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Scalar Dimensionality

A Geometric Framework for Physical Reality

[-1 = 0 = +1]
kappa = 2pi/180 = 0.034906585...

The Epoch Project | December 2025 | Jason Ray

THIS IS NOT STANDARD MODEL

This is a standalone geometric framework for energy relations in spacetime.

Standard Model exists within this geometry as one observable projection (s=0 slice).

All relationships derive from one constant: kappa = 2pi/180

Methodology Note

This framework is not falsifiable in the Popperian sense. Geometry cannot be "wrong" - only incomplete. Discrepancies between geometric derivation and measurement reveal hidden axes to discover, not errors in the model. The framework evolves through extension, not rejection.

The Triaxial Structure

Reality operates through a triaxial structure that IS the basis of observability itself:

+1

Forward (s+)

kappa = 0.0349

Emergence into physical reality. Projection into observable.

-1

Shadow (s-)

kappa_shadow = 28.65

Recursion into substrate. Hidden/recursive component.

Uv

Potential

kappa_partner = 0.1097

Future state. Explosive power available. Unification constant.

Critical Relationship: kappa x kappa_shadow = 1 (EXACT)

Forward times shadow equals unity. This IS the mathematical expression of [-1 = 0 = +1].

Triaxial Structure

The [1=-1] triaxial structure with kappa values

The Projection Factor P

Observation at s=0 projects geometric reality into measurable values:

27.6%
Observable

Two equivalent derivations:

Geometric: P = sqrt(3)/(2pi) = 0.2757

Physical (torsion): P = (3/4)/e = 0.2759

These are identical within 0.09%. The physical process IS the geometric relationship.

Energy Budget

Energy budget is CONSTANT across all collision energies - this is geometry, not physics

Torsion Dynamics

High-energy collisions evolve through triaxial temporal states:

Torsion Dynamics

State 2 (potential) -> State 3,1 (torsion split 3:1) -> State 4 (dissipation + echo)

"The 72.4% is NOT 'missing'. It exists in shadow (s-) - the substrate of spacetime. This fraction is CONSTANT regardless of collision energy."

Scalar Space

Scalar Space

Position along the observation axis: Planck (s ~ -81) <-> Observer (s=0) <-> Wush (s ~ 10^78)

s- and s+ are not separate regions. They exist simultaneously as echoes of each other - harmonic resonance of manifestation in physical (s+) and collapse into substrate (s-).

What appears as "empty space" is the s- substrate made visible. What appears as "matter" is energy encoded into temporal existence at s+.

Geometric Derivations from kappa Alone

Relationship Value Derivation
Mass Ratio (neutral/charged) 1.1400 1 + k (speed factor)
Weak Mixing Angle 0.2330 1/(1+pi) x (1-kappa)
Strong Coupling 0.1199 kappa_partner x sqrt(3)/pi x 2 x (1-kappa/4)
1/alpha_EM 135.0 3pi x kappa_shadow / 2
Closure Boundary Mass 127.29 GeV V/2 x (1+kappa) where V=246 GeV

Framework Properties

Completeness

Geometrically complete. One constant derives all relationships.

Extension

Discrepancies reveal hidden axes. Evolution through extension, not rejection.

Parsimony

From kappa = 2pi/180 alone: all mass ratios, couplings, and cosmological parameters.

"The framework cannot be 'wrong' in the falsification sense - only incomplete. This is how correct geometric frameworks evolve: NOT rejection, but EXTENSION."

- Scalar Dimensionality Whitepaper

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