alice-physics 2.2.0

# Numerical-infrastructure coverage of ALICE-Physics, against an external reference frame.
#
# What this table is: every general-purpose numerical building block that the
# standard references expect (Saad, Iterative Methods for Sparse Linear Systems;
# Hairer-Norsett-Wanner / Hairer-Wanner, Solving ODEs I/II; Hairer-Lubich-Wanner,
# Geometric Numerical Integration; Knoll-Keyes, JFNK survey (J. Comput. Phys. 2004);
# PETSc KSP / PC / SNES / TS / EPS-like eigen solvers; SUNDIALS CVODE / ARKODE /
# IDA / KINSOL; MOOSE Executioner / MultiApp; preCICE coupling schemes), one
# [[item]] per capability, with what the crate has today. The axes and the items
# come from that frame, not from the modules that exist.
#
# Scope and boundary with the other tables:
#   * A row here is about a reusable component: an API that takes the caller's
#     operator, residual, right-hand side or sweep. The same formula embedded in
#     one field's module (the private conjugate gradients of the FEM modules, the
#     FEM Newton / Newton-Krylov / Newmark, the MAC-grid pressure multigrid and
#     its slab decomposition, the per-module Verlet / symplectic Euler steps) is
#     cited in `evidence` but not counted: such a row stays `missing` here and
#     the field's table owns the embedded use.
#   * Rows that sit next to a solid-FE row of docs/coverage/fem.toml name that
#     row's id (COV-FEM-NNN) in `evidence`. The FE row judges the capability for
#     solids; the row here judges the general component. No capability is
#     counted in both tables.
#   * Closed-form results (e.g. the 3x3 polar decomposition, the 3x3 symmetric
#     eigen-decomposition of an inertia tensor) are small dense kernels of the
#     math layer and are counted here.
#   * Transforms (FFT), Monte Carlo estimators, matrix functions (exp(A),
#     CRAM), tridiagonal / dense symmetric eigensolvers and block-structured
#     mesh refinement are general components counted here; the field tables
#     (acoustics, CFD, quantum, nuclear, plasma, relativity) keep their uses.
#     Only a general component a caller can hand its inputs to is counted;
#     a combination of existing parts (e.g. the deterministic random number
#     generator plus a running mean / variance) is cited in the evidence of a
#     missing row.
#
# Search notes: "fft" / "dft" match the deformation-gradient variable names in
# src/linear_elastic_fem/consistent_tangent.rs; "Fourier" matches the replay
# compression description of an external crate; "Pade" matches the tanh
# approximation in src/neural.rs; "bisection" matches scalar root finding
# (Kepler, wall friction velocity, height-field probe); "tridiagonal" matches
# the Thomas linear solve; "refine" matches the tetrahedral longest-edge
# bisection of the FE mesher; "eigen" matches the thermal eigenstrain of the
# FE solver. None of these is the capability of the row it was searched for.
#
# Mesh axis (second wave): mesh generation and geometry processing as general
# components, the rows that the FE, additive-manufacturing, fracture, soft-body,
# coupling and optimisation tables would share. Rows already counted elsewhere
# are cited, not repeated: SDF to tetrahedra COV-OPT-065, SDF to a collision
# surface COV-RIGID-070, quality under refinement COV-FEM-115, h-adaptivity
# COV-FEM-112, design morphing COV-OPT-066, fluid mesh motion COV-COUPLE-016,
# cloth remeshing COV-SOFT-078, remeshing along a crack COV-FRACT-031, interface
# surface extraction COV-MULTIPHASE-024, block-structured refinement COV-NUM-101,
# geometry import into the electromagnetic material map COV-EM-041.
#
# status (exactly one of):
#   implemented+oracle     a general component exists, and at least one
#                          non-ignored test checks it against an independent
#                          reference (closed form, f64 elimination, another
#                          solver, or a pinned bit pattern)
#   implemented-no-oracle  a general component exists, no such test
#   partial                a general component exists with a restriction that the
#                          source states; `limitation` quotes it, and the source
#                          carries a `LIMITATION(<id>)` comment at that place
#   missing                no general component (a field-embedded one may exist,
#                          see `evidence`)
#   out-of-scope           not applicable to this crate (reason in `evidence`)
#
# This axis is separate from the test ignore reasons (`known defect: ...`,
# `src gap: ...`, `diagnostic`, `runtime`). A capability that exists with a
# recorded defect keeps its status and cites the known-defect test in
# `evidence`.
#
# keys: id (COV-NUM-NNN) / axis / item / source (book, chapter, or
# reference-implementation feature; no quoted text) / status / evidence
# (`src/...rs::symbol`, `tests/...rs::test_fn`) / oracle_candidate / limitation
# (verbatim quote of the source, required for `partial`).
#
# Chapter numbers are given from the table of contents and are not checked
# against the original. Reference values marked "参照値要確認" are to be checked
# against the original publication before any test uses them. "(推測)" in
# `evidence` marks a judgement based on a search with synonyms that found
# nothing, not on reading every module.
#
# Checked by scripts/coverage_check.py (tests: scripts/test_coverage_check.py).

[[item]]
id = "COV-NUM-001"
axis = "linear_direct"
item = "small dense direct solve (3x3 inverse)"
source = "Golub-Van Loan, Matrix Computations ch.3; Mat3 closed-form inverse"
status = "implemented+oracle"
evidence = "src/math.rs::inverse (Mat3Fix::inverse、余因子の閉形式) / tests/audit_math.rs::mat3_inverse_closed_form_and_singular / tests/audit_math.rs::mat3_inverse_of_small_scale_matrix"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-002"
axis = "linear_direct"
item = "dense LU with partial pivoting (n x n)"
source = "Golub-Van Loan, Matrix Computations ch.3; PETSc PCLU; LAPACK getrf"
status = "missing"
evidence = "n x n の直接法は無い src/linear_solver.rs::DenseMatrix の DenseMatrix は作用素 (y = A x) のみで分解を持たない tests 側の gauss_f64 は f64 の参照解 (tests/analytic_linear_solver.rs::spd_cantilever_matches_private_cg_and_f64_elimination)"
oracle_candidate = "f64 消去法との突合、Hilbert 行列で pivot 成長の実測"
limitation = ""

[[item]]
id = "COV-NUM-003"
axis = "linear_direct"
item = "dense Cholesky / LDL^T"
source = "Golub-Van Loan, Matrix Computations ch.4; PETSc PCCHOLESKY"
status = "missing"
evidence = "密な Cholesky / LDL^T は無い"
oracle_candidate = "SPD 行列で L L^T = A を bit 近傍で再構成"
limitation = ""

[[item]]
id = "COV-NUM-004"
axis = "linear_direct"
item = "banded / tridiagonal solve (Thomas) as a general API"
source = "Golub-Van Loan, Matrix Computations ch.4.3"
status = "missing"
evidence = "汎用 API は無い src/transient_thermal.rs::thomas_solve_in_place の thomas_solve_in_place は 1D 熱伝導専用の private f32 関数"
oracle_candidate = "既知解の三重対角系 (離散 Poisson 1D) で閉形式解と一致"
limitation = ""

[[item]]
id = "COV-NUM-005"
axis = "linear_direct"
item = "sparse direct LU / Cholesky with fill-reducing ordering"
source = "Davis, Direct Methods for Sparse Linear Systems; PETSc PCLU / PCCHOLESKY with MatOrdering (ND / AMD)"
status = "missing"
evidence = "疎直接法は無い 固体向けは COV-FEM-069 (fem.toml)"
oracle_candidate = "2D Poisson 5 点で反復法の解と突合"
limitation = ""

[[item]]
id = "COV-NUM-006"
axis = "linear_direct"
item = "sparse matrix storage (CSR) and SpMV"
source = "Saad, Iterative Methods for Sparse Linear Systems ch.3; PETSc MATAIJ"
status = "missing"
evidence = "疎行列型は無い (作用素は matrix-free の src/linear_solver.rs::LinearOperator LinearOperator のみ) src/spatial.rs::SpatialGrid の CSR は近傍探索の index 配列で行列ではない 固体の全体行列は COV-FEM-071 (fem.toml)"
oracle_candidate = "CSR の SpMV を DenseMatrix の apply と bit 一致で突合"
limitation = ""

[[item]]
id = "COV-NUM-007"
axis = "linear_direct"
item = "QR / least squares (dense)"
source = "Golub-Van Loan, Matrix Computations ch.5; LAPACK geqrf"
status = "missing"
evidence = "QR 分解・最小二乗の汎用部品は無い (推測)"
oracle_candidate = "過剰決定系の正規方程式解と突合"
limitation = ""

