Questions under active investigation.

Does the Fourier transform of the Tesfa Grid residuals ε(j), computed in logarithmic column-index space, converge as C → ∞ to a spectrum whose peaks coincide exactly with the imaginary parts γ_n of the non-trivial zeros of the Riemann zeta function? Volume II presents strong empirical support. An analytic proof remains open.

The Harmonic Sieve nulls occur at frequencies f_k = k/C. Prove (or disprove) that these nulls are positioned between consecutive γ_n values, making the Tesfa operator a natural band-pass filter for zeta-zero frequencies.

Derive an analytic expression for the matched-filter z-score z(γ_n) as a function of grid width C, zero index n, and the Tesfa operator transfer function. If the formula implies z(γ_n) → ∞ as C → ∞, the Tesfa-Zeta Conjecture follows.

Can the Tesfa spectral framework constrain the real part of the zeta zeros to Re(ρ) = 1/2, providing a new path to the Riemann Hypothesis, one rooted in discrete geometric sieving rather than in contour integration or random matrix theory?

Theorem IV establishes a structural prime-exclusion property for the canonical grid. For what broader class of parameter triples (a, d, C) does an analogous exclusion theorem hold? Is there a modular characterization?

Twin primes concentrate in two specific structural classes within the grid, with approximately symmetric density (~35% each for primes up to 1,200). Is this symmetry asymptotic? Does it provide a new angle on the Twin Prime Conjecture?

The first two perfect numbers (6 and 28) always fall in the upper block of the grid; the third (496) in the lower. Does the Euclid–Euler formula 2^(n−1)(2^n − 1) admit a natural Tesfa Grid factorization? Volume III provides a classification; an algebraic proof for all perfect numbers is open.

The canonical Tesfa Grid construction is tied to the mod-6 structure of primes. Do generalizations with different row counts exhibit analogous structural properties for higher residue moduli (e.g. mod 30, mod 210)? Is there a family of structurally-related grids, each tuned to a different small primorial?

The Harmonic Sieve produces low-frequency power enhancement for the prime sequence at Z ≈ 17σ. Prove analytically that the expected LF power ratio for prime inputs differs from the random baseline by a specific amount depending only on C.

The cross-cycle residual correlation decays from 0.80 at W = 116 to 0.31 at 12 cycles. Would a dynamically-scaled width W(n) ∝ ln(n) maintain maximum resonance across unbounded prime ranges? Characterize the optimal scaling function.

The zeta function is the simplest of the L-functions. Does the Tesfa Grid residual spectrum also align with zeros of Dirichlet L-functions, automorphic L-functions, or Selberg zeta functions? Is there a family of modified Tesfa operators, each tuned to a different L-function?