DOI: 10.5281/zenodo.19651221 ABSTRACT Prior papers in this series have established that the Minimum Informational Boundary enforces probability conservation as a causality protection mechanism, and that the scalar field formalism, Lorentz invariance, and the Einstein field equations each independently encode this requirement. The present paper identifies a common symmetry-conservation structure that may underlie that convergence. Noether's theorem states that every continuous symmetry of the action of a physical system corresponds to a conserved quantity. This paper argues that the conservation requirement identified by the Minimum Informational Boundary framework — the prohibition against Deletion and Insertion Breaches — is best understood as an interpretive extension of the symmetry-conservation structure described by Noether's theorem, with global phase invariance providing the clearest internal-field example of that structure. This symmetry is not a new postulate. It is already present, implicitly, in every physical theory that admits a well-defined action principle. The Information Boundary Principle framework proposes to make this implicit structure explicit by identifying its physical content as a constraint on causally admissible evolution. The convergence of three independent mathematical formalisms on the same conservation requirement is therefore not coincidental. It is the expected consequence of a single symmetry operating at the foundational level of physical law. Noetherian symmetry-conservation structure is the mathematical bridge between that symmetry and the conservation it expresses. In classical action-based theories, this bridge appears through Noether’s theorem. In quantum settings, the corresponding conservation structure is also expressed through unitary evolution, conserved operators, Hamiltonian symmetry, commutation relations, and invariant expectation values. The Minimum Informational Boundary is the point in the present framework where this broader symmetry-conservation structure is interpreted as a physical constraint on admissible evolution. This revised and expanded version adds a causality-protection analysis that was implicit but undeveloped in the original paper. It also clarifies the scope in which Noether’s theorem is used. The article does not claim that the classical Lagrangian form of Noether’s theorem is the exclusive source of conservation in quantum mechanics. Rather, it uses “Noetherian” to refer to the broader symmetry-conservation structure of physical law. In quantum mechanics and quantum field theory, that structure also appears through unitary symmetry transformations, conserved operators, Hamiltonian symmetry, commutation relations, and invariant expectation values. The Minimum Informational Boundary is therefore proposed as a causal-admissibility condition within this broader symmetry-conservation architecture, not as a replacement for quantum mechanics and not as a claim that classical Noether machinery exhausts quantum conservation. The paper proposes that causal consistency is protected through three mutually reinforcing layers: first, the interlocking symmetry-conservation structures considered here; second, irreversible registration once an event crosses the Minimum Informational Boundary; and third, the logical self-termination of any process that attempts to alter the causal conditions of its own existence. The first layer is Noetherian in the broad symmetry-conservation sense. The second and third layers are proposed consequences of the Information Boundary Principle framework, not standard consequences of Noether’s theorem alone. AUTHOR NOTE This paper is part of the Information Boundary Principle series of theoretical papers. This revised version (v2) clarifies the relation between classical Noether theorem, quantum conservation, and the Minimum Informational Boundary framework. The Minimum Informational Boundary is not presented as a direct derivation from classical Noether theorem alone, but as a proposed causal-admissibility interpretation of the broader symmetry-conservation architecture of physical law. Version 2 also adds Section 7A on causality protection, over-determination, and irreversible registration; revises the Abstract, Introduction, and Sections 4 through 9; and adds Endnote 8. The original paper (v1) was uploaded April 19, 2026 under DOI: 10.5281/zenodo.19651221. The present version should be read in conjunction with the preceding paper in this series: Probability Conservation as Causality Protection: The Minimum Informational Boundary as a Structural Constraint of Physical Reality, DOI: 10.5281/zenodo.19647216, and with Paper 15 of this series: The Logical Necessity of a Fifth Local Spatial Dimension, Zenodo, March 26, 2026. All papers in this series are available on Zenodo under ORCID 0009-0001-9148-9221. ZENODO VERSION DESCRIPTION Version 2 clarifies the relation between classical Noether theorem, quantum conservation, and the Minimum Informational Boundary framework. The revision preserves the original thesis while narrowing the claim: the Minimum Informational Boundary is proposed as a causal-admissibility interpretation of the broader symmetry-conservation architecture of physical law, not as a direct derivation from classical Noether theorem alone. Version 2 also adds Section 7A on causality protection, over-determination, and irreversible registration; revises the Abstract, Introduction, and Sections 4 through 9
GERALD GOLL (Sun,) studied this question.