Synapse
⌘+K
Synapse
PulseExploreClubsResearchersJournals
Instagram
HomeClubsExplore
April 6, 2026Open Access

The Toccata Invariant: A Structural Fingerprint of the Prime-Zero Duality

View Full Paper
Ask AI
Bookmark
Share

Authors

MRMaksim Rakhman

Discussion

Loading...

Member takes

Overview

New observable reveals structural properties of Riemann zeta zeros, implying deeper mathematical insights.

Key Points

  • The research aims to introduce and analyze the Toccata Invariant, a new observable related to Riemann zeta zeros.
  • Introduced the lag-2 autocorrelation of the zero-counting deviation, S(t).
  • Analyzed 3,212 zeta blocks, totaling 13,835,800 zeros, with datasets reaching T = 3.06 × 10¹⁰.
  • Conducted perturbation analysis and finite-difference identity linking S-based and gap-based observables.
  • Identified the Toccata Invariant profile characterized by a descent and recovery pattern.
  • Detected zero violations in 69 tests with statistical significance (p < 0.001).
  • Observed that the first-step descent is driven by the lag-2 autocovariance numerator.

Cite This Study

Maksim Rakhman (2026) studied this question.

synapsesocial.com/papers/69d34e3e9c07852e0af97d15https://doi.org/10.5281/zenodo.19411908
View Full Paper
Ask AI
Bookmark
Share