How it works
Rust assembles piecewise-linear finite elements on three nested meshes to solve the fixed-edge or free-edge Laplacian problem. Finite-element eigenvalues and Richardson-extrapolated estimates are reported separately. The finest mesh is bounded to 50,000 triangles; a smaller mesh can carry normalized mode values for visualization.
Inputs and units
Supply a simple polygon with 3–64 vertices in metres, optionally repeating its first point at the end. Coordinates are bounded to ±10,000 m. Request 1–12 modes with fixed or free boundary conditions. An optional second polygon enables comparison; an explicit wave speed in m/s enables frequencies and musical notes.
What the result contains
Eigenvalue upper bounds under the stated numerical assumptions, extrapolated estimates and estimated errors, resolution warnings, nodal-domain counts, modal ratios and optional frequencies. A comparison returns congruent, spectra_differ or not_distinguished_at_this_resolution. Optional mode shapes describe the ideal numerical membrane.
Example MCP call
{
"name": "hear_the_shape",
"arguments": {
"polygon": [
[
0,
0
],
[
0.5,
0
],
[
0.5,
0.5
],
[
0,
0.5
]
],
"boundary": "fixed",
"modes": 3,
"wave_speed": 100,
"include_mode_shapes": true
}
}Send this tool name and arguments through a connected MCP client. Discover the authoritative input schema with tools/list.
Direct MCP access
hear_the_shape is independently callable. Its generated registration deliberately disables orchestration: no planner binding or approved adapter is supplied. Do not infer composability from matching JSON fields.
Execution and availability
ScoreCompute exposes this tool through MCP Streamable HTTP. Rust computation runs on a connected worker; the public website and MCP gateway run separately. Among these 18 scientific tools, CUDA is implemented for simulate_pi; the other engines currently run on CPU. The separate contributor pilot has its own fixed integer Monte Carlo workload. Requests are bounded and concurrent work may be refused when capacity is occupied.
Record inputs, assumptions and returned provenance when sharing a result. The public observatory displays software client names and tool activity, without publishing calculation arguments or results.