{
  "schema": "pymhm-quarter-point-native-verification-v1",
  "scope": "Executed independent same-space comparison of all six specified n32/r2 point-well finite-dimensional cases. The well intensity is explicitly normalized to one; the published rate is not recoverable. This record does not establish continuum exact-solution accuracy, singular energy convergence or original-author application execution.",
  "reference": {
    "project": "FEniCS Basix",
    "module": "basix.finite_element",
    "runtime_version": "0.9.0",
    "upstream_revision": "19555f5b629b4090b14014f9db5f2c9ac80984f9",
    "verified_source_url": "https://github.com/FEniCS/basix/tree/19555f5b629b4090b14014f9db5f2c9ac80984f9",
    "revision_verification": "git ls-remote https://github.com/FEniCS/basix.git refs/tags/v0.9.0",
    "revision_scope": "Verified upstream tag; executed installed extension is separately digested",
    "executed_extension_sha256": "fa14b18f7b393882c9a49e8af6f9e86b47c14f880daee89b7213a894fc8a9fdb",
    "comparison_method": "Independent Basix primal P2 and mixed RT0/P0 assembly with SciPy SuperLU full original uncondensed saddle",
    "independent_modules": [
      "native_owner.py",
      "native_mixed.py"
    ],
    "private_execution_source_sha256": {
      "native_owner.py": "8e1c14bbfca0c12d162d9c545b6b81e229f67ad77fc37dd1ae1b2d79af4cfd64",
      "acquire_mixed.py": "0578c8af0771d2a6bf28f282333ed741c82081847fd7faac6b8fe22b58f00977",
      "acquire.py": "578002b5d872a2c0f9da0822e0bbcd7239b9deeab98d9e15384f28333d6f544c",
      "compare_archives.py": "a1e9ec6ba584d9679ad4e7e3d9210de13d9ea5e162133762ef7ac869063b7510",
      "native_mixed.py": "66c5c1b73d4f09de7619ed44fc6b1c7fdb0a28ca446fa117065914392ac3e0ab",
      "reference_stability.py": "9aaa4b8a27d30459adbff906245c3756f9013ddd0cedbc968c93720ec9e7b3ac",
      "replay_native.py": "abbe869a4a37aba6bb7e629a69db25d2f265f9af8ef46d90cac46b847495827f"
    },
    "private_source_snapshot_bundle_sha256": "4d2e6c99c97c3255b45945af9b2e9dd3765a4d6b401e2c20c2232d03827e0e41",
    "source_access": "Basix upstream release tag is verified; the executed installed extension is separately digested. The instrumented independent drivers, external code and native operator/field archives remain outside the versioned repository and release artifacts."
  },
  "geometry": {
    "domain": [
      0,
      1,
      0,
      1
    ],
    "macro_squares_per_axis": 32,
    "macro_triangles": 2048,
    "macro_diagonal": "southwest-to-northeast",
    "local_refinement": 2,
    "fine_triangles": 8192,
    "material_interfaces_are_original_fine_edges": true
  },
  "source": {
    "functional": "v(1,1)-v(0,0)",
    "wells": [
      [
        0,
        0,
        -1
      ],
      [
        1,
        1,
        1
      ]
    ],
    "macro_partition": "Incident-angle partition; each corner belongs to two macrotriangles with rates -0.5/-0.5 or +0.5/+0.5",
    "primal": "Actual nodal P2 point evaluation once per continuous local pressure mesh",
    "mixed": "Incident-angle allocation of the integrated rate to fine P0 pressure test cells",
    "total_intensity": 0
  },
  "equations": {
    "physical": "q=-K grad(p), div(q)=f, with the declared point functional acting on discrete tests",
    "full_original_saddle": "A u+B lambda+h gamma=f_local; B.T u=0; h.T u=0",
    "primal": "A_ij=integral K grad(phi_i).grad(phi_j); B is the oriented physical normal-flux pairing; f_local is the point functional",
    "mixed": "(K^-1 q,v)-(p,div(v))+(alpha,v.normal)=0; -(div(q),w)=-(f,w); fine boundary normal integrals equal the constant oriented macroface flux",
    "orientation": "Every macroface unit normal points outward from its first adjacent macrocell; physical trace lambda changes outward sign in the second neighbor",
    "prescribed_boundary": "Zero exterior normal-flux trace; weak primal boundary convention, conforming mixed normal moments",
    "physical_gauge": "Integral over the physical domain of p equals zero; no coefficient-average or material-weighted gauge"
  },
  "spaces": {
    "primal": "Continuous nodal P2 within each four-triangle macro refinement, broken across macrofaces; raw Darcy flux is -K grad(p)",
    "mixed": "Contravariant-Piola Basix RT degree1 (RT0), fine P0 pressure, all executed fine-boundary pressure multipliers; original constant-per-macroface physical flux restriction retained",
    "skeleton_degree": 0,
    "skeleton_segments_per_macroface": 1,
    "kernel": "Constant local pressure; mixed kernel also has zero Darcy flux and constant fine-boundary pressure multipliers",
    "kernel_verification": "All 2048 original local blocks per case checked. Represented rank uses NumPy's default SVD threshold; positive K and connected local spaces supply the exact constant-kernel argument. This check is not an inf-sup proof."
