[Noisemaker111]

Physics and movement integrate the same real time at any frame rate.

Three separate causes, each measured with a headless scenario before it was named.

Causes and before/after

• Rapier stepped on the frame's dt instead of accumulating — packages/rapier/src/rapierBackend.ts:125 set world.timestep = fixedDt ?? dt and stepped once per call, contradicting the contract in physicsBackend.ts:151. A ball with fixedDt: 1/60, 2 s of real time: y = 15.075 at 30 fps (half the simulated time) vs 0.199 at 144 fps (2.4×). Now 30 and 60 fps agree exactly and 144 fps is within one fixed step.
• PhysicsWorld floor friction was a 60 Hz multiplicative brake — physicsWorld.ts:779 did velX *= 1 - friction every substep (0.6^60/s), six times stronger than contact friction. A crate at 4 m/s travelled 0.165 m on the world floor and 0.970 m on a floor collider with the same friction: 0.4. Now 0.967 m and 0.970 m.
• Jump gravity was first-order Euler — movementModel.ts:372 and characterController.ts:268. The same jump peaked at 0.933 / 0.992 / 1.026 m at 30 / 60 / 144 fps, an 11% band from frame rate alone (analytic 1.050). Now 1.05000 / 1.05000 / 1.05012 m.

Checked and cleared, so they are not part of this change: the heightfield walker keeps feet exactly on the terrain (clearance 0.00000 over 3 s at every rate, zero drift standing still), PhysicsWorld was already frame-rate invariant, and the gravity sign mapping is correct.

Gates, each proven red on the old code first

• Shared backend conformance "same distance at 30/60/144 fps" (physicsBackendConformance.ts) — red on the old Rapier step, green on both backends now.
• Rapier fixedDt accumulation (createRapierBackend.test.ts) — old code gave 5.0 m instead of 10 m; red, now green.
• Movement apex across four frame rates (movementProbe.test.ts) — old spread 0.093 m; red, now green.
• Resting body: velocity 0, no drift, penetration under 12 mm (physicsWorld.test.ts).
• Floor-friction parity between world floor and floor collider — old 0.80 m apart; red, now green.

bun run verify:fast 11/11. Core physics + movement 682 pass, rapier 11 pass, typechecks clean.

Open, not fixed here

• Stacked bodies still rest in penetration: 8.8 mm for one box, 33.7 mm for a two-box stack. The solver removes 80% of the excess per substep and sleep freezes the rest. Gated as "does not grow", not "reduced".
• Landing while moving is inconsistent: on a floor collider the impact impulse feeds the friction budget, so the body stops dead horizontally; on the world floor it keeps sliding. Both are defensible models, so it is left for a deliberate choice.

Adoption

Games get these from a release. simulation.hz still defaults to "variable", so game-layer per-tick math still runs on frame dt: character travel differed 0.37% and the force-model vehicle 2.8% over 3 s between 30 and 144 fps. Harbor Heat, Scrap Signal and Drift Foundry should declare simulation: { hz: 60 }. Not changed here.

Jump apex at 60 fps is 6% higher than before; jumpVelocity 7.1 → 6.9 keeps the old height if a game wants it.