Build reproducible interoperability benchmarks with Kuramoto ecosystem tools

[anulum]

Goal

Create one-adapter-at-a-time, reproducible comparisons between SPO and established synchronization tools under matched initial conditions and observables.

Initial ecosystem targets

• https://github.com/fabridamicelli/kuramoto — compact Python Kuramoto baseline
• https://github.com/arnaudon/simplicial-kuramoto — simplicial synchronization
• https://github.com/maximelucas/hypersynchronization — hypergraph synchronization
• https://github.com/juanitacabral/NetworkModel_Toolbox — delayed network model workflows
• https://github.com/neurolib-dev/neurolib — domain-specific whole-brain modelling context

These projects are complementary references, not dependencies and not competitors to rank by a single speed number.

Acceptance criteria

• Pin the external tool version and record environment metadata.
• Use identical topology, frequencies, coupling, initial phases, timestep, and horizon where semantics permit.
• Compare physical observables such as order-parameter trajectories and invariant bounds before runtime.
• Export machine-readable results and a human-readable limitations section.
• Separate unsupported semantic differences from numerical disagreement.
• Make no superiority claim without reviewed, repeatable evidence.

Each pull request should add at most one external adapter and one bounded benchmark scenario.