Inextensible Catenary Inverse Endpoint Slack Shape & Tension Solver

Choose this endpoint when you need to solve the inverse catenary problem — recovering the cable model and local physics from geometric and physical cable parameters — rather than a forward simulation. It is specifically suited for inextensible cable models (no elastic stretch), making it appropriate for heavy structural cables, transmission lines, and rigging where material extension is negligible. Prefer this over general numerical ODE solvers when you need fast, closed-form catenary results with per-point tension output.

• Cable length shorter than horizontal span — physically impossible, returns validation error
• Horizontal samples outside the [0, horizontal_span] range may produce extrapolated or error responses
• Extreme weight-per-length or span values near schema limits may cause numerical instability
• Missing required fields (horizontal_span, cable_length, etc.) return schema validation errors
• Claim field mismatch or invalid artifact structure returns a 400-level error