What does this research mean for the field?

Evaluating Connes-Moscovici cyclic cocycle residues under an off-axis hypothesis yields a non-vanishing twisted index mismatch that contradicts Hodge-Arakelov geometry, thereby eliminating off-axis roots in the context of the Hilbert-Pólya conjecture. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

What question did this study set out to answer?

To establish a regularized operator-theoretic framework addressing the Hilbert–Pólya conjecture using non-Archimedean scattering theory, tropical reduction, and bivariant KK-theory.

September 5, 2026Open Access

Adelic Blaschke–Potapov Operator Sheafs and Bivariant KK-Theory Kasparov Pairings on Type II∞ von Neumann Factors over the Berkovich Skeleton

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Authors

OGOleg Glushkov

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Implication

Theoretical analysis reveals an index-theoretic framework eliminating off-axis spectral roots on the Berkovich skeleton, highlighting a potential pathway toward the Hilbert–Pólya conjecture.

Key Points

To establish a regularized operator-theoretic framework addressing the Hilbert–Pólya conjecture using non-Archimedean scattering theory, tropical reduction, and bivariant KK-theory.
Constructed the domain of the dilatation operator on the idèle class group via inductive limits under an invariant measure to evaluate deficiency indices.
Formulated the global scattering matrix as an infinite multiplicative Blaschke–Potapov contractive operator sheaf parameterized by Hecke–Weierstrass L-factors on the Berkovich skeleton.
Embedded the spectral system into a bivariant Kasparov KK-pairing within a hyperfinite type II∞ von Neumann factor and computed Connes–Moscovici cyclic cocycle residues.
Established strictly (0, 0) von Neumann deficiency indices and confirmed a discrete Fredholm spectrum on the cuspidal parabolic subspace.
Derived an operational isomorphism on the Berkovich skeleton yielding a trace-class operator bundle whose Fredholm determinant matches the complete Riemann zeta function.
Demonstrated that off-axis roots generate a non-vanishing negative topological index mismatch, contradicting Hodge–Arakelov geometry and eliminating off-axis zeros.

Cite This Study

Oleg Glushkov (2026) studied this question.

synapsesocial.com/papers/6a9bd4436b95aff0620ebc75 https://doi.org/10.5281/zenodo.22285492

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Implication

Theoretical analysis reveals an index-theoretic framework eliminating off-axis spectral roots on the Berkovich skeleton, highlighting a potential pathway toward the Hilbert–Pólya conjecture.

Adelic Blaschke–Potapov Operator Sheafs and Bivariant KK-Theory Kasparov Pairings on Type II∞ von Neumann Factors over the Berkovich Skeleton

Discussion

Member takes

Implication

Key Points

Cite This Study

Adelic Blaschke–Potapov Operator Sheafs and Bivariant KK-Theory Kasparov Pairings on Type II∞ von Neumann Factors over the Berkovich Skeleton

Discussion

Member takes

Implication

Key Points

Cite This Study

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