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Physics & findings

The lab you just used is driven by a physics engine built from the real device — the {12/5} winding, the EFH1 ferrofluid, and the slug's driven dynamics. Here's what's under it and what it found. Full provenance: docs/SPEC.md in the repo.

The device

A ~3.5″ printed torus with a 1″ tube holds a sealed raceway full of ferrofluid and one free ~12.7 mm N52 slug — axially magnetized, its N–S axis lying tangent to the track. One copper conductor is sewn in a {12/5} star (12 nodes, each stitch skipping 5, through the bore and around the tube), giving 12 poloidal turns and 5 bore-axis encirclements per wrap. A stereo amp drives L = 314 Hz and R = 3140 Hz into the two ends, so the coil sees L − R. The half-covered winding rectifies that differential drive into a one-way orbit whose speed is set by volume; it melts at volume 6.

What the engine found

Single-tone drift vs frequency — **One tone is not dead — frequency is everything.** Net drift is strongest at **low frequency (~60–70 Hz)** and decays to nothing above ~1 kHz. At 314 Hz it's weak.

Dual-tone beat map — **Dual tone works across a range of beats.** With a fixed base tone, rectification rises as the two tones separate.

Biot–Savart field solver validated to 4×10⁻⁶ against the analytic loop. Bore field scales linearly with wrap count — more wraps, stronger field, faster slug (1 wrap = dead).
The {12/5} landscape is nearly reflection-symmetric, so a single tone barely rectifies from the winding alone — which is why frequency and the ferrofluid matter so much.
Bulk fluid flow rigorously cannot drive the orbit: for a single winding the net azimuthal Kelvin force integrates to zero (verified to 10⁻¹²). The driver is the direct force on the slug, rectified by the ~50% coverage asymmetry.
EFH1's larger particles relax at 4–6.5 kHz — right at the 3140 Hz tone — which is why that specific pair is a live operating point.

Honest boundary. The lab uses a fast behavioural surrogate calibrated to the engine's validated structure and the bench anchors, so it stays responsive and controllable. The full driven-ratchet integration (chaotic under interaction) lives offline in the Python engine. The specific 314/3140 pair's robust bench motion ultimately relies on the ferrofluid's full nonlinear response — a 2D/3D ferrohydrodynamic solve is the next build. The bench remains the authority.

Bench predictions worth testing

Prediction	From
A single low tone (~60 Hz) should move the slug better than a ~314 Hz tone did	single-tone sweep
Feeding both channels the same tone (L = R) kills all motion	differential null
More wraps → faster; a single wrap won't start	field ∝ wraps
Two devices bore-to-bore with one magnet inverted counter-rotate and repel	polarity flip

built with Claude Code · ← the lab