Geometric Phase Existence in Tensorial Regimes: A Constructive Structural Result (IM-D008, v0.3)

Anders Nils Gunnar Widgren

Published Feb 21, 2026• 0 citations

Abstract

This document is part of the Informational Mechanics (IM) framework and is published in the IM-D (Core Physics) series within the IM v0.3 corpus. The paper provides a constructive existence result for an effective geometric phase of description within a tensorial entanglement regime. Building on the structural criteria developed in IM-D007 and the tensor minimality results of IM-B004, the analysis demonstrates that a tree tensor network (TTN) regime satisfying admissibility constraints admits a well-defined path-length metric derived from entanglement invariants. The result is regime-conditional and existence-based: it establishes that geometric description can emerge under specific structural conditions without asserting universality, gravitational dynamics, holographic duality, or spacetime ontology. No new axioms, dynamical models, or empirical fits are introduced. The contribution is structural and classificatory, clarifying when entanglement organization supports effective geometric language while preserving locality, operator-defined observability, and regime-bounded validity.

DOI: 10.5281/zenodo.18723147

Related papers

Entanglement Structure and Effective Geometric Classification: A Regime-Conditional Analysis (IM-D007, v0.3)

Anders Nils Gunnar Widgren

This document is part of the Informational Mechanics (IM) framework and is published in the IM-D (Core Physics) series within the IM v0.3 corpus. The paper develops a structural account of when entanglement admits effective geometric classification under regime-bounded admissibility constraints. Building on IM-B004 (tensor minimality), IM-D006 (structural non-factorizability), and IM-C004 (regime-conditional structural principles), the analysis identifies necessary invariance and stability conditions under which entanglement structure supports geometric descriptors. Geometry is treated as an effective, regime-dependent language rather than a primitive ontological layer. The work does not derive spacetime, gravitational dynamics, or holographic dualities; instead, it provides structural criteria for when geometric interpretation is admissible and when it breaks down. No new axioms, dynamical mechanisms, or empirical fits are introduced. The contribution is classificatory and structural, clarifying how geometric description may emerge as an admissible phase of entanglement organization while preserving locality, operator-defined observability, and no-signaling constraints.

Feb 18, 20260 citations

Entanglement as Structural Non-Factorizability: A Regime-Conditional Account of Bell Correlations (IM-D006, v0.3)

Anders Nils Gunnar Widgren

This document is part of the Informational Mechanics (IM) framework and is published in the IM-D (Core Physics) series within the IM v0.3 corpus. The paper develops a structural account of quantum entanglement under regime-limited admissibility constraints. Rather than introducing new dynamics, hidden variables, or collapse mechanisms, it analyzes entanglement as a consequence of structural non-factorizability arising from bilinear composition and tensor minimality within admissible operator regimes. Building on IM-B004 (tensor minimality), IM-C004 (regime-conditional structural principles), and IM-E004 (operator-defined outcome weights), the analysis shows that Bell-inequality violations constrain classical factorizability assumptions without implying superluminal signaling or ontological inseparability. The account preserves the formal structure of quantum mechanics and treats locality and no-signaling conditions as operator-level constraints. No new axioms, empirical fits, or modifications to established physical theories are introduced. The contribution is classificatory and structural: it clarifies how entanglement and Bell correlations emerge within regime-bounded admissibility while explicitly identifying the structural assumptions under which the account would require revision.

Feb 18, 20260 citations

Unitary Evolution Across Regime Transitions: Structural Non-Derivability Under Admissibility Constraints (IM-D005, v0.3)

Anders Nils Gunnar Widgren

This document is part of the Informational Mechanics (IM) framework and is published in the IM-D (Core Physics) series within the IM v0.3 corpus. The paper analyzes the status of unitary evolution when physical description crosses regime boundaries. While unitary time evolution is well-defined within admissible geometric regimes, its extension across inadmissible regime transitions is shown to lack structural derivability unless operator-defined state continuity can be physically implemented. Building on the regime-limited validity arguments of IM-C003 and the operator criteria formalized in IM-E001, the paper demonstrates that global unitarity cannot be presumed as an ontological default. Instead, unitary evolution must be treated as a regime-bound statement whose validity depends on the continued implementability of the operators required to define and compare physical states. The analysis introduces no new axioms, dynamical models, or empirical fits. Its contribution is structural: to clarify the admissibility conditions under which claims of global state continuity remain scientifically meaningful and to show why cross-regime extrapolations of unitarity constitute a category error when operator-access fails. Downstream empirical and simulation-based evaluation of regime transitions is addressed in the IM-G series.

Feb 14, 20260 citations

On the Regime-Limited Validity of Quantum Mechanics (IM-I002, v0.3)

Anders Nils Gunnar Widgren

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.

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

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