[[item]]
id = "COV-NUM-008"
axis = "krylov"
item = "matrix-free operator interface (closure / dense adapter)"
source = "PETSc MatShell; Saad ch.6"
status = "implemented+oracle"
evidence = "src/linear_solver.rs::LinearOperator (LinearOperator) / src/linear_solver.rs::FnOperator (FnOperator) / tests/analytic_linear_solver.rs::closure_operator_and_absolute_tolerance"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-009"
axis = "krylov"
item = "conjugate gradient (general SPD operator)"
source = "Saad, Iterative Methods for Sparse Linear Systems ch.6.7; PETSc KSPCG"
status = "missing"
evidence = "汎用 CG は無い (src/linear_solver.rs の対象は GMRES と BiCGStab のみ、同 file 冒頭に FEM の private CG が 4 本あると記載) 固体の CG は COV-FEM-066 (fem.toml、src/linear_elastic_fem.rs::conjugate_gradient)"
oracle_candidate = "SPD 系で GMRES と同じ解、反復数が n 以下"
limitation = ""

[[item]]
id = "COV-NUM-010"
axis = "krylov"
item = "restarted GMRES(m)"
source = "Saad, Iterative Methods for Sparse Linear Systems ch.6.5; PETSc KSPGMRES"
status = "implemented+oracle"
evidence = "src/linear_solver/gmres.rs::gmres / tests/analytic_linear_solver.rs::gmres_terminates_within_n_on_dense_spd / tests/analytic_linear_solver.rs::gmres_restart_lengths_agree_and_residual_is_monotone 固体向けの非対称 Krylov は COV-FEM-070 (fem.toml)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-011"
axis = "krylov"
item = "BiCGStab"
source = "Saad, Iterative Methods for Sparse Linear Systems ch.7.4; van der Vorst 1992; PETSc KSPBCGS"
status = "implemented+oracle"
evidence = "src/linear_solver/bicgstab.rs::bicgstab / tests/analytic_linear_solver.rs::advection_diffusion_matches_closed_form_across_peclet / tests/analytic_linear_solver.rs::bicgstab_breakdown_where_gmres_succeeds src/eulerian_grid.rs::project_pressure_bicgstab の BiCGStab は MAC 格子の Laplacian 専用で数えない"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-012"
axis = "krylov"
item = "MINRES / SYMMLQ (symmetric indefinite)"
source = "Saad ch.6.6; Paige-Saunders 1975; PETSc KSPMINRES"
status = "missing"
evidence = "無い 固体の不定値接線は CG の負曲率打ち切り (COV-FEM-065、fem.toml)"
oracle_candidate = "対称不定値 2x2 ブロック (鞍点系) で f64 消去法と突合"
limitation = ""

[[item]]
id = "COV-NUM-013"
axis = "krylov"
item = "flexible GMRES (variable preconditioner)"
source = "Saad, Iterative Methods for Sparse Linear Systems ch.9.4; PETSc KSPFGMRES"
status = "missing"
evidence = "FGMRES は無い"
oracle_candidate = "内側に反復法を持つ前処理で GMRES が破綻し FGMRES が収束する系"
limitation = ""

[[item]]
id = "COV-NUM-014"
axis = "krylov"
item = "TFQMR / QMR / IDR(s)"
source = "Saad ch.7.3-7.4; PETSc KSPTFQMR / KSPQMRCGS"
status = "missing"
evidence = "無い"
oracle_candidate = "移流拡散 (Pe 大) で GMRES と同じ解"
limitation = ""

[[item]]
id = "COV-NUM-015"
axis = "krylov"
item = "least-squares Krylov (CGLS / LSQR)"
source = "Saad ch.8; Paige-Saunders 1982; PETSc KSPLSQR"
status = "missing"
evidence = "無い"
oracle_candidate = "過剰決定系で正規方程式の解と突合"
limitation = ""

[[item]]
id = "COV-NUM-016"
axis = "krylov"
item = "stopping on the true residual, with not-converged / stagnated / breakdown verdicts"
source = "Saad ch.6; PETSc KSPConvergedReason"
status = "implemented+oracle"
evidence = "src/linear_solver.rs::LinearSolverError (LinearSolverError) / tests/analytic_linear_solver.rs::inconsistent_singular_system_is_not_reported_as_solved / tests/analytic_linear_solver.rs::small_budget_is_not_converged / tests/analytic_linear_solver.rs::restarted_gmres_on_a_rotation_stagnates / tests/analytic_linear_solver.rs::zero_operator_is_a_breakdown"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-017"
axis = "krylov"
item = "nonzero initial guess (warm start)"
source = "PETSc KSPSetInitialGuessNonzero"
status = "partial"
evidence = "src/linear_solver.rs 初期値は常にゼロ (時間積分や Newton の連続した解で前回解から始められない) tests のみでは測れない: 非ゼロの初期値を受け取る API が存在しない (grep 'initial_guess' の実体ヒットは 0、この limitation の doc comment 自身のみ、2026-10-08 確認)"
oracle_candidate = ""
limitation = "src/linear_solver.rs 'The initial guess is always zero.'"

[[item]]
id = "COV-NUM-018"
axis = "stationary"
item = "Jacobi / Gauss-Seidel / SOR / SSOR as general solvers"
source = "Saad, Iterative Methods for Sparse Linear Systems ch.4; PETSc KSPRICHARDSON + PCSOR"
status = "missing"
evidence = "汎用の定常反復は無い src/eulerian_grid.rs::project_pressure_jacobi (Jacobi) / src/eulerian_grid.rs::project_pressure_red_black_gs (赤黒 Gauss-Seidel) は MAC 格子の圧力専用 (pub(crate))"
oracle_candidate = "1D Poisson で反復行列のスペクトル半径の閉形式 cos(pi h) と収束率を突合"
limitation = ""

[[item]]
id = "COV-NUM-019"
axis = "preconditioner"
item = "Jacobi (diagonal)"
source = "Saad ch.10.2; PETSc PCJACOBI"
status = "implemented+oracle"
evidence = "src/linear_solver/precond.rs::JacobiPreconditioner / tests/analytic_linear_solver.rs::jacobi_reduces_iterations_on_a_badly_scaled_diagonal 固体の Jacobi は COV-FEM-067 (fem.toml)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-020"
axis = "preconditioner"
item = "block Jacobi"
source = "Saad ch.12; PETSc PCBJACOBI"
status = "implemented+oracle"
evidence = "src/linear_solver/precond.rs::BlockJacobiPreconditioner / tests/analytic_linear_solver.rs::block_jacobi_solves_a_block_diagonal_matrix_in_one_iteration"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-021"
axis = "preconditioner"
item = "left / right / split preconditioning"
source = "Saad, Iterative Methods for Sparse Linear Systems ch.9.3; PETSc KSPSetPCSide"
status = "partial"
evidence = "src/linear_solver.rs 右前処理のみ (左前処理の残差ノルムでの停止は選べない)"
oracle_candidate = "左右で解が一致し、右前処理では真の残差で停止することを確認"
limitation = "src/linear_solver.rs 'applied on the **right**'"

[[item]]
id = "COV-NUM-022"
axis = "preconditioner"
item = "SSOR / Gauss-Seidel preconditioner"
source = "Saad ch.10.2; PETSc PCSOR"
status = "missing"
evidence = "無い"
oracle_candidate = "1D Poisson で反復数が Jacobi より減る"
limitation = ""

[[item]]
id = "COV-NUM-023"
axis = "preconditioner"
item = "incomplete LU (ILU(0) / ILUT)"
source = "Saad, Iterative Methods for Sparse Linear Systems ch.10.3-10.4; PETSc PCILU"
status = "missing"
evidence = "無い (疎行列型が無いので前提も無い COV-NUM-006)"
oracle_candidate = "ILU(0) が 5 点 Laplacian で厳密な LU と非零パターン上で一致"
limitation = ""

[[item]]
id = "COV-NUM-024"
axis = "preconditioner"
item = "incomplete Cholesky (IC(0))"
source = "Saad ch.10.3; PETSc PCICC"
status = "missing"
evidence = "無い 固体向けは COV-FEM-068 (fem.toml)"
oracle_candidate = "SPD 系で CG の反復数が減り解は同じ"
limitation = ""

[[item]]
id = "COV-NUM-025"
axis = "preconditioner"
item = "geometric multigrid (V / W / F cycle) as a general component"
source = "Briggs-Henson-McCormick, A Multigrid Tutorial; Trottenberg-Oosterlee-Schuller, Multigrid; Saad ch.13; PETSc PCMG"
status = "missing"
evidence = "汎用の multigrid は無い src/eulerian_grid.rs::project_pressure_multigrid (project_pressure_multigrid) は MAC 格子の圧力 Poisson 専用で、収束率の格子非依存は tests/analytic_multigrid.rs::contraction_rate_is_grid_independent が CFD 側で確認 固体の multigrid 前処理は COV-FEM-068 (fem.toml)"
oracle_candidate = "Poisson で収束率が h に依存しない (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-026"
axis = "preconditioner"
item = "algebraic multigrid (AMG)"
source = "Ruge-Stuben 1987; Vanek-Mandel-Brezina (smoothed aggregation); PETSc PCGAMG; hypre BoomerAMG"
status = "missing"
evidence = "無い"
oracle_candidate = "非構造 Laplacian で反復数が問題サイズに依存しない"
limitation = ""

