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Coherence-Bounded Calculus (IM-B001, v0.3)

Anders Nils Gunnar Widgren

Published Jan 22, 2026• 0 citations
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Abstract

This paper is part of the Informational Mechanics (IM) framework, a coherence- and admissibility-based approach to physical description. The document is published as part of the first public wave of IM papers, establishing the mathematical and axiomatic basis on which downstream regime models and interpretations are built. This work defines the admissible mathematical domain used throughout Informational Mechanics, including bounded local variation and admissible limits. It introduces no physical axioms, interpretations, particles, or modified dynamics.

DOI
10.5281/zenodo.18340937

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This paper is part of the Informational Mechanics (IM) framework, a coherence- and admissibility-based approach to physical description. The document is published as part of the first public wave of IM papers, establishing the mathematical and axiomatic basis on which downstream regime models and interpretations are built. This work defines the admissible mathematical domain used throughout Informational Mechanics, including bounded local variation and admissible limits. It introduces no physical axioms, interpretations, particles, or modified dynamics.
This paper is part of the Informational Mechanics (IM) framework, a coherence- and admissibility-based approach to physical description. The document is published as part of the first public wave of IM papers, establishing the canonical axioms, scope discipline, and foundational claim boundaries of the framework. This work states the axioms and foundational commitments of Informational Mechanics, formulated within the admissible mathematical domain defined in IM-B001. It introduces no regime models, experiments, or applications.
This paper is part of the Informational Mechanics (IM) framework, a coherence- and admissibility-based approach to physical description. The document is published as part of the first public wave of IM papers, providing a regime-based phenomenological bridge to particle-like structure. This work presents a particle-regime interpretation in which stable particle-like structures emerge as coherence-selected discrete invariant carriers under nonzero noise. No new particle species, numerical constants, or modified dynamics are proposed.
This document is part of the Informational Mechanics (IM) framework and is published in the IM-I (Reviews & Syntheses) series within the IM v0.3 corpus. The paper synthesizes recent IM work on universality and regime-limited validity to clarify the status of quantum mechanics under admissibility constraints. Rather than proposing modifications to quantum theory, it analyzes the conditions under which claims of global validity remain scientifically meaningful. Drawing on IM-C003 (regime-limited universality), IM-E001 (operator criteria for universality), and IM-D005 (structural non-derivability across regime transitions), the document shows how quantum-mechanical unitarity and state evolution must be understood as regime-bound statements whose validity depends on operator-defined implementability and cross-regime comparability. The paper introduces no new axioms, models, or empirical results. Its purpose is clarificatory and integrative: to provide a coherent account of how quantum mechanics retains full validity within admissible regimes while avoiding unwarranted global extrapolation beyond operator-defined structure.
This document is part of the Informational Mechanics (IM) framework and is published in the IM-B (Calculus & Admissibility) series within the IM v0.3 corpus. The paper establishes a structural uniqueness result for admissible strength functionals on inner-product spaces under orthogonal additivity, isometry invariance, and minimal regularity conditions. It shows that any such functional must be proportional to the squared norm, up to a positive multiplicative constant. The result is purely mathematical and introduces no physical axioms, dynamics, interpretations, or empirical claims. Its purpose is to provide a domain-neutral lemma intended for potential downstream use in IM-E (Measurement & Operators) and IM-D (Core Physics) papers when formalizing operator-defined comparability or outcome-weight structures. No claim is made that any particular physical system must satisfy the assumptions stated here.