Squared-Norm Uniqueness under Orthogonal Additivity and Invariance: An Admissibility Lemma for Stable Comparability Functionals (IM-B002, v0.3)

Anders Nils Gunnar Widgren

Published Feb 16, 2026• 0 citations

Abstract

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.

DOI: 10.5281/zenodo.18658984

Related papers

Operator Outcome Measures and the Squared-Norm Form: A Structural Admissibility Result (IM-E004, v0.3)

Anders Nils Gunnar Widgren

This document is part of the Informational Mechanics (IM) framework and is published in the IM-E (Measurement & Operators) series within the IM v0.3 corpus. The paper analyzes the structural status of outcome weights in quantum measurement under admissibility constraints. Rather than modifying quantum mechanics or deriving new dynamical laws, it formalizes the operator-defined conditions under which outcome weights must be proportional to the squared norm of state amplitudes. Building on the mathematical uniqueness result established in IM-B002, the analysis shows that orthogonal additivity, invariance under unitary transformations, and minimal regularity conditions constrain admissible strength functionals to the squared-norm form. The result is structural and regime-bounded: it applies within quantum-mechanical regimes where operator-defined observables and comparability are physically implementable. The paper introduces no new axioms, collapse models, hidden variables, or empirical fits. Its contribution is operational and classificatory, clarifying the admissibility conditions under which squared-amplitude outcome weights retain scientific meaning while avoiding unwarranted ontological extrapolation.

Feb 16, 20260 citations

Quadratic Persistence under General Disturbance: Stability of Admissible Comparability Functionals (IM-B003, v0.3)

Anders Nils Gunnar Widgren

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 extends the structural uniqueness result of IM-B002 by analyzing quadratic persistence under general disturbance processes. It shows that strength functionals satisfying orthogonal additivity and invariance remain uniquely stable under Gaussian disturbance, and classifies the conditions under which non-Gaussian perturbations preserve or break quadratic structure. The result is purely mathematical and introduces no physical axioms, dynamics, interpretations, or empirical claims. Its purpose is to establish disturbance-stability conditions within the admissible mathematical domain and to provide structural lemmas intended for potential downstream use in IM-E (Measurement & Operators) and IM-D (Core Physics) papers. No claim is made that any particular physical system must satisfy the assumptions stated here.

Feb 17, 20260 citations

Measurement Update as Operator Reclassification: A Regime-Conditional Account (IM-E005, v0.3)

Anders Nils Gunnar Widgren

This document is part of the Informational Mechanics (IM) framework and is published in the IM-E (Measurement & Operators) series within the IM v0.3 corpus. The paper analyzes quantum measurement update as an operator reclassification problem under admissibility constraints. Rather than introducing collapse dynamics or new axioms, the analysis formalizes the structural conditions under which outcome weights are uniquely determined by orthogonal additivity, invariance, and minimal regularity requirements. Building on the mathematical uniqueness result of IM-B002, the paper shows that admissible strength functionals compatible with operator-defined observables must take the squared-norm form within quantum-mechanical regimes. Measurement update is treated as a regime-bounded representational transformation rather than an ontological discontinuity. The work introduces no new axioms, collapse models, hidden variables, or empirical fits. Its contribution is operational and classificatory: it clarifies the admissibility conditions under which squared-amplitude outcome weights retain scientific meaning while preserving unitarity and operator-defined locality.

Feb 23, 20260 citations

Operator Stability and Classical Emergence: A Regime-Based Criterion for Observable Invariance (IM-E002, v0.3)

Anders Nils Gunnar Widgren

This document is part of the Informational Mechanics (IM) framework and is published in the IM-E (Measurement & Operators) series within the IM v0.3 corpus. The paper formalizes an Operator Stability Condition (OSC) that specifies when quantum-mechanical observables exhibit regime-stable invariance under admissible disturbance. Rather than introducing new dynamics or modifying quantum theory, the analysis provides a structural criterion for when operator-defined quantities become persistently comparable and support classical description. Classical emergence is treated as a consequence of operator stability: when observables retain invariant content under admissible measurement and environmental interaction, effective classical structure arises without invoking collapse models, hidden variables, or additional ontological assumptions. The paper introduces no new axioms, dynamical mechanisms, or empirical fits. Its purpose is operational and disciplinary: to clarify the admissibility conditions under which classical description remains scientifically meaningful and to connect foundational admissibility constraints (IM-C series) with downstream structural consequences (IM-D series).

Feb 15, 20260 citations

Bilinear Composition and Tensor Minimality: A Structural Result under Linear Closure (IM-B004, v0.3)

Anders Nils Gunnar Widgren

This document is part of the Informational Mechanics (IM) framework and is published in the IM-B (Calculus & Admissibility) series. The paper establishes a domain-neutral structural result concerning bilinear composition under admissibility constraints. It shows that minimal linear closure under bilinear composition yields tensor-product structure via the universal mapping property, providing the minimal equivariant linear extension compatible with bilinearity and representation invariance. The analysis is purely mathematical and introduces no physical axioms, dynamics, interpretations, or empirical claims. It clarifies the structural conditions under which bilinear composition forces tensor-product form, and explicitly delimits what is not derived (e.g., no metric, inner-product, probabilistic, or geometric structure is presupposed). The result is intended for potential downstream use in IM-D (Core Physics) and IM-E (Measurement & Operators) documents where composite representation structure and operator-defined composition are formalized under declared scope and regime constraints. No claim is made that any specific physical system must satisfy the assumptions stated here.

Feb 17, 20260 citations

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

Anders Nils Gunnar Widgren

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.

Jan 22, 20260 citations