The Tesfa Grid is a 6×C matrix that reveals proved theorems about prime number structure, gap hierarchy, and cryptographic generation. TesfahSec is one application of a much broader mathematical framework.
Three completed volumes, all results independent of TesfahSec. The framework is an original contribution to analytic number theory.
Defines the 6×C geometric framework with two-phase filling rules. Proves nine structural theorems including the Row-6 exclusion principle, Column Closure, Summation Formula, Block Divergence (R² = 0.9992), and the fundamental gap constraint. Verified on 348,511 consecutive prime gaps.
Introduces the G1–G4 gap hierarchy (gap-of-gaps and higher differences). Proves the Prime Oscillation Law (P0 = 0.6822, Z = 211) and Mean Reversion principle (r = -0.73 correlation). Provides the theoretical basis for the TAPSN prediction architecture.
Introduces TAPSN (Tesfa-Aware Prime Sequence Network). Shows that Theorem 7 as a hard output constraint gives +0.65pp accuracy improvement with zero training data. Achieves 85.3% top-10 accuracy on blind test of 50,000 primes. Discusses applications to genomics, finance, and physics.
The paper behind TesfahSec. Derives formal proof for efficiency of candidate pre-filtering from the geometric framework. Provides benchmark results at 512, 1024, and 2048-bit RSA key sizes. Proves security via classical number theory results on primes in arithmetic progressions.
The Tesfa Grid framework is not specific to cryptography. The same proved constraints apply wherever prime number structure underlies a domain.
Theorem-guided neural prediction where mathematical hard constraints replace training data. Generalises to any domain with proved structural rules — genomics (base-pairing), finance (no-arbitrage), quantum systems (energy levels).
Formally proved efficient prime generation for RSA and ECC. HSM integration, FIPS 186-5 compliance analysis, C implementation for OpenSSL integration. Hardware licensing track.
The Tesfa Grid's harmonic sieve (Theorem 9) shows exact spectral nulls at f = k/C. Investigating connections to the Riemann zeta function and distribution of prime gaps in the spectral domain.
JFS's core research: applying the same proved structure-discovery framework to financial time series. Market price movements share the property of appearing random while having demonstrable underlying structure.
Independent research programme, Addis Ababa, Ethiopia. Mathematical research + commercial application.
AAU graduate 2019. Creator of the Tesfa Grid framework. All nine theorems in Volumes 1–3. TesfahSec product lead. arXiv: tesfadereth.