[[item]]
id = "COV-NUM-027"
axis = "preconditioner"
item = "additive Schwarz / domain-decomposition preconditioner"
source = "Smith-Bjorstad-Gropp, Domain Decomposition; Saad ch.14; PETSc PCASM"
status = "missing"
evidence = "無い"
oracle_candidate = "重なり幅を増やすと反復数が減る"
limitation = ""

[[item]]
id = "COV-NUM-028"
axis = "preconditioner"
item = "field-split / Schur-complement block preconditioner"
source = "Benzi-Golub-Liesen 2005 (saddle point); PETSc PCFIELDSPLIT"
status = "missing"
evidence = "無い src/linear_solver/equilibrate.rs::BlockEquilibration の BlockEquilibration はブロックごとのスケーリングで、ブロック前処理ではない"
oracle_candidate = "鞍点系で厳密 Schur 補元の前処理なら GMRES が 3 反復以内 (Murphy-Golub-Wathen)"
limitation = ""

[[item]]
id = "COV-NUM-029"
axis = "nonlinear"
item = "Newton's method with a caller-supplied residual and Jacobian"
source = "Kelley, Solving Nonlinear Equations with Newton's Method; PETSc SNESNEWTONLS; SUNDIALS KINSOL"
status = "missing"
evidence = "汎用 Newton は無い 固体の Newton は COV-FEM-052 (fem.toml、src/linear_elastic_fem/consistent_tangent.rs::newton_step) src/kepler.rs::solve_kepler の Kepler 方程式の Newton はスカラー専用"
oracle_candidate = "Rosenbrock 関数・Bratu 問題で 2 次収束 (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-030"
axis = "nonlinear"
item = "line search (backtracking with Armijo / Wolfe conditions)"
source = "Nocedal-Wright, Numerical Optimization ch.3; PETSc SNESLineSearch (BT / CP / L2)"
status = "missing"
evidence = "汎用の line search は無い 固体の backtrack は COV-FEM-056 (fem.toml)"
oracle_candidate = "Newton が発散する初期値 (arctan) で line search 付きが収束"
limitation = ""

[[item]]
id = "COV-NUM-031"
axis = "nonlinear"
item = "trust region (dogleg / Levenberg-Marquardt)"
source = "Nocedal-Wright ch.4; Conn-Gould-Toint, Trust-Region Methods; PETSc SNESNEWTONTR"
status = "missing"
evidence = "無い"
oracle_candidate = "Rosenbrock 関数で信頼領域半径の更新規則が教科書どおり"
limitation = ""

[[item]]
id = "COV-NUM-032"
axis = "nonlinear"
item = "inexact Newton with adaptive forcing (Eisenstat-Walker)"
source = "Eisenstat-Walker 1996; Knoll-Keyes 2004; PETSc SNESKSPSetUseEW"
status = "missing"
evidence = "汎用部品は無い 固体の inexact Newton / Newton-Krylov は COV-FEM-054 (fem.toml、src/linear_elastic_fem/consistent_tangent.rs::newton_krylov_step) 適応 forcing term は src 全体で 0 件 (推測)"
oracle_candidate = "forcing を緩めても解が変わらず線形反復の合計が減る"
limitation = ""

[[item]]
id = "COV-NUM-033"
axis = "nonlinear"
item = "Jacobian-free Newton-Krylov (finite-difference J v)"
source = "Knoll-Keyes, J. Comput. Phys. 193 (2004); PETSc MatMFFD + SNES; MOOSE PJFNK"
status = "missing"
evidence = "汎用 JFNK は無い (GMRES は src/linear_solver.rs::FnOperator の FnOperator で作用素を受け取れるが、差分 J v と Newton の外側は無い) 固体は COV-FEM-054 (fem.toml)"
oracle_candidate = "解析 Jacobian の Newton と同じ解、差分幅の選び方で反復数が変わらない範囲を測る"
limitation = ""

[[item]]
id = "COV-NUM-034"
axis = "nonlinear"
item = "quasi-Newton (Broyden / BFGS)"
source = "Nocedal-Wright ch.6; Dennis-Schnabel; PETSc SNESQN"
status = "missing"
evidence = "無い 固体の BFGS は COV-FEM-055 (fem.toml)"
oracle_candidate = "線形系で Broyden が n+1 反復以内に厳密解 (Gay の定理、参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-035"
axis = "nonlinear"
item = "Anderson acceleration of a fixed-point map"
source = "Walker-Ni 2011; PETSc SNESANDERSON; SUNDIALS KINSOL fixed point"
status = "missing"
evidence = "無い"
oracle_candidate = "線形の不動点写像で GMRES と同値になる (Walker-Ni)"
limitation = ""

[[item]]
id = "COV-NUM-036"
axis = "nonlinear"
item = "continuation / pseudo-transient continuation"
source = "Kelley-Keyes 1998 (Psi-tc); Allgower-Georg, Numerical Continuation Methods; PETSc SNESNEWTONLS + TSPSEUDO"
status = "missing"
evidence = "無い 固体の弧長法は COV-FEM-059 (fem.toml)"
oracle_candidate = "折り返し点を持つスカラー方程式で解曲線を追跡"
limitation = ""

[[item]]
id = "COV-NUM-037"
axis = "nonlinear"
item = "bracketed scalar root finding (bisection / Brent) as a general API"
source = "Brent, Algorithms for Minimization without Derivatives; Press et al., Numerical Recipes ch.9"
status = "missing"
evidence = "汎用 API は無い 二分法は src/kepler.rs::solve_kepler (Kepler 方程式) と src/turbulence.rs::FRICTION_VELOCITY_BISECTIONS (摩擦速度) に分野内で埋め込み"
oracle_candidate = "単根を持つ多項式で反復数が log2(幅/許容) と一致"
limitation = ""

[[item]]
id = "COV-NUM-038"
axis = "eigen"
item = "3x3 symmetric eigen-decomposition (cyclic Jacobi)"
source = "Golub-Van Loan, Matrix Computations ch.8.5"
status = "implemented+oracle"
evidence = "src/mass_properties.rs::principal_axes (principal_axes) / tests/analytic_compound.rs::the_principal_axes_diagonalise_a_symmetric_tensor"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-039"
axis = "eigen"
item = "3x3 polar decomposition"
source = "Higham, Functions of Matrices ch.8"
status = "implemented+oracle"
evidence = "src/math.rs::polar_rotation (polar_rotation) / tests/audit_math.rs::polar_rotation_closed_forms_and_error_variants / tests/audit_math.rs::polar_rotation_result_is_orthogonal_to_a_few_ulp"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-040"
axis = "eigen"
item = "power iteration / inverse iteration with shift"
source = "Saad, Numerical Methods for Large Eigenvalue Problems ch.4; Golub-Van Loan ch.7.3"
status = "missing"
evidence = "汎用部品は無い tests/analytic_thermoplastic_coupling.rs::the_monolithic_entry_condition_is_three_decades_away_at_real_heat_capacities の冪乗法は test 内の局所実装"
oracle_candidate = "対角行列・既知固有値の 3 重対角行列で支配固有値と一致"
limitation = ""

[[item]]
id = "COV-NUM-041"
axis = "eigen"
item = "Lanczos / Arnoldi (implicitly restarted) for large sparse problems"
source = "Saad, Numerical Methods for Large Eigenvalue Problems ch.6; ARPACK; SLEPc EPSKRYLOVSCHUR"
status = "missing"
evidence = "無い (src/linear_solver/gmres.rs の Arnoldi は線形方程式用で固有値を返さない)"
oracle_candidate = "1D Laplacian の最小固有値 4 sin^2(pi h/2)/h^2 と突合"
limitation = ""

[[item]]
id = "COV-NUM-042"
axis = "eigen"
item = "generalized symmetric eigenproblem K x = lambda M x"
source = "Bathe, Finite Element Procedures ch.11; SLEPc EPS (GHEP)"
status = "missing"
evidence = "汎用部品は無い FE モード解析は COV-FEM-083 (fem.toml)"
oracle_candidate = "2 自由度ばね質点の閉形式固有振動数"
limitation = ""

[[item]]
id = "COV-NUM-043"
axis = "eigen"
item = "LOBPCG / subspace iteration"
source = "Knyazev 2001; Bathe ch.11.6; SLEPc EPSLOBPCG"
status = "missing"
evidence = "無い"
oracle_candidate = "1D Laplacian の下位 k 個の固有値"
limitation = ""

