[jdeast]

What

Review item 1.2.9 (JDE ruling 2026-10-27: do it now, verify no regression). A logit-transformed element (two finite bounds) no longer gives its raw coordinate an N(0, 1) density that section C then cancels. Its raw coordinate is flat, so its whole prior is the logit_uniform_prior.<label> potential: the sigmoid Jacobian plus the existing saturation guard. Non-logit elements keep their N(0, 1), which is their prior.

Why: the -0.5*raw**2 / +0.5*raw**2 pair added up to zero, but in float64 it left a residual of ~raw**2 * 2**-52. The DC2018_128 PTDE runaway fed on that residual. The clip at |raw| = 1e4 that bounded it put a -0.5*(raw**2 - 1e8) wall into the "uniform" prior, 1e4 whitened widths from seed 0's anchor. The whitening probe had to raise that wall (review 1.2.1). It also cost the close seeds of a multi-seed OGLE-2013-BLG-0341 start -1.5e8 nats. Making the raw coordinate flat deletes both terms. With nothing left to cancel there is no residual and nothing to clip.

Design

• Names and layout do not change. There is still one raw vector RV per parameter, <label>_raw, untransformed, with the same initval. Trace reuse, restart files (mkparam), polish, PTDE start dicts, the persisted whitening (_whitening.json schema unchanged) and trace_meta all key on that name, so a split was ruled out.
• A vector with any logit element is a pm.CustomDist. _raw_logp (module-level, so it pickles) is mask * (-0.5*raw**2) - ln sqrt(2 pi). The mask is a constant 0/1 vector, 1 on the non-logit elements. There is no pt.where, and a NaN still propagates on every element. A vector with no logit element keeps the plain pm.Normal.
• -ln sqrt(2 pi) per logit element is kept on purpose. Because of it, start logp, logged lp, per-term values at raw = 0, the evidence normalization (evidence_log_norm_terms) and the nested sampler's u-space bridge are all unchanged.
• Forward draws: random= draws N(0, 1) on every element, so .eval() on a graph that still contains its RVs behaves as before. This is documented as NOT being the prior. Nothing in exozippy samples a prior predictive.
• Removed: _RAW_CANCELLATION_CLIP, its shared variable, get_/set_/raised_raw_cancellation_clip, whitening's _PROBE_RAW_CLIP and the probe-time raise. _CLIP_HI becomes 0.5 * _WHITEN_MAX_STEP.
• What the wall did that was needed. The wall gave every logit element a 0.5-nat contour within the probe's reach, so an element too tight by more than the reach still escalated. Without the wall, such an element probes FLAT. A logit element cannot really be flat: its Jacobian alone costs 0.5 nats within |delta lq| ~ 1.5. So the new whitening._flat_logit_is_clipped books a flat probe of a logit element at the reach, and escalation proceeds as before. A flat non-logit element keeps NaN.

Audit (what relied on a proper raw N(0, 1) for logit elements)

• sample_prior_predictive / pm.draw: no callers in src. Graph .eval() with RVs left in: tests/test_element_parameterization.py did this. Keeping it working is the reason for the N(0, 1) random=.
• PyMC initial point and jitter, nutpie, numpyro, blackjax: all start from the given initval plus uniform jitter. None draws from the RV. Sampled a mixed logit/unbounded toy with pymc (cores=2), nutpie, numpyro and blackjax; all four recover both marginals. That is now a slow test.
• ADVI: no callers.
• PTDE start populations (ptde.py, system._jitter_*, samplers/_common.py): these are jitter proposals around centers and never use the raw density.
• Seed polish: optimizes the compiled logp. Total logp is unchanged.
• Whitening probe: covered by the flat booking above. Measured multipliers are bit-identical to master on kelt4, ob140939, DC2018_128 and ob161003.
• Anchor re-centering / set_whitening invariance: still a pure change of variables. The flat raw plus the Jacobian gives a uniform prior for any anchor and scale.
• samplers/nested.py: it uses 0.5*raw**2 + ln sqrt(2 pi) only for its own Normal-prior class, which it detects by saturation, so logit elements are unaffected. The constant is kept, so its likelihood is unchanged.
• Evidence normalization (evidence.py, parameter.md): unchanged, because the constant is kept.
• Branch mixtures (system._add_branch_mixtures): free-RV priors are not in the mixture. The logit potential depends only on raw and factors out, as before.
• Per-term logp consumers (the startup table, diagnostics.point_logps, acceptance fixtures, example decomposition scripts): at raw = 0 every term is unchanged. Away from the start, -0.5*raw**2 leaves RV:<x>_raw and +0.5*raw**2 leaves POT:logit_uniform_prior.<x>, and the total stays the same. The example scripts already collapse the pair. Their comments are updated.
• NaN-reject argument (mulensing/physics.py, mulensevent.py): still holds, because mask * NaN**2 is NaN. Pinned by a test.
• Fold of node-degenerate labels (orbit.md, system.fold_degenerate_draws): re-measured. tc's raw-space terms now differ by only its logit Jacobian, -1.386 -> -2.604. On master they differed by -2.97e10 against a correction capped at +5e7. The docs are updated.

