Steady-state analysis and BETSE convergence study

[bshepp]

Summary

Adds the analysis the project's hypothesis calls for, and the first study that uses it.

Stacked on #3. The base is correctness-fixes; retarget to main once #3 is merged.

What is added

• mneme.analysis.steady_state
  • assess_steady_state() decides whether a relaxing run has settled. A low rate of change alone is not accepted: the distance still to travel is estimated from the fitted relaxation time.
  • count_distinct_states() groups end states against a stated threshold and reports how clean the grouping is.
• studies/convergence/: configuration generator, runner, analysis script, and results for a BETSE experiment.

Study result

Thirteen runs of one 42-cell tissue: six starting ion concentrations, with and without gap-junction coupling, plus one exact repeat.

Coupling	Largest gap at start	Largest gap at end	Distinct end states
Off	48.83 mV	0.32 mV	1
On	48.05 mV	0.17 mV	1

No multistability was found. Full write-up in studies/convergence/RESULTS.md.

Limits

• The runs did not meet the settling criterion fixed beforehand. Estimated remaining drift was 0.20 to 0.32 mV against a limit of 0.1 mV. The write-up states this and does not relax the criterion.
• The configuration has no mechanism expected to produce multistability, so this is a baseline, not a test of the hypothesis.
• Coupled runs used a coupling 50 times weaker than BETSE's default, which was numerically unstable at this time step.
• The raw simulation output (about 5,400 CSV files) is not committed. studies/convergence/README.md gives the steps to regenerate it.

Testing

tests/test_steady_state.py: 21 tests against known answers, including exponential relaxations with known time constants and a double-well system with two known stable states.

🤖 Generated with Claude Code