[[item]]
id = "COV-NUM-044"
axis = "eigen"
item = "dense nonsymmetric eigenvalues (QR algorithm) / SVD"
source = "Golub-Van Loan ch.7-8; LAPACK geev / gesvd"
status = "missing"
evidence = "無い"
oracle_candidate = "回転行列の固有値 exp(±i theta)"
limitation = ""

[[item]]
id = "COV-NUM-045"
axis = "time_integration"
item = "general ODE integrator interface (caller-supplied right-hand side)"
source = "SUNDIALS CVODE / ARKODE; PETSc TS"
status = "missing"
evidence = "汎用の時間積分 API は無い 各 module が固有の公式を埋め込む (例 src/nbody.rs::VelocityVerlet / src/molecular_dynamics.rs::VelocityVerlet の Velocity Verlet、src/sdf_sph.rs::step の symplectic Euler、src/transient_thermal.rs::crank_nicolson_step_1d の Crank-Nicolson)"
oracle_candidate = "y' = lambda y で各公式の安定関数と 1 step 一致"
limitation = ""

[[item]]
id = "COV-NUM-046"
axis = "time_integration"
item = "explicit / symplectic (semi-implicit) Euler"
source = "Hairer-Lubich-Wanner, Geometric Numerical Integration ch.I; PETSc TSEULER"
status = "missing"
evidence = "汎用部品は無い (分野内の埋め込みのみ src/sdf_sph.rs::step、剛体 world も同じ形) (推測: 汎用化の 1 番目の候補)"
oracle_candidate = "調和振動子で 1 次の大域誤差と有界なエネルギー誤差"
limitation = ""

[[item]]
id = "COV-NUM-047"
axis = "time_integration"
item = "velocity Verlet / leapfrog"
source = "Hairer-Lubich-Wanner, Geometric Numerical Integration ch.I.3; PETSc TSBASICSYMPLECTIC"
status = "missing"
evidence = "汎用部品は無い src/nbody.rs::VelocityVerlet と src/molecular_dynamics.rs::VelocityVerlet に別型の VelocityVerlet がそれぞれ分野専用で存在"
oracle_candidate = "調和振動子で 2 次の大域誤差、時間反転で初期値に戻る"
limitation = ""

[[item]]
id = "COV-NUM-048"
axis = "time_integration"
item = "higher-order symplectic composition (Yoshida / Forest-Ruth)"
source = "Yoshida 1990; Hairer-Lubich-Wanner ch.II.4"
status = "missing"
evidence = "無い"
oracle_candidate = "Kepler 問題で 4 次の大域誤差"
limitation = ""

[[item]]
id = "COV-NUM-049"
axis = "time_integration"
item = "explicit Runge-Kutta (RK4)"
source = "Hairer-Norsett-Wanner, Solving ODEs I ch.II.1; PETSc TSRK"
status = "missing"
evidence = "無い src/aeroelasticity.rs は f64 RK4 を参照解に使うと記載するが src に汎用 RK4 は無い"
oracle_candidate = "y' = y で 4 次の大域誤差"
limitation = ""

[[item]]
id = "COV-NUM-050"
axis = "time_integration"
item = "embedded Runge-Kutta with adaptive step control (Dormand-Prince 5(4))"
source = "Hairer-Norsett-Wanner, Solving ODEs I ch.II.4-II.5; SUNDIALS ARKODE ERK; PETSc TSRK + TSAdapt"
status = "missing"
evidence = "無い"
oracle_candidate = "Arenstorf 軌道で許容誤差と大域誤差の比例 (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-051"
axis = "time_integration"
item = "implicit Euler / BDF (variable order)"
source = "Hairer-Wanner, Solving ODEs II ch.III / ch.V; SUNDIALS CVODE BDF; PETSc TSBDF"
status = "missing"
evidence = "汎用の陰的積分は無い (陰解法は分野内のみ、例 src/transient_thermal.rs::crank_nicolson_step_1d)"
oracle_candidate = "Robertson 問題 (硬い 3 成分) で参照解と突合 (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-052"
axis = "time_integration"
item = "trapezoidal / theta method"
source = "Hairer-Wanner, Solving ODEs II; PETSc TSTHETA / TSCN"
status = "missing"
evidence = "汎用部品は無い src/transient_thermal.rs::crank_nicolson_step_1d の Crank-Nicolson は 1D 熱伝導専用"
oracle_candidate = "y' = lambda y の安定関数 (1+z/2)/(1-z/2)"
limitation = ""

[[item]]
id = "COV-NUM-053"
axis = "time_integration"
item = "second-order systems: Newmark / HHT-alpha / generalized-alpha as a general integrator"
source = "Chung-Hulbert 1993; Hilber-Hughes-Taylor 1977; PETSc TSALPHA2"
status = "missing"
evidence = "汎用部品は無い 固体の Newmark / HHT / generalized-alpha は COV-FEM-072 / 073 / 074 / 075 (fem.toml)"
oracle_candidate = "1 自由度振動子で数値減衰率の閉形式と突合"
limitation = ""

[[item]]
id = "COV-NUM-054"
axis = "time_integration"
item = "Rosenbrock / linearly implicit methods"
source = "Hairer-Wanner, Solving ODEs II ch.IV.7; PETSc TSROSW"
status = "missing"
evidence = "無い"
oracle_candidate = "van der Pol (mu 大) で参照解と突合 (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-055"
axis = "time_integration"
item = "IMEX additive Runge-Kutta"
source = "Ascher-Ruuth-Spiteri 1997; Kennedy-Carpenter 2003; SUNDIALS ARKODE ARK; PETSc TSARKIMEX"
status = "missing"
evidence = "無い"
oracle_candidate = "移流 (陽) + 拡散 (陰) の 1D で次数を確認"
limitation = ""

[[item]]
id = "COV-NUM-056"
axis = "time_integration"
item = "operator splitting (Lie / Strang) as a general component"
source = "Hairer-Lubich-Wanner ch.II.5; McLachlan-Quispel 2002"
status = "missing"
evidence = "汎用部品は無い (各 module の step が分野内で分割を固定) (推測)"
oracle_candidate = "可換でない 2 線形作用素で Lie 1 次 / Strang 2 次の誤差"
limitation = ""

[[item]]
id = "COV-NUM-057"
axis = "time_integration"
item = "multirate / subcycling"
source = "Gear-Wells 1984; SUNDIALS ARKODE MRIStep"
status = "missing"
evidence = "無い (推測)"
oracle_candidate = "速い成分と遅い成分の線形 2 自由度で閉形式解と突合"
limitation = ""

[[item]]
id = "COV-NUM-058"
axis = "time_integration"
item = "DAE (index 1) / constraint projection"
source = "Hairer-Wanner, Solving ODEs II ch.VI-VII; SUNDIALS IDA"
status = "missing"
evidence = "汎用部品は無い (剛体の拘束は位置補正で解く別系統)"
oracle_candidate = "振り子の Cartesian 定式化で拘束ドリフトが許容内"
limitation = ""

[[item]]
id = "COV-NUM-059"
axis = "coupling"
item = "partitioned (staggered) sub-iteration driver with convergence monitoring"
source = "Felippa-Park-Farhat 2001; MOOSE MultiApp fixed-point iterations; preCICE implicit coupling"
status = "implemented+oracle"
evidence = "src/coupled_iteration.rs::run_sub_iteration (run_sub_iteration) / src/coupled_iteration.rs::ContractionMonitor (ContractionMonitor) / tests/audit_coupled_iteration.rs::run_sub_iteration_passes_zero_based_sweep_indices_and_reports_the_final_state / tests/analytic_added_mass_coupling.rs::the_contraction_ratio_matches_the_closed_form"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-060"
axis = "coupling"
item = "divergence and silent-wrap detection of a coupled iteration"
source = "Causin-Gerbeau-Nobile 2005 (added-mass instability); Fix128 wrap behaviour of this crate"
status = "implemented+oracle"
evidence = "src/coupled_iteration.rs::residual_norm_l2_checked (residual_norm_l2_checked) / tests/audit_coupled_iteration.rs::doubling_residuals_are_diverging_at_the_fourth_sweep / tests/audit_coupled_iteration.rs::two_separate_overshoots_are_not_a_wrap / tests/analytic_added_mass_coupling.rs::a_diverging_iteration_reports_a_zero_l2_residual"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-061"
axis = "coupling"
item = "constant under-relaxation in the general driver"
source = "Kuttler-Wall 2008; MOOSE relaxation_factor; preCICE constant relaxation"
status = "missing"
evidence = "汎用 driver (src/coupled_iteration.rs::run_sub_iteration) は sweep を呼び手に任せ緩和を持たない 定数緩和は熱塑性連成に分野内で実装 (src/linear_elastic_fem.rs::ThermoplasticCoupling、tests/analytic_thermoplastic_coupling.rs::the_fixed_point_does_not_depend_on_the_relaxation)"
oracle_candidate = "added-mass ピストンで最適定数緩和 omega* = m/(m+m_f) が 1 sweep で収束 (閉形式)"
limitation = ""

