Numerical validation policy

Validation is layered. Many public scalar helpers reject nonfinite inputs and impossible physical ranges before division, logarithms or square roots. Geometric/distribution/matrix routines validate ordering, shape or integer indices where needed. Domain guides distinguish enforced bounds from assumptions that cannot be inferred from the arguments. Passing validation does not certify that a physical model applies to a particular apparatus.

Independent benchmark matrix

Domain	Independent evidence
Structural	Beam equilibrium/curvature, support values, bar reaction balance, energy derivative
Electrical	Closed-form transient current, charge integral, RC energy accounting, resonance
Controls	Analytic scalar LQR/Kalman, matrix Riccati residuals and shape/weight failures
Thermodynamics	Integrated P dV, T delta_S, four-state cycle balances and COP identities
Fluids	Integrated parabolic profile, laminar Darcy equivalence, implicit Colebrook residual
Heat transfer	Interface Q*R drops, thin-wall limit, equal-temperature and exchanger limits
Materials	Isotropic modulus identity, elastic strain-energy triangle, fracture inverse, composite bounds
Mechanical	Undamped energy, damping dissipation, critical solution, gear power, forced equilibrium
Aerodynamics	Shock mass/momentum/energy balances, sonic and infinite-wing limits
Signals	Parseval, periodogram integral, cutoff gain, sinc nodes, ADC error bounds
Communications	Analytic FM phase, unsigned bit handling, linear/log link budgets and noise limits
Reliability	Survival integral, SciPy distributions, exhaustive independent system states, sensitivities

Tests use analytical values, invariants, independent quadrature and established SciPy distributions. Where a governing-equation residual is checked, it verifies the numerical solve but does not independently prove the equation’s physics. Most assertions use tight tolerances for algebraic identities; integrations allow appropriate quadrature/discretization error. Source coverage excludes tests and is a diagnostic, not a proof of correctness. Coverage gaps and untested branches are retained in the release report.

Behavior retained in v0.1

SeriesRLC returns current, correcting the previous charge/current mismatch. FM integration starts at zero modulation phase and supports nonuniform grids. Unsigned BPSK/QPSK input is converted before subtraction. Physical range errors raise ValueError instead of propagating NaNs or divisions by zero. Colebrook transition inputs are rejected. Rare-failure PFD and empirical Oswald estimates now enforce their documented implementation ranges. NumPy 1.24 remains supported by using SciPy trapezoid for stress-strain integration.

Coverage gate

The release suite covers all executable production statements. Coverage excludes only test code; production validation, plotting, constants and unit helpers are included. The report’s fail_under=100 gate fails on any missed statement. This is statement coverage; branch coverage is not configured. An executed statement can still contain an error or rely on an invalid model assumption, so analytical benchmarks and the domain guides remain essential.