Whitening assumes a uniform grid, so the sampling scheme cannot be improved on its own

[marcohost33-maker]

Where this comes from

PR #115 review, thread "Preserve early-time sampling for separated decay modes". The reviewer's instinct — keep unit-scaled early-time coverage and the 1/gap horizon — is right. It was not done in that PR, and the reason is worth recording as its own issue rather than as a paragraph in a closed thread.

The coupling

fitting/gls.py::_whiten forms r_k − ρ·r_{k−1} with a single AR(1) coefficient. A constant sample interval is therefore not a convenience of the current grid; it is an assumption of the noise model. That assumption also carries the parametric bootstrap and N_eff.

Put a two-scale or logarithmic grid underneath it and the lag-1 correlation becomes a function of position. The fit still returns numbers, the CI still prints, the AICc still selects — and none of them mean what they claim any more. That is a silent failure, which is the class this project treats as worse than a loud one.

So: the grid and the whitening cannot be changed independently. Either both move or neither does.

The hard limit that motivates it

On the current uniform grid, samples_per_fast_efolding = 1/(r_max·dt) ≈ 7.9·Δ/r_max. One uniform 80-point window straddles at most about an eightfold spread of timescales. Six decades — two independent channels at 1e-6 and 1 — is not reachable by any choice of uniform window. Only by roughly 1e6 points, or by giving up uniformity.

Measured on exactly that system (two amplitude-damped qubits, rates 1e-6 and 1, Δ = 5e-7):

window	beta_D_linear	relative error vs true Δ
old absolute [0, 10]	0.0177	3.5e4
gap-scaled [0, 2e7] (current)	7.9e-7	0.58

Both windows fail; they fail at opposite ends. The current one fails on the quantity that is not the layer's headline output, which is why it was chosen — not because it is adequate.

What PR #115 did instead

Disclosed rather than repaired: samples_per_fast_efolding is measured from the spectrum and an UnderResolvedTransientWarning fires below one sample per fast e-folding. That stops the layer from quietly reporting an unsampled mode as measured. It does not make the mode measurable.

Scope of this issue

1. Make the AR(1) whitening interval-aware (or replace it with a noise model that does not assume uniform spacing), and propagate that through the parametric bootstrap and N_eff.
2. Only then adopt a genuinely two-scale or logarithmic grid that covers both the fast transient and the 1/gap horizon.
3. Discrimination requirement: a test on the 1e-6/1 system in which the current implementation fails and the new one recovers both rates — not merely a test that the new grid runs.
4. The rate-unit invariance already pinned in tests/test_relaxation_grid_scale.py must survive. A guard or estimator that behaves differently at c ∈ {1e-4, 1, 1e4} reintroduces, inside the fix, the defect PR fix: scale the default relaxation window to the system's own relaxation time #115 removed.

Related: #111 (least-squares convergence is not rate-unit invariant at extreme spans) touches the same estimator from the other side.