  },
  "quadrature": {
    "assembly_order": 4,
    "error_order": 4,
    "convention": "Positive four-point Gauss-Legendre rule in each coordinate of an independent triangle Duffy map; native reference weights sum to 0.5",
    "adequacy": "Material is constant on each original fine triangle; P2 squared pressure has degree4, gradient/RT0 squared flux degree2, so the stated positive rule integrates the polynomial discrete norms exactly up to floating-point arithmetic"
  },
  "norms": {
    "pressure": "Broken physical L2 over all original fine triangles",
    "raw_gradient": "Broken physical L2 of the raw pressure gradient for P2 only",
    "darcy_flux": "Broken physical vector L2 of q=-K grad(p) for P2 or Piola RT0 q",
    "relative_denominator": "Corresponding executed native field norm",
    "interfaces": "Independent one-sided macrocell values; no averaging",
    "field_agreement_criterion": 1e-09
  },
  "native_arithmetic": {
    "operator": "Archived float64 original operator fixed throughout solve and controls",
    "backend": "SciPy SuperLU double-precision factorization and backend RHS",
    "precision": "Explicit extended original forcing/residual/correction accumulation uniformly selected for all six references",
    "coefficient_fraction_mantissa_bits": 63,
    "coefficient_storage": "Portable float64 high/correction/tail components with host precision guard",
    "executed_original_equation_corrections": 1,
    "policy": "At least one same-original-operator represented-defect correction unless the defect is exactly zero; the precision policy is independent of candidate agreement or expected fields",
    "original_physical_relative_residual_criterion": 1e-10,
    "physical_residual": "Original local physical rows and global weak trace equations divided by the norm of the complete original point-functional load; artificial gauge loads excluded",
    "additional_precision_control": "One further same-operator correction uses only native archives and compares native physical field norms; no candidate data is read"
  },
  "conservation": {
    "primal": "Macro conservation from the constant local test; no fine-cell H(div) or pointwise exterior-normal-flux claim for the raw gradient",
    "mixed": "Fine-cell integrated divergence equals its allocated point-functional rate; macroface normal conformity retains the original constant trace restriction"
  },
  "runtime": {
    "python": "3.13.15",
    "numpy": "2.5.3",
    "scipy": "1.18.1",
    "native_libraries": [
      {
        "user_api": "blas",
        "internal_api": "blis",
        "num_threads": 1,
        "prefix": "libblis",
        "version": "2.0",
        "threading_layer": "pthreads",
        "architecture": "haswell"
      }
    ],
    "locked_environment": "fem",
    "lockfile_sha256": "80900204082bb85dc2bebfda316053f106277124ca7f252ad9f45271f3591c57",
    "resource_scope": "Serial one-worker/one-thread acquisitions on a shared host. Timings cover the acquisition body: geometry/basis setup, assembly, solve, checks and archive; interpreter/module startup is excluded. Peak RSS is the driver process maximum since startup, rather than incremental case memory. CPU-only execution; no device transfer or synchronization costs. No speedup claim."
  },
  "candidate_source_snapshot": {
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