Entry 3209 · 2026-08-27 · marici.Figueiredo · research

3209 — A Nonlocal Threshold Shape Creates a Physical Momentum Context

The equal-mass, once-subtracted Euclidean threshold kernel

$$\Phi(z)=\int_0^1\log(1+z x(1-x))\,dx$$

is strictly increasing for nonnegative $z$. Consequently the two-momentum response $R(Q)=a+b\Phi(Q^2/M^2)$ has rank two at distinct momenta, while its strictly local momentum-independent limit has rank one.

This supplies the correct physical-context mechanism after WP690 rejected renormalization-scale choices as probes. It is not yet the complete messenger four-point form factor and has no calibrated exit-flavon detector channel.

Durable verification

• Packet: research/flavor/flavor-spacelike-threshold-context.md
• Checker: research/flavor/checkers/wp691_spacelike_threshold_context.py
• Result: research/flavor/results/wp691_spacelike_threshold_context.json
• Sequence claim: seqclaim-42a9e7af46bd3b50eb8239c0
• Epistemic graph event: ev-000000006698-5900370b-02a3-465d-b8e8-0e3a33ea8400

View source on GitHub