Rejected experiment: centered TruncatedNormal bounded group priors

[AlexanderFengler]

Status: rejected experimental candidate

This draft is being closed without merge. It is the complete structural
prototype of an automatic centered hierarchical TruncatedNormal default for
bounded, identity-linked group-only locations, but the candidate failed its
predeclared numerical smoke gate.

The exact candidate head is preserved permanently as
codex/1269-truncated-normal-experimental-base at
9e7002f00e7ff40524a8afc9e83b62723461c98f. The research-only qualification PR
#1288 targets that frozen branch directly, so closing this PR does not change
its diff or evidence history.

What this candidate implemented

• Generated population locations and group coefficients used centered native
  hierarchical TruncatedNormal priors when the parameter had a finite native
  bound and used the identity link.
• Analytical and black-box DDM parameters retained their calibrated HDDM
  Normal/Gamma/Beta hierarchies.
• Transformed-link coefficients, matched deviations, group-only slopes, and
  explicit priors were unchanged.
• Mixed identity predictors received a structural warning because bounding one
  coefficient cannot constrain a complete additive predictor.
• Generated vector initial-value jitter respected finite and one-sided native
  group bounds without silently repairing invalid user starts.

Why it is not being merged

Canonical run
33410419447
returned screening-fail for the frozen candidate:

• direct PyMC lower-only and two-sided Gaussian hierarchies failed divergence
  gates, so the problem is not HSSM- or Bambi-specific;
• the HSSM softmax hierarchy failed its divergence and convergence gates;
• the LBA chain was unusable, with R-hat up to 2.97, bulk ESS 2.33, BFMI 0.029,
  and every retained draw at maximum tree depth;
• completed local finite-difference and PyTensor/JAX checks passed, so the
  evidence does not establish a current PyMC density or gradient defect.

The result rejects this automatic centered TruncatedNormal default. It
does not establish that every explicit hierarchical TruncatedNormal model is
invalid.

Stream boundary

• Core prior matching and ownership policy remains in Fix safe priors for unmatched group-only effects #1272 and proceeds
  independently.
• The numerical root-cause investigation remains in research-only draft Research: investigate hierarchical TruncatedNormal sampling geometry #1288.
• Any production default resulting from that investigation will be introduced
  through a separate, small policy bridge PR based on the merged core stream.
• Generic support-aware initialization, if retained, will be extracted into an
  independent production PR rather than inherited from this rejected default.

This PR is historical implementation evidence for #1269; it does not close
that issue.

Validation recorded for the prototype

• pytest tests/ -m 'not slow': 1,218 passed, 201 deselected
• independent focused review: 505 passed plus float32/float64 boundary fuzzing
• strict marimo validation and output-bearing export
• strict documentation build
• Ruff, Pyrefly, mypy, configured hooks, and git diff --check passed

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[AlexanderFengler]

Closing this draft unmerged because canonical smoke run 33410419447 rejected the automatic centered TruncatedNormal candidate. The exact candidate remains preserved at 9e7002f on codex/1269-truncated-normal-experimental-base, and research-only #1288 now targets that frozen base with its 23-file, 9-commit diff unchanged. Core prior robustification in #1272 proceeds independently; any eventual production default will arrive through a separate evidence-driven bridge PR.