test: execute causal truncated-hierarchy qualification (#1282)

[AlexanderFengler]

Scope

This is the B2 research-only child of #1294. It executes the prospectively frozen causal experiment for #1282 and does not change HSSM prior construction, parameter defaults, or user-facing runtime behavior.

The only future intersection with the robust-prior stream is a separate, evidence-driven defaults PR after this study reaches a causal conclusion.

Design

• two exact v2-failing toy-Gaussian regimes: lower-only weak information and finite-bound near-boundary information;
• five same-natural-model representations:
  • native centered TruncatedNormal hierarchy;
  • independent manual centered density control;
  • centered location + ICDF-noncentered group effects;
  • ICDF-noncentered location + centered group effects;
  • fully ICDF-noncentered hierarchy;
• PyMC and NumPyro executed together on the same worker for each dataset;
• 20 smoke fits in 2 ten-cell jobs and 160 confirmation fits in 16 ten-cell jobs;
• shared byte-identical data and natural-scale starts, fresh process/cache per fit, exact RNG provenance, and all ten fits attempted after scientific failure;
• independent second-order oracle checks for value, gradient, and Hessian at fixed, start, ICDF, and independently selected trajectory points;
• raw posterior and per-draw sampler statistics retained in SHA-256-bound artifacts;
• fail-closed aggregation and classification with smoke explicitly limited to screening.

Frozen manifest semantic SHA-256:

dde2ce8a7bdce1db72c5cb343887be6817cf56177fd9981e7d19d48963d97744

Evidence integrity

The assessor independently verifies artifact bytes, exact source/runtime identity, PyMC/NumPyro RNG semantics, minimum-SHA trajectory selection, source-natural-to-coordinate-to-restored-natural round trips, and raw oracle/sampler summaries. A real numerical failure remains scientific evidence; malformed or forged evidence is rejected as a contract failure.

The earlier v2 experiment and workflow remain byte-identical.

Validation

• 237 passed in the frozen Python 3.12 / PyMC 6.3.1 / PyTensor 3.3.0 / JAX 0.11.1 environment, including tiny real PyMC and NumPyro runs;
• independent final review: no remaining contract, workflow, or scientific blocker;
• Ruff check and format;
• mypy and Pyrefly;
• repository prek hooks on all ten files;
• strict YAML parse (6 jobs);
• contract validation: 20 smoke fits / 160 confirmation fits, 2 / 16 paired jobs;
• frozen v2 byte-hash audit;
• git diff --check.

Run policy

Keep this PR in draft while evidence is generated. First apply the smoke label. Confirmation may run only after smoke evidence is complete and contract-valid; smoke success or failure cannot itself establish a causal root cause. No defaults change belongs in this PR.

Closes neither #1269 nor #1282.

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[AlexanderFengler]

Exact-head smoke is now complete at 9039110538c910f96b0ba2da9a3ba7296c2f15cc: https://github.com/lnccbrown/HSSM/actions/runs/33559164529

• 20/20 cells present; 0 failed; 0 missing
• contract_valid=true, evidence_complete=true
• outcome=screening-fail, proceed_to_confirmation=true
• qualifies_causal_conclusion=false (smoke remains screening-only)
• frozen manifest digest remains dde2ce8a7bdce1db72c5cb343887be6817cf56177fd9981e7d19d48963d97744

Descriptive screen: lower-outside is healthy for group-ICDF/full-ICDF on both backends; two-sided is healthy for PyMC group/full ICDF while every NumPyro form is unhealthy. The earlier JAX central-derivative mismatch is fixed and those deterministic gates now pass. One PyMC/manual-centered/two-sided posterior-trajectory Hessian is non-finite in the bounded diagnostic evaluator even though value, gradient, and the independent Hessian are finite. I am holding the 160-fit confirmation matrix until that single diagnostic edge is reviewed, to avoid an expensive mixed-inconclusive run.