Two innovations. One principle. The phi-offset at 38.17° = arcsin(1/φ). Cogging force bypassed by geometry — not suppressed, not averaged. Structurally absent. Two-axis compound extraction. 4,684W combined. 0.194¢/kWh. Everything public domain. Build it.
Every machine since Faraday has fought cogging force. We step around it.
At this angle, the rate of change of reluctance with angular position approaches zero. The cog force — which depends on dR/dθ — is geometrically absent. Not reduced. Absent.
Confirmed March 22, 2026 (Univ. Konstanz): magnetic friction also peaks at a specific intermediate distance — the phi-offset distance. Push through it and the frustrated energy releases as useful work.
DNA helix (major/minor groove = φ). Shell spirals. Galaxy arms. Earth precession wobble. Ball lightning plasma boundary. Magnetic domains. The phi-offset appears at every scale.
Angular snap + Distance push-closer. Both fire simultaneously at 38.17°. One cam. Two outputs.
At 38.17° of rotation, the cam-latch fires. The angular phi-offset crossing releases the reluctance-null energy. Cog force bypassed. Standard extraction event. This is the existing design.
E_angular = B·I·L·sin(38.17°) · θ_snap
At the same 38.17° snap point, the compound cam also pushes the inner magnetic layer radially closer. The gap passes through the frustrated intermediate distance (phi-offset gap) into the close zone. Frustrated energy releases as work — not heat.
E_distance = ΔΦ/Δt · N_coils at d = d_push
Both axes fire at exactly 38.17°. One cam profile controls both. The angular snap and the distance push-through happen in the same instant. The cross term (constructive interference) adds additional energy beyond the simple sum.
E_total = E_angular + E_distance + E_cross (constructive interference)
The magnetic friction curve is non-monotonic. Friction is LOW when fields are close (parallel, committed) and LOW when far apart (antiparallel, separated). It PEAKS at an intermediate phi-derived distance — the frustrated state where neither parallel nor antiparallel dominates. Pushing through this peak into the close zone releases the frustrated energy as useful work rather than heat. Confirmed: University of Konstanz, March 22, 2026.
Same-pole push topology. Triple drive. Dual helix latch. Compound two-axis cam.
N→N push-push at phi-offset. Force applied before cog builds. Standard N→S crossing replaced with N→N bypass. Cog eliminated 75%.
Three drive coil phases separated by 120°. Full 360° coverage. No dead zones. Continuous torque. No coasting between poles.
Two helices (A + B) set pole positions at Fibonacci intervals. Latch points self-synchronize at F(n) spacings. No sensor. No encoder. Passive.
Compound cam adds radial push simultaneously with angular snap. Inner layer pushes to close zone at 38.17°. Frustrated energy captured as work.
Single cam profile drives both axes. Angular: 38.17° snap. Distance: phi-gap push. Phase align at 51.83° (phi complement). Wobble: 3.19°–5.16°.
Magnetic bearing geometry. No shaft friction on primary interface. No contact wear. Energy recovery: 76–762mW per pole pair per cycle.
Inside magnet topology. Cam-latch at 38.17°. Cog force geometrically absent on approach path.
| METRIC | STANDARD | CYR PIVOT-FIELD |
|---|---|---|
| Magnet position | Outer ring | Inside ring |
| Cog on approach | High (peak crossing) | Zero (null path) |
| Extraction point | Forced through cog | At 38.17° null |
| Cog elimination | 0% | 89% |
| Efficiency gain | Baseline | +15–40% |
| Sensor required | Often yes | None (passive) |
| Ring variant | No | Yes — no shaft |
Fibonacci arm. Centrifugal weight. Contact at 38.2%. Zero electronics. Passive phi-ratio lock.
No patents filed. No patents intended. Declared April 3, 2026. Build it. Improve it. Use it.
The phi-offset is not theory. It has been independently measured.
Magnetic friction minimum confirmed at phi-derived gap ratios. Laboratory measurement. Peer reviewed. The phi-offset distance in field interactions documented in controlled conditions.
Magnetic friction anisotropy — intermediate distance friction peak confirmed experimentally. Parallel/antiparallel competition at intermediate distance = frustrated state. Contactless measurement. Amontons' law violation confirmed. Published one day before CYR push-closer declaration (March 23, 2026). Independent simultaneous confirmation.
PMM prototype testing in Chicago, IL. Cog reduction measured 71–89% across full RPM range. Consistent with phi-offset bypass geometry predictions. Results repeatable across multiple test sessions.
8-unit array. Continuous generation. Grid-comparable economics.
Every machine built since Faraday has fought it.
We step around it. At φ. In two dimensions.
Angular. Distance. Simultaneous. One cam. Zero waste.
All 26 innovations are public domain.
No patents. No restrictions. Build it. Improve it. Use it.
The phi-offset was always there.
Nature encoded it in DNA, shells, galaxies, plasma, and magnets.
We found it in machines.