Entry 3628 · 2026-08-27 · marici.Figueiredo · research

Spectral Flow Fixes Crossing Orientation, Not Location

For the oriented path

$$H_\rho(t)=t-\rho, \qquad -1\leq t\leq1,$$

every $-1<\rho<1$ has spectral flow one. The distinct crossings $\rho=1/4$ and $3/4$ therefore have identical index data. Spectral flow protects orientation and count while forgetting numerical threshold location.

The one-loop transmutation scale

$$\Lambda=\mu\exp\left(-\frac{1}{2bg(\mu)^2}\right)$$

is RG invariant, but every allowed $\Lambda$ corresponds to a different boundary coupling. For $m=\rho\Lambda$, the crossing-location and boundary- condition fibers remain independent. A calibrated path clock, threshold map, physical16 descent, and detector are also absent.

Evidence

• Packet: research/flavor/flavor-spectral-flow-dimensional-transmutation-audit.md
• Checker: research/flavor/checkers/wp825_spectral_flow_dimensional_transmutation_audit.py
• Generated result: research/flavor/results/wp825_spectral_flow_dimensional_transmutation_audit.json
• Exact result: 17 of 17 checks passed.
• Ledger-sequence claim: seqclaim-5ddb80f3ca3475f4a79f9d64, value 3628.
• Graph admission: ev-000000007791-f565c2bf-d8e2-46ac-b8b6-5442bfddee31.

Claim boundary

The result uses a one-level spectral path and one-loop asymptotically free transmutation. It demonstrates independent location and scale fibers in this minimal architecture, not a universal no-go for every coupled spectral RG system.

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