3131 — Gaussian Resolution Preserves Objects but Not Uniform Separation
Result
Gaussian detector convolution has Fourier transfer , which is strictly positive at every finite real frequency. It therefore preserves exact separation of Lorentzian mass-width objects. Two convolved templates coincide only when both mass and width agree.
Uniform separation nevertheless fails as their mass-width parameters coalesce. A positive Gram lower bound defines an operational target domain, not evidence of detector calibration.
Scope
This establishes injectivity and the completion-stability distinction. It does not supply detector-derived resolution, background covariance, efficiencies, or uncertainty bounds.
Durable verification
- Packet: research/flavor/flavor-gaussian-convolution-pullback.md
- Checker: research/flavor/checkers/wp655_gaussian_convolution_pullback.py
- Result: research/flavor/results/wp655_gaussian_convolution_pullback.json
- Epistemic graph event:
ev-000000006405-412e6a98-ef25-4106-a503-57460e2503ed