Numerical policy and compile-time method selection (target)¶

Goal¶

Users declare physics intent and numerical targets; the compiler chooses integrators, solvers, and approximations at compile time (no runtime registry).

User surface (planned)¶

@physics(tier = simulation, fps = 60)
def step_world(world: PhysicsWorld, dt: float) -> unit
  requires dt > 0
  targets energy_drift < 1e-3
  targets momentum_drift < 1e-4

Defaults (`NumericalTargets`)¶

Field	Default	T0 arcade	T2 scientific
`max_energy_drift`	1e-3	5e-2	1e-4
`max_momentum_drift`	1e-4	1e-2	1e-6
`target_fps`	60	60	N/A
`cfl_safety`	0.9	0.8	0.95

Selection rules (v1 table)¶

Problem class	T0	T1	T2
ODE (generic)	Semi-implicit Euler	Velocity Verlet	RK4 / symplectic
N-body	Euler + softening	Verlet	Barnes–Hut + Verlet
Grid PDE	Explicit Euler	CFL-limited explicit	CN / implicit
Fluids	PBD / cheap SPH	WCSPH	MLS-MPM
Quantum	—	—	Split-operator TDSE

Agent skill¶

Contributors use .cursor/skills/research-li-numerics before adding a new kernel: survey references, document error bounds, add a Tier-0 stability row.

Proof surface¶

requires dt > 0, CFL inequalities as requires where explicit schemes are chosen
ensures energy drift bounds for symplectic integrators when G-vc / G-lean support them

Status: Library types in li-physics-core today; decorator elaboration is planned (see provability gaps).

For floating-point expression stability (subtraction cancellation, compensated sums), see fp-numerical-stability.md (lic build --numerically-stable).