This project validates the unpolarized spike detector and reconstruction against exact true- and false-spike Gowdy families. It also preserves the unseen-parameter confirmation that qualified the first favorable control result.
CBE-3T-R1-A — the amended analytic formulas, implementation-equivariance checks, and half-cell unseen reconstructions pass.
- Re-derived true- and false-spike formulas solve the displayed field equations to numerical precision; the literal printed alternatives fail.
- Exact-family tests show that four-function VTD data loses the spike while enriched spike parameters restore it in centered controls.
- Integer cyclic shifts give identical centered and shifted errors, as required by discrete shift equivariance. This is an implementation check rather than a positional-robustness result.
- A separate Fourier half-cell shift samples the spike off the grid nodes. Both unseen families converge at approximately second order and fall below the (10^{-2}) reconstruction threshold on the finest grid.
run_cbe3t.py— exact-family control battery.run_cbe3t_r1.py— unseen-parameter confirmation.CBE3T.json,CBE3T_R1.json— machine-readable results.cbe3t_log*.txt— preserved logs.
Place this repository beside bb-cbe3, then install Python 3, NumPy, SciPy, and SymPy:
parent/
├── bb-cbe3/
└── bb-cbe3t/
python3 run_cbe3t.py
python3 run_cbe3t_r1.pyThis validates a class of exact spike controls. It does not establish that the production feature in bb-cbe3 belongs to that family.