fix(rhat): subnormal floor, discriminating tolerance probes, corrected docstring (#39 follow-up)

[marcohost33-maker]

Follow-up to #39 from its second delta review (P3 items; two of them are corrections of my own docstrings/tests).

Changes

• Upper-tolerance probe was too weak. It used a difference of 1e-13 at scale 1 and called it "~30 eps"; it is ~450 eps (28× the 16-eps tolerance), so a 16× looser tolerance survived. Now 1e-14 (~45 eps). Measured on 8db2b7d: tolerance ×4 → the probe goes red, ×2 → stays green; the tolerance is pinned to a factor 2–4.
• Non-discriminating location case replaced: (-1000.25, -999.5) was already caught by the old (location-blind) rule; (-1000.3, -1000.1) is not.
• Subnormal hole closed: a balanced chain (1e-315, 2e-315+5e-324) still reported OK/converged because eps*scale underflows to 0 while folding rounds by one ulp. The tolerance is now max(16·eps·scale, 16·spacing(scale)) — unchanged for normal numbers.
• Docstring rhat_defined wrongly said that under DEGENERATE_FOLDED rhat is the bulk R-hat; the reviewer measured rhat = 1.0 in 234/400 cases. Now: max(bulk, folded) with a non-meaningful folded component.

Evidence (Windows, py3.12) at d46e768

• new subnormal test red on 8db2b7d, green after the fix
• tests/test_rhat.py tests/test_manifest.py tests/test_checkpoint.py: 49 passed, exit 0; ruff check + ruff format --check clean
• diskriminierung.py run DK-20260926T095204-ad146ec2860f (provenance VOLL): 4/4 — spacing floor, tolerance ×4, location term (new case), positive control
• full suite and selftest: CI

🤖 Generated with Claude Code

[chatgpt-codex-connector]

You have reached your Codex usage limits for code reviews. You can see your limits in the Codex usage dashboard.
To continue using code reviews, you can upgrade your account or add credits to your account and enable them for code reviews in your settings.

[marcohost33-maker]

Independent round (Equalita role, same family) at d46e768: PASS (P3 only). (a) For normal s, spacing(s) ≤ eps·s, so the new floor never binds there — probed over 206 138 values, the only exception is s = DBL_MAX (np.spacing overflows, verdict flips OK → DEGENERATE_FOLDED, i.e. fail-closed); verdict comparison old vs new over 1000 cases (60/40, 2001/1999, iid, 1e6+N(0,1), shifted two-point) — 0 differences. (b) The upper-tolerance probe is exactly 45 eps: tolerance ×2 and ×2.8 green, ×2.9/×3/×4 red, identical over 50 seeds (median is global) — pinned to factor ~2.8. (c) Old rule: (-1000.25,-999.5) has ptp 0 (already caught), (-1000.3,-1000.1) ptp 512 eps (missed) — the replacement discriminates. Reviewer's runs: 49 passed, selftest 45/45, exit 0; discrimination DK-20260926T103544-a8db82703e88 5/5 (VOLL). P3: 'unchanged for normal numbers' does not hold at DBL_MAX; '234/400' not reproduced by the reviewer (165/400 with their distribution; qualitative 'often 1.0' holds). Tracked in #46's follow-up.

🤖 Generated with Claude Code