[[item]]
id = "COV-NUM-062"
axis = "coupling"
item = "Aitken dynamic relaxation"
source = "Irons-Tuck 1969; Kuttler-Wall 2008; MOOSE secant / Steffensen; preCICE aitken"
status = "missing"
evidence = "src には無い tests/fix128_vs_f64_coupling_hypotheses.rs::aitken_reaches_the_unstable_upper_branch_under_fix128_too の Aitken は test 内の局所実装"
oracle_candidate = "2 自由度の分離反復で Aitken が定数緩和より少ない sweep で同じ不動点 (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-063"
axis = "coupling"
item = "interface quasi-Newton (IQN-ILS)"
source = "Degroote-Bathe-Vierendeels 2009; preCICE IQN-ILS"
status = "missing"
evidence = "無い"
oracle_candidate = "線形 2 場で n 反復以内に収束"
limitation = ""

[[item]]
id = "COV-NUM-064"
axis = "coupling"
item = "monolithic coupled Newton (block Jacobian)"
source = "Keyes et al., Multiphysics simulations (IJHPCA 2013); MOOSE single-app fully coupled"
status = "missing"
evidence = "無い src/coupled_iteration.rs 以降に入口条件と見送りの判断 (Krylov は src/linear_solver.rs で用意済、ブロック等化は src/linear_solver/equilibrate.rs::solve_equilibrated)"
oracle_candidate = "分離反復を収束させた解と同じ不動点"
limitation = ""

[[item]]
id = "COV-NUM-065"
axis = "coupling"
item = "field transfer between discretisations (sample / splat, conservative)"
source = "Farhat-Lesoinne-LeTallec 1998 (conservative load transfer); preCICE mapping"
status = "implemented+oracle"
evidence = "src/coupled_field.rs::sample (sample) / src/coupled_field.rs::splat (splat) / tests/analytic_coupled_field.rs::splat_is_the_adjoint_of_sample / tests/analytic_coupled_field.rs::splat_conserves_the_total_within_the_derived_rounding_bound"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-066"
axis = "distributed"
item = "domain decomposition with halo exchange as a general component"
source = "Smith-Bjorstad-Gropp, Domain Decomposition; PETSc DMDA + VecScatter"
status = "missing"
evidence = "汎用部品は無い z slab 分割と halo 交換は MAC 格子の圧力専用 (src/eulerian_grid.rs::RankTransport RankTransport、pub(crate))"
oracle_candidate = "1D Poisson の Jacobi 反復を 1/2/4 分割で bit 一致"
limitation = ""

[[item]]
id = "COV-NUM-067"
axis = "distributed"
item = "deterministic global reduction (all-reduce) API"
source = "MPI_Allreduce; Demmel-Nguyen 2013 (reproducible summation)"
status = "missing"
evidence = "汎用 API は無い Fix128 の加算が順序非依存である性質は COV-NUM-074 で確認済 分割数を変えた bit 一致は CFD の圧力でのみ (tests/analytic_pressure_solvers.rs::the_decomposed_multigrid_reproduces_multigrid_to_the_bit_for_every_rank_count)"
oracle_candidate = "rank 数・到着順を変えた総和が bit 一致"
limitation = ""

[[item]]
id = "COV-NUM-068"
axis = "distributed"
item = "distributed Krylov (global inner products across ranks)"
source = "Saad ch.11-12; PETSc KSP on MPI vectors"
status = "missing"
evidence = "無い (src/linear_solver.rs の Krylov は単一アドレス空間)"
oracle_candidate = "分割数を変えた GMRES の解が bit 一致"
limitation = ""

[[item]]
id = "COV-NUM-069"
axis = "distributed"
item = "multi-process / MPI transport backend"
source = "MPI-3.1 standard; PETSc PetscSF"
status = "missing"
evidence = "src には無い src/eulerian_grid.rs::RankTransport の doc に MPI backend は feature で後から入る予定と記載 (CFD 圧力専用)"
oracle_candidate = "loopback の 2 プロセスで単一プロセス解と bit 一致"
limitation = ""

[[item]]
id = "COV-NUM-070"
axis = "distributed"
item = "shared-memory parallel kernels with a deterministic result"
source = "OpenMP / rayon; PETSc with threads"
status = "missing"
evidence = "汎用 solver の並列化は無い (src/linear_solver.rs は逐次) (推測)"
oracle_candidate = "スレッド数を変えて bit 一致"
limitation = ""

[[item]]
id = "COV-NUM-071"
axis = "distributed"
item = "load balancing / repartitioning"
source = "Karypis-Kumar (METIS / ParMETIS); Zoltan"
status = "missing"
evidence = "無い"
oracle_candidate = "不均一な負荷で各 rank の作業量の最大 / 平均を測る"
limitation = ""

[[item]]
id = "COV-NUM-072"
axis = "representation"
item = "Q64.64 fixed-point scalar with bit-exact arithmetic"
source = "Yates, Fixed-Point Arithmetic; IEEE 754 is deliberately not used"
status = "implemented+oracle"
evidence = "src/math.rs::Fix128 (Fix128) / tests/audit_math.rs::mul_matches_256_bit_reference / tests/audit_math.rs::div_matches_192_bit_reference_and_truncates_toward_zero / tests/audit_math.rs::add_sub_neg_match_i128_wrapping_arithmetic"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-073"
axis = "representation"
item = "bit-identical results across platforms (pinned hashes)"
source = "Reproducible numerics (Demmel-Nguyen); deterministic lockstep simulation"
status = "implemented+oracle"
evidence = "tests/determinism_golden.rs::determinism_freefall / tests/determinism_golden.rs::determinism_fluid_step / tests/determinism_golden.rs::determinism_cascade"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-074"
axis = "representation"
item = "order-independent summation (bit-identical under permutation)"
source = "Demmel-Nguyen 2013; Kahan summation as the floating-point counterpart"
status = "implemented+oracle"
evidence = "tests/analytic_linear_solver.rs::fix128_sum_of_products_is_order_independent / tests/analytic_linear_solver.rs::bit_identical_and_permutation_equivariant"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-075"
axis = "representation"
item = "compensated (Kahan) summation"
source = "Higham, Accuracy and Stability of Numerical Algorithms ch.4"
status = "out-of-scope"
evidence = "Fix128 の加算は整数加算で丸めが無いので補償する誤差が無い (COV-NUM-074)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-076"
axis = "representation"
item = "overflow detection in multiplication"
source = "Higham ch.2; checked arithmetic"
status = "partial"
evidence = "src/math.rs::checked_mul (checked_mul、明示的に呼んだ経路のみ) / tests/audit_math.rs::checked_mul_is_sound / tests/audit_math.rs::checked_mul_basic_range_boundaries / known defect: tests/audit_math.rs::checked_mul_is_complete 既定の * は巻き戻る (src/math.rs::sub)"
oracle_candidate = "範囲外の積で None、範囲内の積で Some"
limitation = "src/math.rs 'There is no saturation and no panic, in debug builds too'"

[[item]]
id = "COV-NUM-077"
axis = "representation"
item = "scaled inner products and norms (power-of-two rescaling per vector)"
source = "Higham ch.3; LAPACK dnrm2 scaling"
status = "partial"
evidence = "src/linear_solver.rs ベクトルごとの 2 冪スケーリング、1 本のベクトル内で 2^32 倍小さい成分は救えない (ブロック等化 COV-NUM-079 で補う) / tests/analytic_linear_solver.rs::pla_block_ratio_needs_equilibration"
oracle_candidate = "大小 2 ブロックの内積で小ブロックの寄与が残る"
limitation = "src/linear_solver.rs 'it cannot rescue entries of one vector that are `2³²` times smaller than that vector's largest entry'"

