{
  "family_id": "376",
  "title": "Universal computation in forced Navier–Stokes flows",
  "discipline": "Partial differential equations",
  "source_commit": "fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb",
  "papers": [
    {
      "title": "Finite Instructions and Solenoidal Shear Flows",
      "path": "preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026/manuscript.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026/manuscript.pdf",
      "readme_path": "preprints/Finite-Instructions-and-Solenoidal-Shear-Flows-September-27-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "A Fixed Particle Test for Computation in a Forced Viscous Flow",
      "path": "preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026/manuscript.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026/manuscript.pdf",
      "readme_path": "preprints/A-Fixed-Particle-Test-for-Computation-in-a-Forced-Viscous-Flow-September-27-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Universal Computation with Eventually Stationary Navier–Stokes Forcing",
      "path": "preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf",
      "readme_path": "preprints/Universal-Computation-with-Eventually-Stationary-Navier-Stokes-Forcing-September-27-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Geometric Programs for Solenoidal Forcing",
      "path": "preprints/Geometric-Programs-for-Solenoidal-Forcing-September-27-2026/manuscript.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Geometric-Programs-for-Solenoidal-Forcing-September-27-2026/manuscript.pdf",
      "readme_path": "preprints/Geometric-Programs-for-Solenoidal-Forcing-September-27-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Prefix Instructions and Incompressible Flows",
      "path": "preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026/manuscript.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026/manuscript.pdf",
      "readme_path": "preprints/Prefix-Instructions-and-Incompressible-Flows-September-27-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Computation under Rapidly Vanishing Navier–Stokes Forcing",
      "path": "preprints/Computation-under-Rapidly-Vanishing-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Computation-under-Rapidly-Vanishing-Navier-Stokes-Forcing-September-27-2026/manuscript.pdf",
      "readme_path": "preprints/Computation-under-Rapidly-Vanishing-Navier-Stokes-Forcing-September-27-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Velocity-Field Detection of Computation in Forced Navier–Stokes Flows",
      "path": "preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/manuscript.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/manuscript.pdf",
      "readme_path": "preprints/Velocity-Field-Detection-of-Computation-in-Forced-Navier-Stokes-Flows-September-27-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Scalar Potentials and Slow Clocks for Forced Fluid Computation",
      "path": "preprints/Scalar-Potentials-and-Slow-Clocks-for-Forced-Fluid-Computation-September-27-2026/manuscript.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Scalar-Potentials-and-Slow-Clocks-for-Forced-Fluid-Computation-September-27-2026/manuscript.pdf",
      "readme_path": "preprints/Scalar-Potentials-and-Slow-Clocks-for-Forced-Fluid-Computation-September-27-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    },
    {
      "title": "Incompressible Box Transport and Finite Computation",
      "path": "preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026/manuscript.pdf",
      "url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026/manuscript.pdf",
      "readme_path": "preprints/Incompressible-Box-Transport-and-Finite-Computation-October-6-2026/README.md",
      "tex_paths": [],
      "pdf_exists": true
    }
  ],
  "lean_scope_path": "lean/docs/376.md",
  "lean_scope_url": "https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/lean/docs/376.md",
  "verification_status": "scope_document_available_not_independently_verified",
  "review_status": "inventory_complete_deep_review_pending"
}
