The Tesfa Grid — three-volume programme
Volume II · Preprint · March 2026 · HeadlineEmpirical Evidence for the Tesfa-Zeta Conjecture: Spectral Alignment of Tesfa Grid Residuals with Riemann Zeta Zero Frequencies
First direct experimental test of the Tesfa-Zeta Conjecture. Three independent spectral methods across five grid widths with 300 randomized controls. Lomb-Scargle peaks align with known zeta zeros at sub-0.1 accuracy; matched-filter finds 10 of 30 zeros significant at p < 0.001. All signals absent in shuffled, noise, and fake-prime controls. The Riemann Hypothesis remains unproved; the Tesfa-Zeta Conjecture passes its first direct experimental test.
Volume I · Preprint · March 2026The Tesfa Grid: A Deterministic Harmonic Sieve and Its Structural Interactions with Prime Numbers
Foundational volume. Nine proved theorems: Column Closure Law, Upper and Lower Diagonal Mean Laws, Row-6 Prime Exclusion, General Summation Formula, Block Divergence (R² = 0.9992), Mod-6 Gap Constraint, Twin Prime Hex-Spacing, and the Harmonic Sieve Theorem. Introduces the Tesfa Wave and the Tesfa Gap Code. Statement of the Tesfa-Zeta Conjecture.
Volume III · In preparation · Late 2026The Multi-Level Gap Hierarchy and Structural Extensions
Extends the programme to the fine structure of prime gaps. Scale Invariance (Theorem X), Perfect Number Classification (Theorem XI), Mean Convergence Law, and the Prime Oscillation Law. Preliminary summary available; full preprint expected late 2026.
Research notes
Shorter expository notes on specific theorems and empirical results from the programme.
Research noteThe Mod-6 Gap Constraint (Theorem VII)
Statement, proof, and empirical verification of the Mod-6 Gap Constraint: every prime gap after the initial gap of 1 is congruent to 0, 2, or 4 modulo 6. Verified over 348,511 consecutive prime gaps with zero violations.
Research noteThe Harmonic Sieve Theorem (Theorem IX)
Statement and proof of the Harmonic Sieve Theorem: the generalized Tesfa Grid operator T_{C,w} has exact spectral nulls at frequencies k/C. Proved via the Dirichlet kernel and the Shift Theorem.
ConjectureThe Prime Oscillation Law
A statement of the Prime Oscillation Law as an empirical conjecture. Prime gaps display a structured grow-and-shrink behavior that is significantly distinct from random walks. Full quantitative characterization forthcoming in Volume III.