IndisputableMonolith.NumberTheory.RecognitionTheta.MellinFactor
This module marks the current status of the abstract A.3 structure in the Recognition Theta program by direct instantiation with the constant function 1. Researchers tracing the RS-native zeta bridge from theta kernels would cite it as a temporary placeholder before analytic Mellin factorization. The argument is a status assertion rather than a derivation from the phi-ladder or Poisson summation.
claimThe abstract A.3 structure is inhabited by the constant function $1$, where this serves as a status marker for the Recognition Theta Mellin factor prior to full analytic factorization.
background
The Recognition Theta program connects the phi-ladder theta kernel to the completed zeta functional equation. Upstream ModularIdentity tracks sub-conjecture A.2 and requires a Poisson-summation theorem for the 8-tick theta kernel on the phi-ladder. ZetaFromTheta isolates the exact bridge via a theta-style Mellin transform compatible with the completed zeta function.
proof idea
This is a status module. The declaration directly asserts that the abstract A.3 structure is inhabited by the constant 1 function as a temporary stand-in.
why it matters in Recognition Science
This module records the current state of the A.3 structure in Phase 4 of the RS-native zeta program. It feeds the theta-to-zeta bridge and addresses the gap in the modular identity for the phi-ladder theta kernel before Poisson summation is available.
scope and limits
- Does not derive the Mellin factor from the theta kernel or Poisson summation.
- Does not claim analytic continuation or the full functional equation.
- Does not implement the lattice package required for recognitionTheta.
- Does not provide the complete factorization theorem.
depends on (2)
declarations in this module (7)
-
theorem
recognitionThetaMellinFactor_placeholder -
structure
StrongRecognitionThetaMellinFactor -
def
thetaCompletedZetaBridge_of_strongMellinFactor -
def
strongMellinFactor_of_thetaCompletedZetaBridge -
theorem
strongMellinFactor_iff_thetaCompletedZetaBridge -
structure
RecognitionThetaMellinFactorAttackSurface -
def
recognitionThetaMellinFactorAttackSurface