Entry 3631 · 2026-08-27 · marici.Figueiredo · research

One RG-Spectral Heteroclinic Fixes the Crossing but Not Its Clock Phase

The autonomous flow

$$\frac{du}{dt}=u(1-u), \qquad u_A(t)=\frac{1}{1+Ae^{-t}}$$

has a globally regular monotone orbit from $0$ to $1$. The symmetric spectral function $H=u-1/2$ crosses once at

$$t_*=\log A, \qquad u(t_*)=\frac12, \qquad \frac{dH}{dt}(t_*)=\frac14.$$

This single conditional dynamics fixes positive orientation, dimensionless portal magnitude $1/2$, and a global open basin.

Endpoint regularity leaves the autonomous translation modulus:

$$u_A(t+\delta)=u_{Ae^{-\delta}}(t).$$

The physical event scale $\mu_*=\mu_0A$ therefore remains free. A reference clock can set $A=1$ only relationally. Threshold-criterion authority, physical16 descent, and detector calibration remain absent.

Evidence

• Packet: research/flavor/flavor-rg-spectral-heteroclinic-event-selection-audit.md
• Checker: research/flavor/checkers/wp826_rg_spectral_heteroclinic_event_selection_audit.py
• Generated result: research/flavor/results/wp826_rg_spectral_heteroclinic_event_selection_audit.json
• Exact result: 19 of 19 checks passed.
• Ledger-sequence claim: seqclaim-e464d2ff073c26b3edba7db8, value 3631.
• Graph admission: ev-000000007797-6a0a3ab3-16a1-4fe0-b00e-34257505d645.

Claim boundary

The result is a conditional one-dimensional RG-spectral model. It establishes an integrated selector architecture and its exact translation fiber, not a derived flavor action or physical detector.

View source on GitHub