The tetrahedron is the only Platonic solid with no inversion centre and no parallel faces. Its mirror image cannot be superimposed through rotation. When it precesses in a continuous field, four fundamental physical properties emerge — without additional postulates.
Matter — left-handed precession
0°of 720° topological cycle
Spin ½
720° Periodicity
Objects entangled with a continuous field require two full rotations to return to their original topological state. The Pauli Exclusion Principle follows as geometric impossibility — co-location demands conflicting phase windings.
Local Time
Precession Rate
The local rate of time is the local precession rate of tetrahedral field configurations. Dense filaments: fast precession, fast clocks. Cosmic voids: slow precession, slow clocks. The ~35% Timescape differential, explained.
Charge ±
Projection Remainder
The 8-dimensional octonionic driving field projects onto a 3D associative quaternionic slice. What cannot be expressed in 3D appears as a scalar residue — electric charge. Two signs = two projection handednesses. Conserved globally.
Matter / Antimatter
Intrinsic Chirality
The tetrahedron is the only Platonic solid whose mirror image requires reflection — not rotation — to superimpose. Left-handed precession = matter. Right-handed precession = antimatter. Toggle above to see the distinction.
§ 2 — 150 Years of Empirical Confirmation
The Geometric Periodic Table
The Janet Left-Step table arranges elements by orbital subshell completion — revealing what Mendeleev's arrangement obscures. Within Field Topology Theory, the four orbital blocks correspond to four levels of tetrahedral precession complexity. Click any element.
f-block — polyhedral · 14/period = G₂ dimension
d-block — rosette · 10/period
p-block — triaxial · 6/period
s-block — spherical · 2/period
Highlighted: C · Fe · He · Gd
§ 3 — Dimensional Projection
From 8 Dimensions to Charge
The octonionic driving field contains geometric relationships across 8 dimensions. Our 3D space corresponds to the largest associative sub-algebra — the quaternionic slice. The projection remainder is electric charge. Gravity is categorically different: it is the projecting geometry, not a product of projection.
The four forces are not separate phenomena. They are four distinct aspects of the same tetrahedral precession geometry.
Gravity
The geometry itself
The metric field — not a projection. Gravity cannot be quantised by gauge boson machinery because it is the space within which projection occurs.
Electromagnetism
Projection remainder dynamics
Charge (geometric frustration) seeking equilibrium. Maxwell's equations are the projection shadow geometry in 3D. Fleming's rules encode precession handedness.
Strong Force
Internal topological stability
The 3-simplex maintaining its own coherence against perturbation. Confinement is topological lock. G₂ ≅ SU(3): the strong force gauge symmetry emerges from octonionic automorphisms.
Weak Force
Handedness inversion
Precession chirality flipping at the projection boundary. Matter ↔ antimatter transitions. W/Z bosons are the flip mediators — geometry changing handedness.
§ 4 — Falsifiability
Five Testable Predictions
A theory that cannot be falsified is not physics. These predictions follow directly from the framework and can be tested with existing or near-future instrumentation.
P1
Precession rate gradient in cosmic voidsAtomic transition rates and radioactive decay rates should differ ~35% between void centres and filament environments, beyond standard gravitational time dilation. Target: precision atomic clocks in void-surveyed environments.
P2
Lorentz invariance violation at void-filament boundariesUltra-high-energy cosmic rays traversing void-filament boundaries should show systematic energy-dependent velocity anomalies. Target: LHAASO and Pierre Auger Observatory cross-referenced with cosmic web maps.
P3
Electron g-factor corrections near the Schwinger limitField-dependent corrections to the anomalous magnetic moment should emerge where interaction timescale approaches tetrahedral precession period. Target: bound-electron g-factor in highly charged medium-heavy ions.
P4
Handedness-dependent scattering asymmetriesSpin-resolved interferometry should detect asymmetries in scattering cross-sections consistent with geometric handedness distinction. Magnitude depends on field strength relative to Schwinger limit.
P5
G₂ symmetry in f-block magnetic propertiesIf f-block elements are G₂ representations of the octonionic driving field, their magnetic properties should map onto the G₂ root system. Gadolinium's anomalous ferromagnetism is the specific initial test case.