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.
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.
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.
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.
The Admissibility of Natural Physics, Part I begins where an admissibility-first reconstruction of single-system quantum mechanics ends. Its central question is not whether the familiar tensor-product formalism can be assumed, but whether any physical composition law can be derived without importing composite systems, global state spaces, entanglement, locality, or signalling as primitives. The book develops a disciplined reconstruction of binary quantum composition from operational and structural requirements. It first records the exact content and limitations of the inherited single-system closure, establishes dependency and non-circularity statutes, and introduces the possible object of natural physics only as a provisional target ledger rather than as an assumed ontology. It then examines joint preparation, product states and effects, marginal consistency, operational no-signalling, minimal and maximal probabilistic composites, local tomography, and the classification of admissible tensor-product representations. Particular attention is given to the distinction between a mathematical representation theorem and the uniqueness of a physical composition rule. Real, complex, quaternionic, Jordan-algebraic, minimal, maximal, restricted, and non-tomographic alternatives are compared under explicitly declared admissibility conditions. The complex Hilbert-space tensor product is recovered only on branches satisfying the required factorization, coherence, scalar, and operational closure conditions. Where several inequivalent composites survive, the result is a classified family rather than a falsely asserted uniqueness theorem. Entanglement is introduced only after composition has been commissioned. It is defined as the failure of an admitted joint state to belong to the convex closure of admitted product preparations. The analysis proves, within the resulting predictive grammar, that entanglement is a property of composite-state geometry, not an additional force, substance, interaction mechanism, or signalling channel. Throughout, the argument enforces quotient primacy, refinement stability, finite diagnostic closure, regeneration stability, explicit dependency receipts, local termination, and the possibility of Undefined as a legitimate scientific outcome. Part I therefore supplies neither a speculative ontology nor a presupposed many-world formalism. It provides a conditional classification theorem for binary physical composition and identifies precisely what remains to be established before interaction, repeated composition, particle identity, locality, fields, symmetries, and particle content may be addressed.
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.
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.
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.