What does this research mean for the field?

One-degree homogeneous recurrence structures for identity persistence can be classified as point, line, or circle (ℝ/H), where finite comparison covering radius is equivalent to cocompactness of the return subgroup and forces the circle S¹. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To classify recurrence normal forms for identity persistence under declared regimes and resolve complete invariant canonicalization on the circle boundary.

August 14, 2026Open Access

Recurrence Normal Forms for Identity Persistence: Declared Scale, Contextual Quotients, and the S¹ Boundary

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To classify recurrence normal forms for identity persistence under declared regimes and resolve complete invariant canonicalization on the circle boundary.
Quotiented recurrence distinctions irrelevant to target identity behaviors to classify one-degree homogeneous structures as closed subgroups ℝ/H.
Analyzed topological return subgroups, forward-semigroup connectivity, and algebraic invariant representations on the circle S¹.
Proved that non-triviality combined with a finite comparison covering radius (cocompactness) uniquely restricts the recurrence structure to the circle S¹.
Showed that Fourier magnitudes are incomplete rotation invariants, whereas the finite-bandlimit weight-zero invariant algebra is finitely generated and orbit-separating.
Characterized bispectral completeness using support-sensitive rank and lattice-saturation conditions.

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Implication

Theoretical analysis demonstrates that recurrence structures reduce to circle topologies under bounded comparability, establishing exact criteria for invariant canonicalization.

Cite This Study

Devin Bostick (2026) studied this question.

synapsesocial.com/papers/6a7ec775b70b84ec8b913e47 https://doi.org/10.5281/zenodo.21899125

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Implication

Theoretical analysis demonstrates that recurrence structures reduce to circle topologies under bounded comparability, establishing exact criteria for invariant canonicalization.

Recurrence Normal Forms for Identity Persistence: Declared Scale, Contextual Quotients, and the S¹ Boundary

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Discussion

Implication

Cite This Study

Recurrence Normal Forms for Identity Persistence: Declared Scale, Contextual Quotients, and the S¹ Boundary

Key Points

Discussion

Implication

Cite This Study

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