Conciseness

The body is dense and lean — minimal prose, tables for method selection and troubleshooting, and no explanation of what ODEs or scipy are; every section delivers new information. It falls short of anchor 5 only because each example carries plotting boilerplate (plt.legend/grid/savefig) repeated across sections that could be trimmed or shown once.

Actionability

All six workflows are fully executable, copy-paste-ready code with realistic parameters (e.g., 'sol = solve_ivp(stiff_system, (0, 3000), [2.0, 0.0], method=\"Radau\", rtol=1e-8, atol=1e-10)'), and the method-selection and troubleshooting tables give concrete commands and fixes. The examples correctly cover the common cases named in the description.

Workflow Clarity

Each workflow is a self-contained recipe, and the skill supplies explicit validation ('Validation Checklist: ... Confirm convergence: halve max_step and check solution doesn't change') plus feedback loops for error recovery in the Troubleshooting symptom→cause→fix table. This matches anchor 5's 'explicit validation steps; feedback loops for error recovery; checklists', not anchor 4 which tolerates missing checkpoints.

Progressive Disclosure

The skill is fully self-contained with no bundle files, so there are no nested or buried references to penalize; section headers (When to Use, Do NOT Use When, Core Workflows, Method Selection, Validation, Troubleshooting) make navigation easy. It scores 4 rather than 5 because at ~230 lines some advanced material (e.g., the full symplectic integrator implementation or BVP details) could arguably live in a reference file, and the simple-skill exception (under 50 lines) does not apply.

Specificity

"Solve ordinary differential equations (initial and boundary value problems). Supports stiff/non-stiff systems, event detection, Hamiltonian/symplectic integration, parameter sweeps, and phase space analysis" lists multiple specific concrete capabilities covering the domain comprehensively. It clearly matches the anchor 'Lists multiple specific concrete actions; comprehensive coverage' rather than the level-4 anchor, which explicitly allows 'minor gaps in coverage'.

Completeness

Both parts are explicit: the 'what' is the first two sentences of concrete capabilities, and the 'when' is 'Use for any ODE system in physics, engineering, or applied math.' It falls short of the anchor-5 example because the trigger clause names broad domains rather than concrete user-side trigger phrases (e.g., 'when the user mentions ODEs or asks to integrate a system'), but it is well above the anchor-3 case where 'when' is missing or only weakly implied.

Trigger Term Quality

Natural terms include 'ordinary differential equations', 'ODE', 'initial and boundary value problems', 'stiff', 'Hamiltonian', 'event detection', and 'parameter sweeps' — good keyword coverage a user would actually say. It is not a 5 because common variations like 'system of differential equations', 'trajectory', 'integrate equations of motion', or file/extension synonyms are absent.

Distinctiveness Conflict Risk

'Solve ordinary differential equations' carves out a clear niche with distinct triggers (stiffness, symplectic integration, event detection, BVP) that few other skills would claim, so it is mostly distinct with only minor overlap risk against adjacent simulation/dynamics skills. It is not a 5 because the broad 'physics, engineering, or applied math' scope and terms like 'dynamics'/'simulation' leave some room for overlap with general simulation or fitting skills.