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Other literature type . 2026
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Conference object . 2026
License: CC BY
Data sources: Datacite
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Conference object . 2026
License: CC BY
Data sources: Datacite
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MONSTROUS MOONSHINE AND THE DEDEKIND ETA FUNCTION ARCHITECTURE

Authors: Aksman, Michael;

MONSTROUS MOONSHINE AND THE DEDEKIND ETA FUNCTION ARCHITECTURE

Abstract

This addendum establishes formal mathematical correspondences between the DSM-861 spectral manifold and structures appearing in Monstrous Moonshine and the Dedekind eta function.Three precise connections are identified. First, the geometric commensurability defect δ = N/G−12 = 861/72 − 12 = −1/24 is exactly the exponent in the eta function prefactor q 1/24, and theEuler-Maclaurin Casimir residue |ε| = B2/2! = 1/12 satisfies |ε| = 2|δ| (corrected from the originalequation which incorrectly stated |ε| = |δ|/2). Second, the June 2026 Dehn twist proof establishes that η(τ + 1) = exp(iπ/12)η(τ) is the modular identity that directly produces the −1/12 anomalous dimension in the Navier-Stokes regularity proof—so the Moonshine connection is not merely analogical but is the operative mathematical mechanism. Third, the specific Moonshine coefficient 196884 appears explicitly in the DSM-861 quality factor: ∆j = 196884exp(−π√163) = 7.4993 × 10−13. The coefficient 196884 is the first non-trivial coefficient of the j-function j(τ) =q−1 +744+196884q+..., which by McKay’s observation equals 196883+1, where 196883 is the dimension of the Monster group’s smallest faithful representation. This is the precise Monstrous Moonshine link for DSM-861: the j-function residue at the Heegner point τ∗ directly encodes a Monster representation dimension. The paper does not claim direct equivalence between DSM-861 and V♮ (which has c = 24 and Monster symmetry); DSM-861 has c = 1 and C72 symmetry. The correspondences are genuine and precise but operate at the level of shared modular structures, not group isomorphisms.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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