K4 — from tetrahedral field geometry to a buildable electromagnetic instrument

K4 is a tetrahedral electromagnetic-field synthesis instrument. Six straight current-carrying bundles form the edges of a regular tetrahedron; four outward-facing air-core coils at the vertices provide a second magnetic family; corner electrodes complete the design with the electric field. The central idea is controlled superposition — not exotic energy production: tetrahedral symmetry organizes physical currents into mathematically distinct modes, and an inverse solver turns a requested field behavior into drive waveforms for real hardware.

The first physical build (V1) is the magnetic realization — a 100 mm PLA-and-copper bench device designed to answer a plain question: does the clean decomposition survive contact with tolerances, lead routing, electronics, ambient noise, and calibration?

V1 controls the field through the six edge bundles and four vertex coils. The build proceeds in order — calibrate single edges, assemble the full tetrahedron, then add the corner electrodes that bring the electric field into the instrument. Every number on this site carries its model and claim class.

The instrument — live, in this browser

Rotate and zoom the V1 build model below — the exact geometry the printer will produce: grooved spars, parallel strand bundles, LW181 vertex coils at their canonical offsets.

For the full field instrument — drive the channels, solve to a target, watch the field, load, and fidelity respond in real time — open the Cockpit →

What exists now

An inverse solver with forward-validation and audit tests (residuals, singular values, null space, regime, model, claim class, and leak share on every report) · a choreographer that compiles pattern sets into time-indexed drive trajectories · a calibrated physical topology (v1build: straight parallel bundles — Schur-exact cut null — plus loop-stack-matched vertex coils) · a frozen V1 build canon with bill of materials and acceptance numbers · this cockpit.

The V1 build at a glance

100 mm edges · printed PLA spars with twenty keyed grooves (the groove floor is the datum) · 20 parallel strands of 22 AWG per edge, one direction, tied at both ends · resistive conductive-PLA screens, bonded at exactly one end · four Dayton LW181-class air-core vertex coils at vertex + 25 mm · overhead star-grounded electronics platform · stage-1 electronics: Teensy 4.1, audio shield (a phase-locked lock-in pair for free), dual amplifier, 2 Ω non-inductive ballasts.

Two bench truths the math insisted on: a serpentine-wound edge passes every continuity check and produces almost no field (adjacent passes cancel) — strands must run one way and be paralleled. And an edge's return lead must never hug its own edge, or it cancels the actuator while everything still measures fine.

The structure tests itself

Drive all four vertex coils equally and the centroid should stay dark — any residual is a direct measurement of the build's asymmetry. Drive one edge's two half-bundles against each other and the edge goes field-dark at full current. These diagnostics are first-class operations, because the instrument is most useful while it is being assembled and calibrated.

Capacity here is an ellipsoid, not a row of parking spaces: rank survives only as a diagnostic chip, while live capacity is priced continuously — current, RMS, power, amplifier headroom, residual, and remaining authority after the arrangement takes its share.

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