feat(report): state the grid probabilities arrived on, and show it costs the floor nothing

[TMHSDigital]

Part of #9. It answers two of the three open questions.

Should the report state the observed grid? Yes. calibration.probability_grid(values) returns the coarsest of 0.1, 0.05, 0.01, 0.005 and 0.001 that every value sits on, or None. It needs at least 20 values, because a handful landing on a grid says nothing about the vendor. When there is a grid, the arm's section gets a line like this:

• Resolution: all 80 probabilities this arm returned are multiples of 0.01, so no bin or threshold finer than 0.01 can mean anything, and a tie for the top option is ordinary rather than rare.

When the bins are narrower than the grid, the line adds a warning that the binning measures the rounding.

Is the achievable ECE floor higher than the one computed? No. scripts/quantization_floor.py simulates a perfectly calibrated model with continuous true probabilities, sends them rounded to the grid, and reads ECE on the rounded values against calibration_floor of those same values, as the report does. If rounding cost calibration that the floor doesn't model, the calibrated model would clear the floor's 95th percentile more than 5% of the time.

With 200 trials per cell:

rows	bins	grid	mean ECE	floor mean	above p95
40	10	0.01	0.1141	0.1149	5.5%
500	10	0.01	0.0345	0.0339	5.5%
10,000	10	0.01	0.0074	0.0076	2.5%
10,000	10	0.05	0.0080	0.0075	6.5%
105	20	0.01	0.1002	0.0994	7.0%

The false-alarm rate stays at the nominal 5% (sampling error is about 1.5 points), even on a grid five times coarser than the vendor's. Rounding moves each value by at most half a step, in both directions, and since the floor is computed from the rounded values those errors cancel within a bin. METHODOLOGY has the full table, and the script reproduces it.

Still open on #9: whether the grid varies by model or by option count. That needs live runs against more than one model version.

Tests cover grid detection at 0.05, 0.01 and 0.001, no grid for values finer than that or for too few values, and the report line for an adapter on the 0.01 grid. docs/example-report.md is unchanged, since the mock's probabilities are continuous. The gate, the site checks and the prose checks all pass.

🤖 Generated with Claude Code