Latest research
All publications →Empirical Evidence for the Tesfa-Zeta Conjecture: Spectral Alignment of Tesfa Grid Residuals with Riemann Zeta Zero Frequencies
We present the first direct experimental test of the Tesfa-Zeta Conjecture the proposition that the Fourier transform of the Tesfa Grid residuals, computed in logarithmic column-index space, produces spectral peaks coinciding with the imaginary parts of the non-trivial zeros of the Riemann zeta function. Three independent methods applied across five grid widths (C = 500 to 10,000) with 300 randomized controls. Lomb-Scargle peaks align with known zeta zeros at sub-0.1 accuracy. Matched-filter tests find 10 of 30 zeros significant at C = 10,000 (p < 0.001).
Volume I · Preprint · March 2026The Tesfa Grid: A Deterministic Harmonic Sieve and Its Structural Interactions with Prime Numbers
The foundational volume. Nine proved theorems including the Column Closure Law, Diagonal Mean Laws, Row-6 Structural Prime Exclusion, General Summation Formula, Block Divergence, Mod-6 Gap Constraint, Twin Prime Hex-Spacing, and the Harmonic Sieve Theorem. Introduces the Tesfa Wave, the Tesfa Gap Code, and the Tesfa-Zeta Conjecture.
Volume III · In preparation · Expected late 2026The Multi-Level Gap Hierarchy and Structural Extensions
Extends the research programme with further structural theorems on the multi-level gap hierarchy, including the Mean Convergence Law and the Prime Oscillation Law. A deeper investigation of scale invariance, perfect number classification within the grid, and the fine structure of prime gap sequences.
Guiding principles
Geometry first, primes second
The grid's construction is defined purely geometrically, independent of any property of its entries. All structural theorems are established before primes are introduced. What remains after primes enter must be a genuine interaction between structure and sequence, not an artifact of the definition.
Statement, proof, verification
Every claim is either a proved theorem with an algebraic or spectral proof, or an empirical observation with full statistical support and specified null hypothesis. Conjectures are clearly labeled as conjectures.
Open research
The mathematics is for everyone. Correspondence, critique, and collaboration are welcomed. Open problems are stated explicitly in each volume. Students and researchers at any career stage are invited to engage.
Deliberate disclosure
The mathematical framework is published freely. Applied engineering built on top of the framework is pursued through a separate commercial venture and is not part of the research programme's public output.
Selected findings
A small selection of quantitative results from the two published volumes.
An open invitation
The Tesfa Grid is an independent research programme. If you work in number theory, spectral analysis, discrete geometry, or computational mathematics and you find these questions worth your time, we would be delighted to hear from you.