Add intrinsic resampling with absorbing states for particle filtering

[georgosgeorgos]

Summary

Implement intrinsic resampling with absorbing states for the particle filtering algorithm in its_hub/algorithms/particle_gibbs.py.

Background

The current particle filter supports systematic and multinomial resampling (ResamplingMethod enum). However, it lacks absorbing states — a mechanism where particles that reach a terminal/stopped condition are permanently frozen and excluded from resampling. Currently, when a reference particle is resampled, its is_stopped flag is reset to False (line ~455), which allows "dead" trajectories to be revived.

Intrinsic resampling conditions resampling on the particle system's own state (e.g., ESS dropping below a threshold) rather than resampling at every step. Combined with absorbing states, this means:

1. Particles that reach a stop condition (EOS, max steps, valid answer) enter an absorbing state — they keep their weight but are never resampled or propagated further
2. Resampling only occurs among active (non-absorbed) particles when ESS drops below threshold
3. The final population is a mix of absorbed particles (finished early with high confidence) and active particles (still being refined)

Current State

• Particle.is_stopped exists but is used as a soft flag — stopped particles skip propagation but can be resampled and revived
• ESS is computed (_effective_sample_size) but only used for entropic temperature annealing, not to gate resampling
• No distinction between "stopped because done" and "stopped because resampled away"

Proposed Changes

• Add ResamplingMethod.INTRINSIC or a separate resampling_trigger parameter
• Enforce absorbing state semantics: once is_stopped = True, the particle is permanently frozen
• Partition particles into absorbed/active pools before resampling
• Only resample among active particles; absorbed particles pass through unchanged
• Track absorbed particle count in traces for diagnostics