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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Complement Conjugacy on the Digital Root Ring: Harmonic Analysis, Unit Group Filtration, and Conductor-9 L-Functions

Authors: Eckert, Anthony;

Complement Conjugacy on the Digital Root Ring: Harmonic Analysis, Unit Group Filtration, and Conductor-9 L-Functions

Abstract

Proves that the additive complement involution on the digital root ring DR9 = Z/9Z acts as exact complex conjugation on the character group: chi_k(phi9(n)) = chi_k(n)* for all k, n. Establishes a three-class unit group filtration (units, zero-divisors, kernel) and verifies all primitive Gauss sums lie on a circle of radius 3 in C. Identifies chi3 as the self-conjugate character — the algebraic signature of voluntary constraint reduction, corresponding to the Bird of Hermes mechanism. Connects to conductor-9 L-functions and the Pe=1 critical line. 6 falsifiable predictions.

Part of the Void Framework research project (MoreRight DAO).

Keywords

coniunctio, cyclic group, Gauss sums, zero divisors, Dirichlet characters, complement conjugacy, conductor 9, Peclet number, void framework, opacity measurement, unit group, digital root ring, L-functions, complex conjugation, alchemical manuscripts, harmonic analysis, digital root, complement involution, Péclet number, Bird of Hermes

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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!
0
Average
Average
Average
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