Test PROBE-mode tie-break for the Xavier/He blind spot (negative result)

[rustnew]

What changed and why

Third fix attempt for zc_jacobcov's proven blind spot: jacob_cov's binary
activation-sign statistic is exactly invariant to the positive rescaling
that separates Xavier from He, so no PURE-mode secondary proxy can ever
break that tie -- both static attempts already in
scripts/compare_meta_predictors.py (TieBreakHeuristicPredictor's raw
and population-normalized gradient_norm variants) failed for exactly
this reason. This tests the other option named in the original audit
report: a minimal, explicitly-costed PROBE-mode run (docs.md §5).

Adds precog.meta_predictor.ProbeTieBreakPredictor: when jacob_cov
ties, spend a real, bounded PROBE budget (50 steps -- the cheapest the
Zero-Training Contract allows) on just the tied candidates, and pick
whichever ends with the lower loss.

Evidence

• Ran the new script locally end-to-end:

$ python scripts/explore_probe_tiebreak.py
test (locked): 180 rows (60 tasks)

zc_jacobcov                accuracy=47% (28/60)  he_recall=0% (0/10)  mean_regret=+14.6 steps  mean_probe_cost=0.0 steps
zc_jacobcov_tiebreak       accuracy=47% (28/60)  he_recall=0% (0/10)  mean_regret=+14.6 steps  mean_probe_cost=0.0 steps
zc_jacobcov_probetiebreak  accuracy=43% (26/60)  he_recall=30% (3/10)  mean_regret=+45.4 steps  mean_probe_cost=68.3 steps

Full report: results/reports/2026-09-03T12-59-38Z_explore_probe_tiebreak.md.

• Old vs new numbers both shown: zc_jacobcov raw (he-recall 0%,
  regret +14.6) vs zc_jacobcov_probetiebreak (he-recall 30%, regret
  +45.4). he-recall genuinely improves; regret -- this project's
  primary metric, see compare_meta_predictors.py's own
  regret-first winner selection -- gets worse. Not cherry-picked to
  look good.
• Negative result, kept and labeled as such: verdict is "NOT a net
  improvement", same treatment as LSUV init and active sampling
  before it.

Checklist

• CI (reproduce.yml) passes on this branch (new step added:
  "PROBE-mode tie-break for the Xavier/He blind spot").
• No claim asserted without a script/report backing it.
• data/meta_dataset.db / results/gate_evaluations.csv changed
  with reason: record_gate_evaluation() logs this run's one new
  gate row (docs.md §12 meta-dataset) -- a real, explained addition
  (single row, single clean run), not a side effect of local
  iteration left uncommitted.
• docs/index.html's "bug we found but can't fix" section updated
  from "two attempted fixes" to "three", linking the new report. No
  README change needed -- that section only exists on the project
  page, not the README.

Open questions / requested feedback

The 50-step probe budget is the contractual minimum (docs.md §5: PROBE is
50-1000 steps). I didn't sweep larger budgets since the failure mode here
(picking "he" because it looks locally good, then it stalls) seems more
about the kind of horizon needed (long enough to see non-convergence,
not just "more steps") than a simple budget increase -- but if a reviewer
thinks a quick sweep (e.g. 100/200 steps) is worth a follow-up before
closing this avenue, happy to add it.

[coderabbitai]

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[Christiantyemele]

@rustnew please what is the intend of this pull request

[rustnew]

here is another zc-jacobcov @Christiantyemele please check more

[Blindspot22]

LGTM

[rustnew]

@Christiantyemele This PR tests a third fix attempt for jacob_cov's Xavier/He tie (the two prior static-proxy fixes in compare_meta_predictors.py both failed for the same structural reason). It adds a bounded PROBE-mode tie-break (50 real training steps) instead.

Result: he-recall improves (0%→30%) but overall regret gets worse (+14.6→+45.4 steps) — a documented negative result, not a fix proposed for adoption, consistent with how this project logs failed attempts (see the report and PR description for full numbers).