[[item]]
id = "COV-NUM-078"
axis = "representation"
item = "silent-truncation guard for squared norms (L2 checked / L-infinity norm)"
source = "this crate's Fix128 product floor 2^-64"
status = "implemented+oracle"
evidence = "src/coupled_iteration.rs::residual_norm_l2_checked / tests/audit_coupled_iteration.rs::l2_refuses_every_component_whose_square_leaves_the_representable_range / tests/audit_coupled_iteration.rs::l2_floor_is_exactly_the_square_root_of_one_ulp"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-079"
axis = "representation"
item = "block equilibration of multi-field systems (power-of-two factors)"
source = "Bunch 1971 (equilibration); Higham ch.7; PETSc MatDiagonalScale"
status = "implemented+oracle"
evidence = "src/linear_solver/equilibrate.rs::BlockEquilibration / src/linear_solver/equilibrate.rs::solve_equilibrated / tests/analytic_linear_solver.rs::pla_block_ratio_needs_equilibration / tests/analytic_linear_solver.rs::unscaled_floor_check_matches_the_material_table / known defect: tests/audit_coupled_iteration.rs::covering_scales_only_down_and_leaves_a_magnitude_of_one_or_less_alone"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-080"
axis = "representation"
item = "ill-conditioned systems (condition number above 2^40)"
source = "Higham ch.7; iterative refinement (Wilkinson)"
status = "partial"
evidence = "src/linear_solver.rs 条件数が 2^40 を超える系は解かずに breakdown として返す / tests/analytic_linear_solver.rs::rounded_rank_deficient_matrices_break_down_at_the_second_step / tests/analytic_hilbert_breakdown_boundary.rs (Hilbert 行列 n=9 vs n=10 境界、published cond(H_n) 突合、n=9 は closed form 誤差域で解き n=10 は known defect として ignore で pin) known defect: 既存 test は rank-deficient な系の breakdown のみ確認、単に ill-conditioned (非特異) な Hilbert 系では n=10 (cond~1.6e13 > 2^40) で gmres が Err(Breakdown) でなく Ok を返す (誤差 1.31 自体は cond(H_10)*tol≈14.6 の範囲内で収束としては正当、欠陥は breakdown 分類が付かない点のみ) (hilbert_ten_is_past_the_breakdown_threshold_and_should_report_breakdown、#[ignore] で pin)"
oracle_candidate = ""
limitation = "src/linear_solver.rs 'a system whose condition number exceeds about `2⁴⁰` is reported as breakdown rather than solved to digits the representation does not hold.'"

[[item]]
id = "COV-NUM-081"
axis = "representation"
item = "iterative refinement / mixed precision"
source = "Wilkinson; Carson-Higham 2018; PETSc KSPPREONLY + refinement"
status = "missing"
evidence = "無い"
oracle_candidate = "条件数 2^30 程度の系で残差補正 1 回ごとに桁が伸びる"
limitation = ""

[[item]]
id = "COV-NUM-082"
axis = "representation"
item = "f64 <-> Fix128 conversion"
source = "IEEE 754 binary64"
status = "implemented+oracle"
evidence = "src/math.rs::Fix128 / tests/audit_math.rs::f64_and_f32_conversions / known defect: tests/audit_math.rs::from_f64_non_finite_and_out_of_range_are_not_silently_plausible / known defect: tests/audit_math.rs::to_f64_is_relatively_accurate_for_small_negative_values"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-083"
axis = "representation"
item = "elementary functions (sqrt / exp / ln / sin / cos / atan2)"
source = "Muller, Elementary Functions"
status = "implemented+oracle"
evidence = "src/math.rs::sqrt (sqrt) / tests/audit_math.rs::sqrt_is_exact_floor / tests/audit_math.rs::exp_ln_powf_accuracy_claims / tests/audit_math.rs::sin_cos_accuracy_over_the_reduced_range_and_identities / known defect: tests/audit_math.rs::exp_is_accurate_up_to_the_representable_maximum"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-084"
axis = "benchmark"
item = "advection-diffusion non-symmetric system across Peclet numbers"
source = "Saad ch.6 / ch.7 model problems; Elman-Silvester-Wathen ch.6"
status = "implemented+oracle"
evidence = "tests/analytic_linear_solver.rs::advection_diffusion_matches_closed_form_across_peclet"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-085"
axis = "benchmark"
item = "Krylov solution cross-checked against an independent solver (SPD cantilever)"
source = "PETSc -ksp_type comparison practice"
status = "implemented+oracle"
evidence = "tests/analytic_linear_solver.rs::spd_cantilever_matches_private_cg_and_f64_elimination"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-086"
axis = "benchmark"
item = "Poisson multigrid convergence factor independent of h (general component)"
source = "Briggs-Henson-McCormick ch.4; Trottenberg et al."
status = "missing"
evidence = "汎用 multigrid が無い (COV-NUM-025) CFD の圧力では tests/analytic_multigrid.rs::contraction_rate_is_grid_independent"
oracle_candidate = "既存の CFD 圧力 multigrid の測定値を汎用化時の参照に流用 (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-087"
axis = "benchmark"
item = "stiff ODE: Robertson chemical kinetics"
source = "Hairer-Wanner, Solving ODEs II ch.IV.1"
status = "missing"
evidence = "陰的汎用積分が無い (COV-NUM-051 / 054)"
oracle_candidate = "長時間 (t = 1e11) で質量保存と参照解 (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-088"
axis = "benchmark"
item = "stiff ODE: van der Pol oscillator (large mu)"
source = "Hairer-Wanner, Solving ODEs II ch.IV.1"
status = "missing"
evidence = "陰的汎用積分が無い (COV-NUM-051 / 054)"
oracle_candidate = "周期の漸近式との突合 (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-089"
axis = "benchmark"
item = "long-time energy behaviour of a symplectic integrator (harmonic oscillator / Kepler)"
source = "Hairer-Lubich-Wanner ch.IX"
status = "missing"
evidence = "汎用の symplectic 積分が無い (COV-NUM-046 / 047) nbody / molecular_dynamics の分野内実装は各分野の表"
oracle_candidate = "1e6 step でエネルギー誤差が有界、位相誤差が線形"
limitation = ""

[[item]]
id = "COV-NUM-090"
axis = "benchmark"
item = "two-field partitioned coupling with closed-form contraction (added-mass piston)"
source = "Causin-Gerbeau-Nobile 2005; Forster-Wall-Ramm 2007"
status = "implemented+oracle"
evidence = "tests/analytic_added_mass_coupling.rs::the_contraction_ratio_matches_the_closed_form / tests/analytic_added_mass_coupling.rs::refining_the_time_step_does_not_rescue_a_divergent_splitting"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-091"
axis = "benchmark"
item = "two-field partitioned coupling with Aitken relaxation (sweep count vs constant relaxation)"
source = "Kuttler-Wall 2008"
status = "missing"
evidence = "汎用 Aitken が無い (COV-NUM-062)"
oracle_candidate = "added-mass ピストン + 2 自由度で sweep 数を比較 (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-092"
axis = "benchmark"
item = "nonlinear test set (Rosenbrock function / Bratu problem)"
source = "More-Garbow-Hillstrom 1981; Knoll-Keyes 2004 (Bratu)"
status = "missing"
evidence = "汎用 Newton が無い (COV-NUM-029)"
oracle_candidate = "Bratu の臨界パラメータ lambda_c (参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-093"
axis = "transform"
item = "complex discrete Fourier transform, 1-D (radix-2 / mixed-radix FFT, forward and inverse)"
source = "Cooley-Tukey 1965; Press et al., Numerical Recipes ch.12; FFTW"
status = "missing"
evidence = "無い (推測: fft / dft / fourier で src を検索、当たるのは src/linear_elastic_fem/consistent_tangent.rs::ElementState の行列変数名 F Fᵀ と src/replay.rs の外部 crate の圧縮方式の説明だけ) 前提の複素数の型も無い (src/math.rs::Fix128 は実数の Q64.64 のみ、複素数の行は量子力学の表)"
oracle_candidate = "O(n^2) の直接和と突合、逆変換で元に戻る (Fix128 で bit 一致か誤差上界)、Parseval、純音で単一ビン"
limitation = ""

[[item]]
id = "COV-NUM-094"
axis = "transform"
item = "real-input FFT and multi-dimensional FFT (2-D / 3-D, periodic grids)"
source = "Press et al., Numerical Recipes ch.12; FFTW r2c / plan_dft_3d"
status = "missing"
evidence = "無い (COV-NUM-093 と同じ検索) 周期格子の FFT Poisson は COV-CFD-077 (missing)"
oracle_candidate = "実入力の Hermite 対称性、多次元は 1-D の積と突合、周期箱の単一 Fourier モード"
limitation = ""

[[item]]
id = "COV-NUM-095"
axis = "stochastic"
item = "plain Monte Carlo estimate of an integral / expectation with its sample variance and standard error"
source = "Robert-Casella, Monte Carlo Statistical Methods ch.3; Owen, Monte Carlo theory, methods and examples ch.2"
status = "missing"
evidence = "推定量の API は無い 部品として標本は src/rng.rs::DeterministicRng (src/rng.rs::next_fix128 一様 [0, 1)、src/rng.rs::next_gaussian_pair、tests/analytic_rng_wiring.rs::bounded_is_uniform_chi_square)、平均と標本分散は src/anomaly.rs::ZScoreDetector (Welford、src/anomaly.rs::observe / src/anomaly.rs::variance、std feature、tests/audit_anomaly.rs::zscore_matches_two_pass_mean_variance) にあるが、その組み合わせは呼び手が渡せる汎用の推定量ではないので数えない 標本は Fix128、統計量は f64"
oracle_candidate = "∫_0^1 x^2 dx = 1/3 を N 標本で推定し、誤差が標準誤差の数倍に収まることと標準誤差が 1/sqrt(N) で減ることを seed 固定で確認"
limitation = ""

