What does this research mean for the field?

For an observed representation, perturbations acting as a single state-independent symmetry form a maximal subgroup K with a normal subgroup H of strictly invisible perturbations, where the quotient K/H uniquely factors every compatible group-valued description and determines information transmission properties. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish the algebraic and information-theoretic structure of the universal boundary quotient governing intermediate symmetries in observed representations under perturbation groups.

August 29, 2026Open Access

The Universal Boundary Quotient of an Observed Representation

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Authors

CBCsaba BaloghSemmelweis University

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Implication

Theoretical analysis establishes a canonical boundary quotient for observed representations under perturbation groups, demonstrating exact entropy splitting and information transmission limits.

Key Points

To establish the algebraic and information-theoretic structure of the universal boundary quotient governing intermediate symmetries in observed representations under perturbation groups.
Characterized perturbation group actions by isolating the maximal subgroup of state-independent symmetries and the normal subgroup of strictly invisible perturbations.
Formulated quotient factorizations, residual entropy decompositions, and zero-error channel capacities for both finite groups and closed Lie subgroups with Haar measure.
Proved that all group-valued descriptions insensitive to invisible perturbations factor uniquely through the canonical universal boundary quotient.
Demonstrated that finite uniform perturbations partition residual entropy additively into boundary and invisible components, enabling zero-error transmission of log |B| bits per use.
Established that sector sizes alone fail to determine the boundary homomorphism or the quotient isomorphism type, showing that no general minimal repair exists.

Cite This Study

Csaba Balogh (2026) studied this question.

synapsesocial.com/papers/6a9299ac8e5d7d1fc0c11c4c https://doi.org/10.5281/zenodo.22126695

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Implication

Theoretical analysis establishes a canonical boundary quotient for observed representations under perturbation groups, demonstrating exact entropy splitting and information transmission limits.

The Universal Boundary Quotient of an Observed Representation

Discussion

Member takes

Implication

Key Points

Cite This Study

The Universal Boundary Quotient of an Observed Representation

Discussion

Member takes

Implication

Key Points

Cite This Study

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