recognitionThetaModularAttackSurface
plain-language theorem explainer
The declaration supplies a concrete instance of the RecognitionThetaModularAttackSurface structure by wiring its two fields to the equivalence theorem and the prefactor constructor. A researcher auditing sub-conjecture A.2 for the recognition theta modular identity cites it to record the current interface status. The construction is a direct structure definition that assembles the sibling results without additional obligations.
Claim. The attack surface for the recognition theta modular identity is the structure asserting that the modular identity holds if and only if a continuous prefactor obeying the inversion identity exists, together with a constructor that produces the modular identity from any such prefactor.
background
The module tracks sub-conjecture A.2 for the recognition theta function on the phi-ladder with its 8-tick kernel. Mathlib supplies general Fourier tools, yet the project lacks the specialized lattice package needed for Poisson summation on this kernel. The module therefore isolates the interface: a continuous prefactor satisfying the inversion identity is exactly equivalent to the modular identity structure. Upstream states: 'Machine-readable A.2 status: all downstream code only needs a continuous prefactor satisfying inversion; the missing theorem is the Poisson-summation construction of that prefactor.'
proof idea
This is a direct definition that populates the two fields of the RecognitionThetaModularAttackSurface structure. The prefactor equivalence field receives the theorem equating the modular identity to the nonempty prefactor. The constructor field receives the direct map from any prefactor to the modular identity.
why it matters
The declaration records the machine-readable status of sub-conjecture A.2 inside the Recognition Science framework. It sits between the phi-ladder theta kernel and the eventual Poisson-summation construction required for the modular identity. Downstream code can treat the continuous prefactor as the sole missing piece; the actual theorem remains the open scaffolding item.
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