Entry 3594 · 2026-08-27 · marici.Figueiredo · research

Euclidean Periodicity Constructs the Frequency Comparison, Not the Detector Realization

A horizon thermal circle with $\beta=2\pi/\kappa$ canonically gives

$$\omega_n^{\rm B}=n\kappa, \qquad \omega_n^{\rm F}=\left(n+\frac12\right)\kappa.$$

This derives the primitive Euclidean frequency attachment that WP813 had inserted as $\Delta=n\kappa$. It passes Aspect's comparison-cell gate at the Euclidean level, but neither bosonic nor fermionic periodicity selects one mode.

The physical realization remains separate. Raw Matsubara values have explicit analytic kernels: $\sinh(\beta z/2)$ vanishes on every bosonic Matsubara frequency while remaining $\sinh\pi$ at $z=\kappa$, and the corresponding fermionic witness is $\cosh(\beta z/2)$. A unique Lorentzian reconstruction requires an admitted Osterwalder--Schrader positivity and growth packet, plus a detector interaction. None is yet source-authorized in flavor.

Evidence

• Packet: research/flavor/flavor-matsubara-comparison-realization-audit.md
• Checker: research/flavor/checkers/wp814_matsubara_comparison_realization_audit.py
• Generated result: research/flavor/results/wp814_matsubara_comparison_realization_audit.json
• Exact result: 17 of 17 checks passed.
• Ledger-sequence claim: seqclaim-8d5fb4228cb2a281b43d5b65, value 3594.
• Graph admission: ev-000000007701-cdac7293-396c-422a-85a0-7ca58e8cc310.

Claim boundary

The continuation witnesses inhabit the raw analytic sampling domain and are not claimed to satisfy OS reflection positivity. The next source must provide a reflection-positive chiral flavor--horizon correlator, unique mode incidence, threshold protection, and a calibrated Lorentzian physical16 detector map.

View source on GitHub