Add optional frozen complete-path bias functions

[Zhang-pchao]

Summary

Add an optional pathbias module with PATH_LOGMEANEXP, PROBABILITY_MIX and CONDITIONAL_PATH. These stateless actions combine fixed complete-path potentials with explicit normalization and full derivatives. They do not train a model or define a PIMD integrator.

Dependencies and license

Stacked on the shared-path OPES feature #1471 and its #1463/#1467 prerequisites. The final module commit contains the new source, module metadata, manual examples and three native regression suites. The module is distributed under LGPL version 3 or later; the source headers and module documentation agree.

Contracts

Keep global partition-function normalization distinct from coordinate-dependent conditional normalization. Preserve all derivatives of fixed normalization functions. Replica-root aggregation and force ownership are explicit. Every bead of a complete path shares a statistical weight; beads are not independent samples. No claim of improved sampling, marginal preservation with an approximate normalizer, or scientific convergence is made.

Validation

Independent MPI/current-master build with all modules passed. Native regressions cover stable log aggregation, analytic/finite-difference derivatives, domain rejection, replica layouts and frozen OPES integration. All OPES regressions also passed. No private models, trajectories or host paths are included.

Documentation

The native current-master new-manual generator and MkDocs build completed. All changed action examples have empty stderr and are absent from the broken-example list. The full manual reports 36 failing example pages outside these actions and missing optional-module/link warnings; the full manual is not claimed to be warning-free. Inherited generic keywords are not all covered by examples.

Python/OpenMP CI follow-up

Includes the separately reviewable regression-process lifetime fix #1470, which retains the dynamically loaded kernel during Python shutdown. It preserves two-thread execution and the original numerical reference. This addresses the rt-symfunc shutdown failure observed on the debug runner.

Regression follow-up

Included the accepted rt-protein shutdown fix #1473, the rt-grid follow-up #1477, and the timestep-test initialization fix accepted in #1464. The Python configs pass three direct two-thread runs per case with byte-identical reference output; the existing build reports Python unavailable to the native runner. The timestep regression passes through the native runner with poisoned automatic-variable initialization against both v2.10 and master kernels. No reference values, tolerances or thread counts were changed. The Autoconf download failure has a separate upstream CI proposal in #1474.

Terminology and companion integration

The module documentation now distinguishes coordinate averaging, CV averaging, bias-energy averaging and probability-ratio averaging. COUPLING is distinct from coordinate contraction. The complete-path adapter is proposed in lammps/lammps#5232; lammps/lammps#5233 is an optional coordinate-contraction extension, not a dependency of these stateless functions. Zhang-pchao/molsimflow#1 provides a separate numerical oracle and complete-path analysis.