detailed referee feedback.