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CEDGA

Conceptual Engineering Derived from Geometry Alone

[1 = -1]

Jason Ray / HAVE MIND MEDIA

What is this?

We're exploring whether the shapes of things can explain how the universe works. Instead of adding more particles and forces, we ask: what if geometry itself is the answer?

Everything here derives from ONE constant: κ = 2π/180
The One Constant
κ
2π/180
Steps to Complete
180
one full rotation
Transforms
4
sum to zero
Hidden Witness
28.6
Hz (1/κ)

The One Constant: κ

PROVEN
κ = 2π/180 = 0.034906585...
Current Step: 0 / 180
Plain English:

This is the angle that makes a spiral close on itself. Take 180 steps of this tiny angle (about 2° each), and you've made one complete turn. It's the twist that connects counting angles (degrees) to measuring circles (radians).
In Degrees
per step
In Radians
π/90
= 0.0349...

Derived Constants

κ_shadow (1/κ)
28.65
Hidden witness frequency
σ (Overlap)
5/16
= 0.3125
cos(BC)
2/3
Tetrahelix angle
P (Projection)
√3/2π
= 0.2757

The Four Transforms

PROVEN
T₁ + T₂ + T₃ + T₄ = (0, 0)
T₁ (NW) - Facing
Operation: (x, y)
Direct view - what you see straight on
T₂ (NE) - Mirror
Operation: (-x, y)
Horizontal flip - like looking in a mirror
T₃ (SW) - Recursive Mirror
Operation: (x, -y)
Vertical flip - like a reflection in water
T₄ (SE) - Recursive Upside Down
Operation: (-x, -y)
180° rotation - completely inverted
The Proof:

T₁ + T₂ + T₃ + T₄ = (x, y) + (-x, y) + (x, -y) + (-x, -y)
= (x - x + x - x, y + y - y - y)
= (0, 0) ✓

The four perspectives always balance at the crossroads.

The Tetrahelix

PROVEN
Helix Level: 0
The Boerdijk-Coxeter Helix

Tetrahedra stacked in a helix, each rotated by the angle where cos(BC) = 2/3.
This gives BC = 48.19° - the fundamental tetrahelix twist angle.

This is not invented - it's geometric necessity. Stack tetrahedra as tightly as possible, and this is the only way they fit.
Tetrahelix Angle
48.19°
arccos(2/3)
Steps per Turn
180
κ steps
Energy Decay
59/60
per step
After Full Turn
4.8%
(59/60)^180

The Balance Law

PROVEN
τ₁ + τ₂ + τ₃ + τ₄ = 0
The Fundamental Constraint

Three torsions are APPARENT - you can measure them.
The fourth is SILENT - it's whatever is needed to make the sum zero.

τ₄ = -(τ₁ + τ₂ + τ₃)

This is not optional. Any valid Epoch derivation MUST satisfy this law.
τ₁ = +0.00 (facing) τ₂ = +0.00 (mirror) τ₃ = +0.00 (recursive) τ₄ = -0.00 (silent) ───────────────────── SUM = 0.00 ✓
τ₁ (Facing): 0
τ₂ (Mirror): 0
τ₃ (Recursive): 0

M4 Array Implementation

VALIDATED
Physical Implementation

5 Apple Silicon machines arranged in triaxial dipyramid configuration:
• 1 Mac Studio M4 Ultra at CENTER (crossroads, s=0)
• 4 Mac Mini M4s at NW, NE, SW, SE (the four transforms)
• N, S, E, W positions ABSENT (the shadows define the space)

The hardware IS the geometry. The shape IS the calculation.
Center (Crossroads)
M4 Ultra
Mac Studio
Diagonals (4)
M4
Mac Mini × 4
Cardinals (4)
Absent (shadows)
Total Cost
~$12.6K
Already owned

Vessel Geometry

PARTIAL DERIVATION

What IS Derived

  • 4 diagonal nodes (Balance Law)
  • Central crossroads (s=0)
  • Absent cardinal positions
  • 48.19° coil winding angle
  • 180-fold periodicity

What is ASSUMED

  • Ellipsoid envelope (not derived)
  • Specific dimensions
  • Material composition
  • Whether it needs to be hollow
Honest Assessment

The underlying geometry is a triaxial dipyramid. The ellipsoid shape is ONE possible smooth envelope, but geometric necessity only proves the node structure - not the surface. More work needed to derive exact form.

Base-60 Mathematics

PROVEN
60 = 2² × 3 × 5
Why Base-60?

60 contains ALL THREE structural primes:
• 2² = the coin (raised to dipyramid)
• 3 = the triad (Energy, Now, Facing)
• 5 = the helix (σ = 5/16)

The Sumerians knew this 4,000 years ago. It's why we have 60 seconds, 60 minutes, 360 degrees.
Divisible By
12
factors
Circle
360°
= 6 × 60
Decay Ratio
59/60
per step
κ in Base-60
π/90
= 2π/(3×60)
Base-60 Factorization: ───────────────────────────── 60 = 2² × 3 × 5 360 = 2³ × 3² × 5 180 = 2² × 3² × 5 ← κ steps Energy decay after one turn: (59/60)^180 = 0.0478... ≈ 4.8% The "tax" of moving through scalar space.