Primary repository: HowToFit. Branch: feature/howtofit-ep-shared-centre.
Local clone: /workspace/scratch/a05dd794807b/HowToFit, main clean and fetched before work. Mind has no conflicting claim in these repositories. The two HowToFit changes are coordinated sequentially in this authorized batch on separate branches; no separate bundle backlog.

Assign the same centre prior to all dataset models. Replace the constant regression likelihood with an explicitly explained width-relation model; validate likelihood sensitivity and shared identity, run real EP and inspect updates/figures. Regenerate notebooks/catalogue. Remove the no-run entry only if real-sampling evidence supports it; retain and document any remaining blocker.

Heart door: STALE, release stale and monitoring red; not a release-readiness claim. Recheck authoritative readiness before shipping. Use Python 3.12 local runtime.

HowToFit tutorial 5 (EP) never shares the centre it says it shares

Type: bug
Target: HowToFit
Repos:

• HowToFit
  Themes:
• graphical-ep
• tutorials
  Difficulty: small
  Autonomy: supervised
  Priority: normal
  Status: formalised
  Consequence: glance
  Witness: af.ModelPlotter(factor_graph.global_prior_model).figure() for tutorial 5 shows one shared centre (the blue shared badge), the EP state figure shows every dataset factor updating with no STALE FACTORS line, the headless run exits 0 and the notebook is regenerated.
  Review-minutes: 3
  Unattended: ready
  Filed: 2026-09-13

Found 2026-09-13 while rolling the model figure into
HowToFit/scripts/chapter_3_graphical_models/tutorial_5_expectation_propagation.py
(model-figures phase 6a, task model-figures-rollout-autofit, PyAutoFit#1620).

Symptom

The tutorial's prose says "We will assume all Gaussians share the same centre"
and creates centre_shared_prior = af.GaussianPrior(...), but never assigns it:
each per-dataset model gets a fresh af.GaussianPrior for centre, so nothing
is shared across the datasets. The new model figure makes this visible: no
shared badge appears anywhere on the map (only the orange relation pills
into linear_regression), and the EP run prints
STALE FACTORS: dataset_0 never completed a single update.

Related: the tutorial is listed in config/build/no_run.yaml as NEEDS_FIX 2026-08-05 (PyAutoFit#1454, LinearRegressionAnalysis.log_likelihood_function
returns a constant -1), so CI never runs it and neither defect is caught.

Fix

• Assign centre_shared_prior to every per-dataset model's centre (mirror how
  tutorial 2 / tutorial 3 share the centre), so the map shows the blue shared
  badge and the EP fit actually passes messages about one centre.
• Re-check the __Seeing the EP run__ prose added in phase 6a against a fresh
  render once the centre is shared (it was written to describe only what the
  unshared map showed).
• If PyAutoFit#1454 is fixed alongside, drop the no_run.yaml entry so smoke CI
  runs the tutorial again; otherwise leave it and say so in the PR.

Acceptance

• af.ModelPlotter(factor_graph.global_prior_model).figure() shows one shared
  centre; the EP state figure shows every dataset factor updating.
• Headless run exits 0; notebook regenerated.