What does this research mean for the field?

Uniform cyclotomic Frobenius coupling recovers absolute prime gaps and yields a first-order interpretation of full arithmetic, motivating a new target regime of unbounded resolution depth with bounded independent shattering width to understand global coupling between primes. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

Investigate the expressive boundary between prime-permutation symmetry and full arithmetic by analyzing cross-prime coupling and structural resolution regimes.

August 27, 2026Open Access

Depth, Width, and Minimal Global Coupling between Primes. Reflections on the Corridor between Symmetry and Arithmetic with Commander Sol

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Authors

AMAlex Malachevsky

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Implication

Mathematical analysis reveals how cyclotomic Frobenius coupling enables full arithmetic interpretation across prime systems, indicating new structural bounds between symmetry and arithmetic.

Key Points

Investigate the expressive boundary between prime-permutation symmetry and full arithmetic by analyzing cross-prime coupling and structural resolution regimes.
Evaluated multiplicative arithmetic, operator lifts, and rational adeles to establish a finite-color locality no-go theorem.
Applied the Chinese remainder theorem and Dirichlet's theorem to test prime-set shattering under uniform cyclotomic Frobenius coupling.
Analyzed finite S-adic congruence towers and prime-shattering dimension using model-theoretic VC/NIP concepts.
Established that uniform cyclotomic Frobenius coupling recovers absolute prime gaps and induces full arithmetic through Cyclotomic Coding Collapse.
Demonstrated that finite S-adic congruence towers maintain nontrivial automorphisms despite unbounded resolution depth, failing to orient primes.
Formulated a target structural regime combining unbounded resolution depth with bounded prime-shattering width, proposing Ramanujan's Delta form as a test class.

Cite This Study

Alex Malachevsky (2026) studied this question.

synapsesocial.com/papers/6a8fe9c910c91c1e92621b4e https://doi.org/10.5281/zenodo.22092012

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Implication

Mathematical analysis reveals how cyclotomic Frobenius coupling enables full arithmetic interpretation across prime systems, indicating new structural bounds between symmetry and arithmetic.

Depth, Width, and Minimal Global Coupling between Primes. Reflections on the Corridor between Symmetry and Arithmetic with Commander Sol

Discussion

Member takes

Implication

Key Points

Cite This Study

Depth, Width, and Minimal Global Coupling between Primes. Reflections on the Corridor between Symmetry and Arithmetic with Commander Sol

Discussion

Member takes

Implication

Key Points

Cite This Study

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