What question did this study set out to answer?

To investigate geometric foundations of conductor rigidity and static conduit in the context of the Goldbach conjecture.

February 23, 2026Open Access

The Goldbach Mirror II: Geometric Foundations of Conductor Rigidity and the Static Conduit in GSp(4)

Key Points

To investigate geometric foundations of conductor rigidity and static conduit in the context of the Goldbach conjecture.
Introduced Chen's ratio as a measure of conductor in Siegel moduli space.
Conducted computational scanning over a specified range of N values.
Performed geometric obstruction analysis to formalize observations.
Found that Goldbach pairs are constrained to a narrow ρ-band, indicating rigidity.
Identified that conductor dips occur at N = 2^k, isolating boundary-prime structures.
Established an analytic gap necessary for proving the Goldbach conjecture.

Abstract

Building on the algebraic framework established in the companion paper (Zenodo: 10. 5281/zenodo. 18684892), we introduce Chen's ratio ρ (N, p) = log 𝒩 (J₍, ₏) / log N as a normalised measure of the conductor of the Goldbach–Frey Jacobian in the Siegel moduli space. Computational scanning over N ∈ 10², 10⁴ reveals that Goldbach pairs are rigidly confined to a narrow ρ-band—the static conduit stability band—while composite decompositions spread over a range roughly three times wider. At N = 2ᵏ, the odd radical of the static conduit vanishes, producing dramatic conductor dips that isolate the pure boundary-prime structure. We formalise these observations through a geometric obstruction analysis and identify the precise analytic gap (effective GSp (4) Sato–Tate equidistribution) required to convert this framework into a proof of the Goldbach conjecture.

The Goldbach Mirror II: Geometric Foundations of Conductor Rigidity and the Static Conduit in GSp(4)

Key Points

Abstract

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