No runaway. Far from the anchor a logit element's logp is log q(1-q) ~ -|lq| plus the quadratic saturation guard. Both are computed directly, both are monotone past the logistic peak, and neither ever exceeds the prior's own maximum. A sampler that accepts increases has nothing to ratchet. tests/test_flat_logit_raw.py pins this out to |raw| = 1e17, plus 2000 random large excursions. test_runaway_logp_regression.py, which replays the historical DC2018_128 runaway draw, still gives a hugely negative logp, and its good-draw lp is unchanged.

Bit-identity (start logp, repr, master bfa0ea1 vs this branch)

The same sweep driver as #498/#501/#502/#503 (every top-level shipped config), plus a second point displaced +0.37 on every raw element. Table and scripts are in the session scratch; summary:

• 37/45 bit-identical.
• 8/45 differ by 1-2 ulp at the start: gj1214, hat3, hat3_mist_claret, hd80606, kelt17_all, kelt17_dt, kelt17_rm, wasp18. Example: gj1214 108507.98057121363 -> ...364. Traced term by term on gj1214: the only terms that move are the RV terms of all-logit vectors, by one ulp each (transit.baseline_raw -7.35150826563738 -> -7.351508265637381). The cause is that the masked quadratic constant-folds away, so the n copies of -ln sqrt(2 pi) are summed one at a time. pm.Normal's graph produced n*c. This is float summation order, not a model change.
• At the displaced point every config agrees to <= 1.7e-15 relative. That point is inside the old clip, where the cancellation was exact up to round-off.
• theophylline fails the same way on both sides (its data file is not shipped).

Total-logp claim: identical inside the old clip, as measured above. Past it, the old wall is gone; that is the fix.

OGLE-2013-BLG-0341 (private config, built read-only from a scratch copy, ulimit -v 12000000, serial; peak RSS 0.95 GB)

seed	solution	source.t_0_raw	master	this branch
0	Wide(+)	0	149673.19832904811	149673.19832904811
1	Wide(-)	-2331	160464.93845465267	160464.93845465282
2	Close(-)	20082	-151477592.43	161311.12
3	Close(+)	20082	-151476115.42	161006.56
4	Wide*(-)	-2082	159874.13587441234	159874.13587441263

The closes lose the -1.515e8 wall and land where their data fit puts them. Seeds 1 and 4 move by about 1e-10 nats. That is the old cancellation's round-off at |raw| ~ 2e3, gone.

Tests

• New tests/test_flat_logit_raw.py, which fails on master at every point past the old clip:
  • uniform physical density out to +/-1e7 widths from the anchor;
  • a seed 2e4 widths away pays exactly the Jacobian difference (< 0.1 nat; on master, -1.5e8);
  • no runaway out to 1e17;
  • NaN propagates;
  • a mixed vector keeps N(0, 1) on its unbounded element only;
  • an all-non-logit vector is still pm.Normal;
  • (slow) all four NUTS backends sample it.
• tests/test_whitening.py: the clip-raise test is replaced by tests for the flat-logit booking and for a non-logit NaN surviving. The ">= 3 escalation rounds" case moves from 1e-19 to 1e-28, because one round now reaches ~9 orders instead of 6. The "What flat means" table in whitening.md is re-measured; 1e-9 now resolves in one round.
• Locally, on this box at load ~28: fast tier -m "not slow" -n6: 4513 passed, 1 skipped. Targeted slow set (mulens acceptance a/b, multiseed PTDE, ptde, ptde_async, nested, runaway regression, polish, nuts_start, node_degeneracy, whitening_anchor, evidence, mode evidence, the new file): 113 passed. CI is the gate for the rest.
• Note for CI time: this changes the graph of every logit element, so expect one cold compile-cache run (docs/testing-cache.md).

Docs

• parameter.md: new section "The raw coordinate of a logit element is FLAT -- do not give it back an N(0, 1), and do not re-add a clip", written as a why-it-is-this-way ruling.
• whitening.md: the third-limit bullet is now history plus what replaces it; the flat table is re-measured.
• orbit.md: node-degeneracy labels re-measured.
• Comments in system.py, polish.py, run.py and mulensing/*.
• docs/testing-cache.md.
• The example decomposition scripts' comments.

Review item 1.2.9.

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