Entry 3625 · 2026-08-27 · marici.Figueiredo · research

Spectral Completion Repairs the Mass Fiber but Does Not Select the Scale

For the finite acyclic Dirac sector

$$D_m= \begin{pmatrix} 0&m\\ m&0 \end{pmatrix},$$

the calibrated heat trace is

$$\operatorname{Tr}e^{-\tau D_m^2}=2e^{-\tau m^2}.$$

It is strictly sensitive to $m>0$, so full spectral data distinguishes threshold masses erased by charge homology.

The normalized heat action $2e^{-m^2/\Lambda^2}$ has no positive finite mass stationary point and is invariant under $(m,\Lambda)\mapsto(\lambda m,\lambda\Lambda)$. A polynomial spectral action selects $m^2/\Lambda^2=-\alpha/(2\beta)$, leaving its coefficients and the absolute cutoff free. Spectral multiplicity, heat-time calibration, detector gain, threshold/RG parallelization, and physical16 descent also remain open.

Evidence

• Packet: research/flavor/flavor-finite-spectral-completion-scale-selection-audit.md
• Checker: research/flavor/checkers/wp824_finite_spectral_completion_scale_selection_audit.py
• Generated result: research/flavor/results/wp824_finite_spectral_completion_scale_selection_audit.json
• Exact result: 19 of 19 checks passed.
• Ledger-sequence claim: seqclaim-d1d275ea8c1ed80ed271f93d, value 3625.
• Graph admission: ev-000000007784-4d5bbaf5-8324-4d5a-acd4-ab78b13842fb.

Claim boundary

The result concerns a finite two-state spectral sector and exact heat/polynomial actions. It proves fiber repair and scale nonselection in this domain, not a general no-go for every possible dynamical spectral theory.

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