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Multiply-Connected Conformal Mapping to a Normalized Slit-Like Canonical Domain

  • Task ID: math.multiply_connected_conformal_mapping
  • Domain: math
  • Subdomain: computational_complex_analysis
  • Status: final
  • Benchmark set: seed42 (60 tasks)
  • Tags: conformal_mapping, multiply_connected_domains, slit_domain, slit_like_obstacles, boundary_integral_equations, complex_analysis, nystrom, canonical_domain

Runtime and requirements

  • Estimated time: 120-360 minutes
  • Python: >=3.11
  • Packages: numpy>=1.26, scipy>=1.11
  • GPU required: no
  • Network required: no

Public input and output contract

Inputs

  • file_00.json (data): Opaque task data file.
  • file_01.npy (data): Opaque task data file.
  • file_02.npy (data): Opaque task data file.
  • file_03.npy (data): Opaque task data file.
  • file_04.npy (data): Opaque task data file.
  • file_05.npy (data): Opaque task data file.
  • file_06.npy (data): Opaque task data file.
  • file_07.npy (data): Opaque task data file.

Outputs

  • solver.py (code): Agent-written conformal mapping solver that generates the required output files.
  • slit_params.csv (data): Canonical-domain geometry. Must contain exactly 4 data rows: the explicit outer_boundary row followed by slit_1, slit_2, slit_3. Columns: component_id, role, center_re, center_im, half_length, half_thickness, angle_rad.
  • canonical_boundary.npy (data): Mapped public boundary samples in the normalized slit-like canonical domain.
  • canonical_probes.npy (data): Mapped interior probes in the normalized slit-like canonical domain.
  • canonical_probe_derivatives.npy (data): Complex derivative of the same normalized conformal map at the probe points.
  • canonical_sample_values.npy (data): Images of source sample points from file_05.npy under the normalized conformal map.
  • canonical_sample_derivatives.npy (data): Complex derivatives of the normalized conformal map at source sample points from file_05.npy.
  • canonical_boundary_sample_values.npy (data): Images of source boundary sample points from file_06.npy under the normalized conformal map.
  • canonical_boundary_sample_derivatives.npy (data): Complex derivatives of the normalized conformal map at source boundary sample points from file_06.npy.
  • source_inverse_sample_values.npy (data): Source-domain inverse-map values at canonical sample points from file_07.npy.
  • source_inverse_sample_derivatives.npy (data): Complex derivatives of the canonical-to-source inverse map at canonical sample points from file_07.npy.

Public repository files

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Provenance

This task is included in the current seed42 benchmark set at dataset revision f11a199f71fb4b854ac43a1bf548d5df519141a9.

This page is generated only from files tracked in the public ASI-Bench repository at commit f18382f03faf. Submission bundles, run logs, private scoring configuration, and private reference answers are not read by this page generator.