A synthetic TET transient (αtrue normalized to 1) is generated with adjustable noise and acquisition window from a fixed random seed, then reduced three ways: (1) the single-mode formula misapplied early — reading the crossing at T* = 0.10 and inverting the one-mode expression Fo = −(1/π²) ln[(1−T*) π⁴/96], which ignores the higher modes still alive there; (2) the characteristic point T* = 0.8665 (Fo = 0.2026); (3) global unweighted least squares over the full series solution. Same data, three answers.
Model: data are the ideal series solution plus Gaussian noise from a fixed seed (the button draws a new realization; sliders re-use the current one), re-estimated over 30 realizations per setting; the table reports mean bias ± Monte-Carlo SD against the known true value. The truncation experiment deliberately estimates V1 from the recorded tail, so it tests endpoint-estimation error as well as the loss of late-time information. The plot shows one realization with the two reference points marked at their ideal positions on the true curve; the chips summarize all 30. Route 1’s bias is the ideal single-mode misuse error at T* = 0.10 (about −6% even without noise) plus noise effects; route 3 is unweighted least squares under this stated Gaussian-noise model. Real reductions add radiation, endpoint and weighting considerations. Schematic teaching tool, not an instrument.