[[item]]
id = "COV-NUM-096"
axis = "stochastic"
item = "variance reduction: importance sampling with weights, antithetic variates, control variates, stratified sampling"
source = "Owen, Monte Carlo theory, methods and examples ch.8-9; Lux-Koblinger, Monte Carlo Particle Transport Methods"
status = "missing"
evidence = "無い (推測: importance / antithetic / control variate / stratif で src 0 件) 一様と正規以外の分布から引く部品も無い (src/rng.rs) 原子核の表の MC 輸送の分散低減行はこの部品の用途"
oracle_candidate = "指数関数の積分で重点サンプリングの分散比が閉形式と一致、antithetic で単調関数の分散が減ること"
limitation = ""

[[item]]
id = "COV-NUM-097"
axis = "matrix_function"
item = "dense matrix exponential exp(A) (Pade approximation with scaling and squaring)"
source = "Moler-Van Loan 2003 (Nineteen dubious ways); Higham 2005; scipy.linalg.expm"
status = "missing"
evidence = "無い (推測: expm / matrix exp で src 0 件) Pade で当たるのは src/neural.rs::fix128_tanh_approx の tanh の有理近似、src/math.rs::exp の exp はスカラー"
oracle_candidate = "2x2 回転生成子の exp が cos / sin の回転行列、冪零行列で有限和と一致、対角行列で要素ごとの exp"
limitation = ""

[[item]]
id = "COV-NUM-098"
axis = "matrix_function"
item = "Chebyshev rational approximation (CRAM) for exp(A) v with eigenvalues on the negative real axis"
source = "Pusa-Leppanen 2010 (CRAM); Pusa 2016; ORIGEN / OpenMC depletion"
status = "missing"
evidence = "無い (推測: CRAM / Chebyshev rational で src 0 件) 硬い崩壊連鎖での使い方は原子核の表の行"
oracle_candidate = "2 段崩壊連鎖の Bateman 閉形式と突合、崩壊定数の比が極端な連鎖で負の数密度が出ないこと (係数は参照値要確認)"
limitation = ""

[[item]]
id = "COV-NUM-099"
axis = "eigen"
item = "symmetric tridiagonal eigenproblem (Sturm-sequence bisection, inverse iteration for eigenvectors, implicit QL)"
source = "Golub-Van Loan ch.8.4-8.5; Wilkinson-Reinsch Handbook (tql2 / bisect); LAPACK stebz / stein / steqr"
status = "missing"
evidence = "無い (推測: sturm / tql / implicit QL で src 0 件) bisection で当たるのはスカラーの根探索 (src/kepler.rs::KEPLER_MAX_ITERATIONS、src/turbulence.rs::FRICTION_VELOCITY_BISECTIONS、COV-NUM-037)、tridiagonal で当たるのは src/transient_thermal.rs::thomas_solve_in_place の Thomas 法 (連立 1 次方程式、COV-NUM-004) 一般の逆反復は COV-NUM-040"
oracle_candidate = "1D Laplacian (2, -1) の固有値 2 - 2 cos(k pi / (n + 1)) と固有ベクトル sin(j k pi / (n + 1)) の閉形式"
limitation = ""

[[item]]
id = "COV-NUM-100"
axis = "eigen"
item = "dense symmetric n x n eigen-decomposition (cyclic Jacobi, Householder tridiagonalisation + QL / QR)"
source = "Golub-Van Loan ch.8.3, 8.5; LAPACK syev / syevd"
status = "missing"
evidence = "3x3 に限った cyclic Jacobi だけ (src/mass_properties.rs::principal_axes principal_axes、COV-NUM-038) n x n の汎用部品は無い (推測: householder / tridiagonalis で src 0 件) 非対称と SVD は COV-NUM-044"
oracle_candidate = "n = 3 で principal_axes と突合、1D Laplacian の閉形式、直交性 Q^T Q = I と A Q = Q Λ の残差"
limitation = ""

[[item]]
id = "COV-NUM-101"
axis = "mesh_adaptivity"
item = "block-structured adaptive mesh refinement hierarchy as a general component (Berger-Oliger / Berger-Colella: tagging, regridding, coarse-fine interpolation, refluxing, subcycling in time)"
source = "Berger-Oliger 1984; Berger-Colella 1989; AMReX; Chombo; p4est"
status = "missing"
evidence = "格子の階層は無い (推測: AMR / octree / quadtree / Berger で src 0 件、COV-CFD-006 は「格子は固定解像度のみ」で missing) 四面体の最長辺二分割は src/sdf_fem_mesh.rs::refine_by_max_edge_length refine_by_max_edge_length / src/sdf_fem_mesh.rs::try_refine_marked try_refine_marked で固体 FE の h 適応 (COV-FEM-112) 専用、構造格子の階層ではない 分割: 子の行 COV-NUM-121〜124 この行の status は子のうち最も実装の少ないもの (missing) に合わせて手で保つ (検査器は親子を見ない)"
oracle_candidate = "細分化境界を越える一様流が不変、粗密境界の refluxing で保存量の総和が bit 一致で保たれる"
limitation = ""

[[item]]
id = "COV-NUM-102"
axis = "mesh"
item = "Delaunay tetrahedralisation of a point set (incremental Bowyer-Watson with robust orientation and in-sphere predicates)"
source = "Cheng-Dey-Shewchuk, Delaunay Mesh Generation ch.3-5; Shewchuk 1997 (robust predicates); CGAL / TetGen feature lists"
status = "missing"
evidence = "四面体 mesh の生成は SDF の格子を切る方式だけ (src/sdf_fem_mesh.rs::generate / src/sdf_fem_mesh.rs::generate_marching_tets、形状最適化の表 COV-OPT-065 が I+O で数える) grep: delaunay は src/sdf_fem_mesh.rs の「Delaunay 細分ではない」という注記のみ"
oracle_candidate = "空の外接球の検査と Euler 標数 (行 COV-NUM-120)"
limitation = ""

