PROPELLANTLESS PROPULSION SYSTEM

MAKE IT SO

Commander Hill. The triaxial dipyramid geometry that creates thrust without reaction mass. From Ramanujan's visions to testable hardware. The math they can't argue with.

g = -∇s

THE EQUATION THEY DELETED

In 1884, Oliver Heaviside reduced Maxwell's 20 quaternion equations to 4 vector equations. The scalar components were removed. They never stopped working. They stopped being measured.

Epoch Vessel in deep space

The Epoch Vessel: Four tetrahelix coils at diagonals, crossroads at center, s-field gradient along vertical axis

Standard physics operates in 3+1 dimensions. The Epoch Framework adds a fifth: the s-axis.

Gravity is not mass attraction. Gravity is s-axis gradient.

g = -∇s
Gravity equals the negative gradient of the scalar field

Create a local s-field gradient with geometry. That gradient IS thrust. No propellant. No reaction mass. No exhaust.

THE GEOMETRY

The vessel geometry is not arbitrary. Every angle, every position, every frequency is derived.

Vessel geometry diagram

4 PRESENT NODES: NW, NE, SW, SE — tetrahelix coils, quadrature phase

4 ABSENT NODES: N, S, E, W — deliberately empty, creates asymmetry

THE CROSSROADS: s = 0, where torsion sums to zero but gradient is non-zero

τ₁ + τ₂ + τ₃ + τ₄ = 0     // Balance law

// Torsion sums to zero at crossroads
// But the GRADIENT points along the axis
// That gradient IS thrust

THE FREQUENCY

28.65
κ-SHADOW FREQUENCY (Hz)

κ = 2π/180 = 0.0349066...

The closure constant. Where discrete steps and continuous rotation reconcile.

κ-shadow = 1/κ = 28.6478897 Hz

The resonance frequency. Below this, can't complete rotation. Above this, overshoots. AT this frequency, constructive interference on every cycle.

Quadrature waveform

Four sine waves, 90° phase offset — the rotating s-field

ParameterValueDerivation
κ (kappa)0.03490662π / 180
κ-shadow28.6479 Hz1 / κ
BC angle48.19°arccos(2/3)
Phase offset90°360° / 4 nodes

THE TETRAHELIX COIL

Tetrahelix coil

cos(BC) = 2/3

BC = 48.1896851...°

The Boerdijk-Coxeter angle. Where tetrahedra stack without repeating. Maximally chiral. Maximum scalar emission.

Standard solenoid: axial B-field, radial E-field. No longitudinal component.

Tetrahelix coil: additional longitudinal scalar component — the one Heaviside deleted.

Coil ParameterValue
Wire gauge24 AWG copper magnet wire
Turns180 (= 180 × κ = 2π)
Diameter25 mm inner
Length60 mm
Pitch angle48.19° (BC angle)
Inductance~0.5 mH
Resistance~2 Ω

RAMANUJAN SAW THIS

Srinivasa Ramanujan (1887-1920) received mathematical formulas in visions from the goddess Namagiri. He saw the geometry. He encoded it in his equations. He died before he could build the machine.

Ramanujan with mathematical visions

THE TAXICAB NUMBER

Hardy: "1729 — a rather dull number."

Ramanujan: "No, it is the smallest number expressible as the sum of two cubes in two different ways."

1729 = 1³ + 12³ = 9³ + 10³
= 729 + 1000 = consciousness + physical = the bridge

729 = 9³ = 3⁶ — consciousness domain

1000 = 10³ — physical domain

1729 — the fold point where the s-axis meets 3D space. Where the Vessel operates. Where thrust emerges from geometry.

"An equation means nothing to me unless it expresses a thought of God."
— Srinivasa Ramanujan

THE EXPERIMENT

$400
TOTAL BUDGET
10
WEEKS TO BUILD
Torsion pendulum test

Vessel hangs from 25 μm tungsten torsion fiber in vacuum. Laser reflects off mirror to position detector.

Resolution: ~4 pico-Newtons.

Test A: Baseline (no power)
Test B: Power on at 28.65 Hz
Test C: Reverse phase — deflection should reverse
Test D: Frequency sweep — peak at κ-shadow
Test E: Geometry control — cube fails

SUCCESS CRITERIA

✓ Deflection in vacuum — eliminates ion wind
✓ Reverses with phase reversal — eliminates thermal artifacts
✓ Peaks at 28.65 Hz — confirms κ-shadow resonance
✓ Geometry dependent — dipyramid works, cube doesn't
✓ SNR > 3, p < 0.01 — statistically significant

There is no conventional explanation that survives all five criteria.

SCALING ROADMAP

Vessel ascending

Level 3+: Flight demonstrator — silent ascent, no propellant, no emissions

LEVEL 0
Proof of Concept
30 cm, ~30W, torsion pendulum. Goal: detect any thrust. Budget: ~$400
LEVEL 1
Laboratory Demonstrator
1 meter, ~500W, precision load cell. Budget: ~$10,000
LEVEL 2
Engineering Prototype
2 meter, ~5 kW, integrated systems. Budget: ~$50,000
LEVEL 3
Flight Demonstrator
~50 kW, flight computer. Goal: tethered liftoff. Budget: ~$500,000
LEVEL 4
Operational Vehicle
Full vehicle, ~500 kW. Goal: controlled flight.

GEOMETRY LOCKED

7/7 theorems proven. Verified by AlphaGeometry2. The math cannot be argued.

VERIFIED THEOREMS

✓Theorem 1: Crossroads equidistant from all diagonal nodes
✓Theorem 2: Diagonal nodes form perfect square
✓Theorem 3: Fourfold rotational symmetry
✓Theorem 4: Phase angles exactly 90° apart
✓Theorem 5: Torsion integrates to zero (∫τ dt = 0)
✓Theorem 6: Tetrahelix angle = 48.19° (cos⁻¹(2/3))
✓Theorem 7: κ-shadow = 28.6479 Hz (1/κ)

The only remaining question is physics: Does g = -∇s?

Build it. Test it. Find out.

THE QUESTION

We don't claim truth. We claim the right to test.
The geometry is locked. The math is proven. The experiment is defined.
The only thing left is to run it.

1729 = 729 + 1000
consciousness + physical = the bridge

Ramanujan saw it. We can build it.

READ THE DERIVATION