IndisputableMonolith.NumberTheory.RecognitionTheta.ModularIdentity
Module supplies candidate modular prefactor data for the Recognition Theta identity. Researchers tracking sub-conjecture A.3 would cite it to inhabit the Mellin factor placeholder. It imports the upstream convergence comparison theorem to prepare explicit prefactor candidates without proving the identity.
claimThe modular prefactor data for the Recognition Theta identity consists of a nonzero function $G : ℂ → ℂ$ that serves as candidate input to the Mellin relation.
background
The module imports Convergence, whose result states that if Recognition Theta terms admit a summable nonnegative majorant for each positive t, then sub-conjecture A.1 follows via a general comparison theorem. This supplies the summability tool needed downstream. The module itself introduces candidate modular prefactor data to support the Recognition Theta identity in the NumberTheory.RecognitionTheta setting.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module feeds the MellinFactor module for sub-conjecture A.3. The downstream doc states that the existing structure is only a placeholder asking for nonzero G and leaving the Mellin identity as True; this module makes that explicit by supplying the candidate prefactor data.
scope and limits
- Does not prove summability of the Recognition Theta term for every t > 0.
- Does not establish the Mellin identity as a theorem.
- Does not connect the prefactor to specific values such as alpha inverse or phi.