[[item]]
id = "COV-NUM-103"
axis = "mesh"
item = "boundary recovery of a given surface (constrained Delaunay) and Delaunay refinement for quality (Ruppert / Shewchuk)"
source = "Si 2015 (TetGen); Shewchuk 2002"
status = "missing"
evidence = "四面体 mesh の生成は SDF の格子を切る方式だけ (src/sdf_fem_mesh.rs::generate / src/sdf_fem_mesh.rs::generate_marching_tets、形状最適化の表 COV-OPT-065 が I+O で数える) FE の側の細分の品質は COV-FEM-115 (partial、最長辺の二分で Delaunay 細分ではない) 本行は汎用部品"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-104"
axis = "mesh"
item = "advancing-front tetrahedral meshing from a surface mesh"
source = "Löhner, Applied CFD Techniques ch.3; Frey-George, Mesh Generation ch.6"
status = "missing"
evidence = "四面体 mesh の生成は SDF の格子を切る方式だけ (src/sdf_fem_mesh.rs::generate / src/sdf_fem_mesh.rs::generate_marching_tets、形状最適化の表 COV-OPT-065 が I+O で数える)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-105"
axis = "mesh"
item = "size-graded meshing of an SDF (octree or graded lattice with the cell size from curvature, local feature size and distance to the surface)"
source = "Labelle-Shewchuk 2007 (isosurface stuffing); Frey-George ch.5"
status = "missing"
evidence = "四面体 mesh の生成は SDF の格子を切る方式だけ (src/sdf_fem_mesh.rs::generate / src/sdf_fem_mesh.rs::generate_marching_tets、形状最適化の表 COV-OPT-065 が I+O で数える) 格子は一様で、セルより細い特徴は黙って埋まる (src/sdf_fem_mesh.rs の Limitations に記載)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-106"
axis = "mesh"
item = "hexahedral and hex-dominant meshing (sweeping, grid-based with boundary projection)"
source = "Frey-George ch.8; Owen 1998 (survey)"
status = "missing"
evidence = "hex 要素も固体 FE の表で missing (COV-FEM-012 / 013)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-107"
axis = "mesh"
item = "element quality measures as a callable component (radius-edge ratio, minimum dihedral angle, aspect ratio, scaled Jacobian)"
source = "Shewchuk 2002 (What is a good linear element?); Knupp 2001"
status = "missing"
evidence = "品質を測る関数は test の中だけ (tests/mesh_quality.rs、tests/refinement_conformity.rs) で、呼び手に渡せる API は src/ に無い"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-108"
axis = "mesh"
item = "mesh improvement with fixed topology and with local reconnection (Laplacian and optimisation-based smoothing, edge and face swaps, sliver removal)"
source = "Freitag-Ollivier-Gooch 1997; Klingner-Shewchuk 2007"
status = "missing"
evidence = "四面体 mesh の生成は SDF の格子を切る方式だけ (src/sdf_fem_mesh.rs::generate / src/sdf_fem_mesh.rs::generate_marching_tets、形状最適化の表 COV-OPT-065 が I+O で数える) 生成後に node を動かす・接続を変える操作は無い"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-109"
axis = "mesh"
item = "conforming local refinement of marked tetrahedra (edge bisection propagated until no hanging node remains)"
source = "Rivara 1984 (longest-edge bisection); Arnold-Mukherjee-Pouly 2000"
status = "implemented+oracle"
evidence = "src/sdf_fem_mesh.rs::try_refine_conforming / src/sdf_fem_mesh.rs::try_refine_marked oracle は面の使用回数の数え上げ (内部面はちょうど 2 回) tests/refinement_conformity.rs::uniform_refinement_stays_conforming / tests/refinement_conformity.rs::graded_refinement_stays_conforming FE の適応は COV-FEM-112 が数える 既知の欠陥 tests/audit_sdf_fem_mesh.rs::refinement_keeps_every_element_positively_wound (ignore = known defect AUD-A-S2W3-012、子の向きが混ざる)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-110"
axis = "mesh"
item = "coarsening and full adaptive remeshing with a size field (refine, coarsen and smooth to a target metric)"
source = "Frey-George ch.21; Alauzet-Loseille 2016 (metric-based adaptation)"
status = "missing"
evidence = "細分 (行 COV-NUM-109) だけで粗くする操作が無い 布の適応 remesh COV-SOFT-078、き裂に沿う remesh COV-FRACT-031 (いずれも missing) が引く"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-111"
axis = "mesh"
item = "boundary-surface extraction of a tetrahedral mesh (faces used once; a non-manifold face is refused)"
source = "Frey-George ch.1 (mesh data structures)"
status = "implemented+oracle"
evidence = "src/sdf_fem_mesh.rs::boundary_faces tests/analytic_sdf_fem_mesh_wiring.rs::a_non_cubic_block_matches_the_closed_form_tet_vertex_and_boundary_counts / tests/analytic_sdf_fem_mesh_wiring.rs::boundary_faces_reports_which_face_and_how_many_tets_claimed_it"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-112"
axis = "mesh"
item = "element-quality guarantee of the lattice SDF mesher (uniform quality of the whole-cube dicing, crossing snap that keeps slivers out under refinement)"
source = "Labelle-Shewchuk 2007 (quality bounds of lattice-based meshers)"
status = "implemented+oracle"
evidence = "src/sdf_fem_mesh.rs::generate_marching_tets tests/mesh_quality.rs::whole_cube_dicing_has_uniform_quality / tests/mesh_quality.rs::marching_tets_stays_out_of_the_sliver_population oracle は二面角の下限の数え上げ 細分した後の品質の漂いは COV-FEM-115 (partial)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-113"
axis = "mesh"
item = "surface mesh simplification by edge collapse that keeps a closed surface closed and its genus"
source = "Garland-Heckbert 1997; Hoppe 1996"
status = "implemented+oracle"
evidence = "src/collision_mesh_gen.rs::simplify_collision_mesh tests/analytic_collision_mesh.rs::simplifying_never_breaks_the_mesh / tests/analytic_collision_mesh.rs::simplifying_a_torus_keeps_its_hole / tests/analytic_collision_mesh.rs::simplifying_a_ball_keeps_a_closed_outward_sphere 生成は剛体の表 COV-RIGID-070 (同じ test が生成の行の evidence にも出る)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-114"
axis = "mesh"
item = "surface remeshing and repair (isotropic remeshing, hole filling, removal of self-intersections, watertightness check)"
source = "Botsch et al., Polygon Mesh Processing ch.6-8"
status = "missing"
evidence = "表面 mesh の修復・再分割は無い (推測: remesh / repair で 0 件)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-115"
axis = "mesh"
item = "mesh deformation with fixed connectivity as a general component (Laplacian or pseudo-elastic smoothing of interior nodes, radial-basis interpolation of a boundary displacement)"
source = "de Boer-van der Schoot-Bijl 2007 (RBF mesh motion); Stein-Tezduyar-Benney 2003"
status = "missing"
evidence = "設計変数による mesh morphing COV-OPT-066 と流体 mesh の界面追従 COV-COUPLE-016 (いずれも missing) の共通部品"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-116"
axis = "mesh"
item = "signed distance field from a closed triangle mesh (closest triangle with the sign from the winding number or angle-weighted pseudo-normals)"
source = "Bærentzen-Aanæs 2005; Jacobson et al. 2013 (generalised winding number)"
status = "missing"
evidence = "SDF から mesh への向きはある (COV-RIGID-070、COV-OPT-065) が逆向きが無い (推測: mesh_to_sdf / winding で 0 件) 電磁の材料の取り込み COV-EM-041 (missing) が使う"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-117"
axis = "mesh"
item = "mesh exchange formats for tetrahedral and surface meshes (Gmsh .msh, VTK / VTU, STL, Exodus II)"
source = "Gmsh, VTK and Exodus II format specifications"
status = "missing"
evidence = "mesh の読み書きは無い (推測: vtk / gmsh / exodus で 0 件) 場の書き出しは電磁の表 COV-EM-100 (missing)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-118"
axis = "mesh"
item = "curved boundary for higher-order elements (edge and face nodes projected onto the SDF surface)"
source = "Sherwin-Peiró 2002; Persson-Peraire 2009"
status = "missing"
evidence = "P2 / P3 の辺 node は直線辺上 (固体 FE の曲辺アイソパラメトリック COV-FEM-016、missing) 本行は SDF の表面へ射影する汎用部品"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-119"
axis = "mesh"
item = "mesh partitioning for distributed runs (graph partitioning, space-filling-curve ordering)"
source = "Karypis-Kumar 1998 (METIS); Bader, Space-Filling Curves"
status = "missing"
evidence = "分散の負荷分散 COV-NUM-071 (missing) が使う 格子の領域分割は一様な立方体の分割だけ (推測)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-120"
axis = "benchmark"
item = "Delaunay property of a random point set: empty circumspheres and the Euler characteristic of the result"
source = "Cheng-Dey-Shewchuk ch.4"
status = "missing"
evidence = "Delaunay 分割が無い (行 COV-NUM-102)"
oracle_candidate = ""
limitation = ""

[[item]]
id = "COV-NUM-121"
axis = "mesh_adaptivity"
item = "AMR: error tagging of cells and regridding into nested patches (Berger-Rigoutsos clustering)"
source = "Berger-Oliger 1984; Berger-Colella 1989; AMReX; Chombo; p4est"
status = "missing"
evidence = "COV-NUM-101 の子 階層の格子が無い (推測: AMR / Berger で src 0 件)"
oracle_candidate = "既知の誤差指標の帯を tag して作った patch が tag を全部覆い、efficiency の閾値を満たす"
limitation = ""

[[item]]
id = "COV-NUM-122"
axis = "mesh_adaptivity"
item = "AMR: coarse-fine interpolation of ghost cells (conservative, order-preserving)"
source = "Berger-Oliger 1984; Berger-Colella 1989; AMReX; Chombo; p4est"
status = "missing"
evidence = "COV-NUM-101 の子 階層の格子が無い"
oracle_candidate = "線形場を粗から細へ補間して厳密、2 次場で補間誤差の次数"
limitation = ""

[[item]]
id = "COV-NUM-123"
axis = "mesh_adaptivity"
item = "AMR: refluxing at coarse-fine faces (flux correction for conservation)"
source = "Berger-Oliger 1984; Berger-Colella 1989; AMReX; Chombo; p4est"
status = "missing"
evidence = "COV-NUM-101 の子 階層の格子が無い"
oracle_candidate = "粗密境界を越える移流で保存量の総和が bit 一致"
limitation = ""

[[item]]
id = "COV-NUM-124"
axis = "mesh_adaptivity"
item = "AMR: subcycling in time on the finer levels (time interpolation of boundary data)"
source = "Berger-Oliger 1984; Berger-Colella 1989; AMReX; Chombo; p4est"
status = "missing"
evidence = "COV-NUM-101 の子 階層の格子が無い"
oracle_candidate = "細格子の時間刻み比 r で時間精度の次数が保たれる"
limitation = ""