What is the Tesfa Grid?
The Tesfa Grid is a structured matrix construction parameterized by an offset, a common difference, and a column count. The construction itself is purely geometric independent of any property of the sequence used to populate it. Structural theorems are proved at the geometric level first, and once proved they hold regardless of what sequence is used as input.
The full construction rule, including the placement procedure and the proofs that depend on it, is set out in Volume I (preprint available; full peer-reviewed version forthcoming) and in the applied work documented in Volume III (in preparation).
The programme's central question is: when the prime sequence is used as input to this geometric construction, what interactions visible, measurable, provable arise between the structure of the grid and the structure of the primes?
The three volumes
Each volume is a standalone monograph with its own scope, theorems, and numerical experiments. Together they form a unified research programme now in its twelfth year.
Methodology
Algebraic proof
Every structural theorem of the grid (Theorems I–V, VII, VIII, IX) has an algebraic proof. These are short, checkable, and require no probabilistic reasoning.
Statistical verification
Every empirical claim is stated as a hypothesis test with explicit null, test statistic, and p-value. 300 randomized controls per reported result is a typical baseline.
Adversarial controls
All significance claims include specificity controls: shuffled inputs, random-gap surrogates, Gaussian noise. Where controls eliminate the signal, the signal is reported as structurally dependent on the prime sequence.
Conjecture discipline
Conjectures are labeled. The Tesfa-Zeta Conjecture and the Prime Oscillation Law are stated explicitly as open conjectures supported by empirical evidence, not as theorems.