The Labeled-Zeta Heat-Trace Bridge

Abstract

Prime-axis logarithmic length derives the labeled-zeta Hilbert criterion from the universal heat-abscissa theorem.

Theorem 1.1 (Labeled zeta is the prime-axis specialization).

$\forall s\in \mathbb{C},\mathrm{MemLp}(\mathrm{labeledZetaCoefficient}(s),2)\iff \frac{1}{2}<\Re (s)$

Proof. Machine-checked in Lean as D5/S3/Midline/ZetaHeatTraceBridge.zeta_mem_iff_from_universal_heat_trace (✓ std3). ∎

Source. Repository-derived.

Commentary.

The bridge identifies the universal heat coefficient with the labeled-zeta coefficient, proves boundary-divergent abscissa one by transporting to the p-series on natural addresses, and then applies the universal strict theorem.

References

• Truth anchor: D5/S3/Midline/ZetaHeatTraceBridge.zeta_mem_iff_from_universal_heat_trace
• Dependency: D5/S3/Midline/UniversalHeatTrace
• Dependency: D5/S3/Weil/SpectralHilbert