Entry 3597 · 2026-08-27 · marici.Figueiredo · research

Reflection Positivity Reconstructs a Supplied Pole but Does Not Select It

The one-pole Euclidean correlator

$$C(\tau)=A e^{-\Delta\tau}, \qquad A,Delta>0,$$

has a positive rank-one reflection Gram matrix and is completely monotone. On an independently authorized one-pole domain, its first two exact moments reconstruct $A$ and $\Delta$, closing the raw Euclidean continuation kernel.

Reflection positivity admits every positive pole and residue. It is also blind to the sign transformation $O\mapsto-O$, and positive threshold shifts move the pole without violating positivity. A one-pole measure and an equal-weight two-pole measure at energies $1/2$ and $3/2$ share the first two moments, so finite readout does not authorize the one-pole domain.

OS positivity is therefore a faithful realization condition on a declared domain, not a source selector, sign law, numerical threshold protector, or detector calibration.

Evidence

• Packet: research/flavor/flavor-reflection-positive-reconstruction-selection-audit.md
• Checker: research/flavor/checkers/wp815_reflection_positive_reconstruction_selection_audit.py
• Generated result: research/flavor/results/wp815_reflection_positive_reconstruction_selection_audit.json
• Exact result: 18 of 18 checks passed.
• Ledger-sequence claim: seqclaim-5187bb305d3e5e513c148d32, value 3597.
• Graph admission: ev-000000007708-9e36c384-dbf8-4ace-926f-79a8d9adc482.

Claim boundary

The faithful reconstruction result is restricted to the declared one-pole domain. The required successor is a source-derived reflection-positive odd correlator with unique chiral pole incidence, protected normalization, and the same operator's calibrated physical16 detector coupling.

View source on GitHub