Discrete space
Physical space is a tessellation of rhombic-dodecahedral cells (14 vertices, 12 faces, 24 edges). Energy comes in finite face units; there is no infinitely divisible void.
Type IV unification · discrete physics
Space is not empty.
It is a crystal.
The Lama Architecture rebuilds physics on a single discrete substrate — a face-centred-cubic lattice of rhombic-dodecahedral cells — where matter is trapped light, mass is closure energy, and gravity is elastic strain with a curvature-squared ornament.
- |τG|
- 1/12 face tension
- Ef
- 11/12 – 13/12 content bound
- α−1
- 137 routing capacity
- ξ100/ξ111
- 3/4 exact FCC ratio
The idea
One substrate, everything emergent
No void, no continuum, no separate forces at the bottom. A single FCC crystal and a two-phase clock. Everything else — light, matter, gravity, quantum rules — is what the crystal does.
Tick–Tock time
Time is a bipartite rhythm, not a dimension. Tick manifests geometry; Tock reconfigures relations. One full cycle is one Planck time; inertia lives in the memory carried through Tock.
Matter is trapped light
Light is an unlocked massless pulse. Matter is light wound into a self-avoiding 720° knot inside a cell. Mass is the closure energy of that trap.
Content vs stiffness
Face content energy is bounded (11/12–13/12) and sources matter; vacuum stiffness sets the Planck scale and sources gravity. Two energies, two phenomena, one crystal.
The architecture
From 24 dimensions to one crystal
- E8 relational seedEven, unimodular 24-D architecture selects E8; an order-3 symmetry fixes a transverse plane.
- FCC latticeEach symmetry orbit completes to A3 — the face-centred-cubic lattice, nine equivalent completions, one class.
- RHD cellsThe FCC Voronoi cell: rhombic dodecahedron. 12 faces carry energy, tension, gauge flux.
- HFF actionHybrid face-field dynamics: dilation, shear, rotation, phase — with Grout-Tax confinement and the Leibniz ornament.
- Emergent regimesPhotons, Dirac fermions, ornamented gravity, capacitor cosmology — derived in the long-wavelength limit.
12faces per cell
24edges per cell
14vertices per cell
2clock phases
Results
Proven, conditional, open — labelled honestly
Every claim below carries its epistemic status. That discipline is part of the result.
- LIV triplet. Photon dispersion anisotropy ξ = −1/24, −5/96, −1/18 along [100]/[110]/[111]; ratio 3/4 exact; sky bound Δξ ≤ 1/72.
- Charge quantisation. Q ∈ {0, ±1/3, ±2/3, ±1} as a theorem of the RHD switch algebra; eight colour modes.
- Regge consistency. Affine flatness to ~10⁻¹³; trace → 8/3, TT → −4, vector → 0 in Fourier probes.
- Decay-rate check. (3477/207)⁵ agrees with the measured τ/μ leptonic ratio to 0.9%.
- Einstein–Maxwell vertex. Face algebra reproduces εijTEMij exactly with unique coefficients.
- β/α = 3/4. Exact as FCC kinematics; as a curvature coupling it awaits the trace/traceless matching (Ctl = Ctr).
- α−1 = 137. Routing capacity 144 − 7 constructed; physical identification conjectural.
- Dynamic gravity (RSDG). Candidate completion: exact static reduction, massless isotropic wave, cg = cγ in the scalar channel. TT variable and constraint algebra outstanding.
- Tensor constraints. Ten componentwise modes vs two required; no native constraint algebra found.
- Infrared TT stiffness. Negative sign vs positive candidate operator — sharp yes/no pending.
- Matter equilibria. Self-consistent defect states, 511 keV ratio fix, composite stability.
- Continuum limit. Uniform discrete Sobolev inequality; all-N mesh theorem.
Predictions
Ways to kill it
A theory that can't be falsified is a story. Each of these is a standing bet against observation.
Sky-pattern LIV
No two photon sources may differ in inferred dispersion by more than Δξ = 1/72, following a fixed octahedral sky pattern. Multi-source timing either confirms or ends it.
Massless graviton
Graviton mass exactly zero; gravitational and light speeds identical by construction. Any measured lag or mass falsifies.
Lepton hierarchy
Bare masses 1 : 207 : 3477 from graph combinatorics, with the decay-rate cross-check at 0.9%. Dressing corrections must preserve it.
Capacitor dark energy
Vacuum density scales as inverse cell-count squared; redshift without expansion; Hubble tension as charging asymmetry — distinct high-z drift from ΛCDM.
Research programme
What remains is execution
- Tensor constraints. Find the native gauge reduction, or show the extras decouple — the single gate to dynamical gravity.
- Matter equilibria. Self-consistent defect states; 511 keV scale; stable composites.
- Trace/traceless matching. Derive Ctl = Ctr dynamically; fix α, β.
- Continuum limit. Discrete Sobolev inequality; Γ-convergence; Hodge construction.
Library
Read the record
Beyond Continuum
The main Type-IV manuscript: ornamented general relativity, full derivation record. Manuscript
Get the PDFThe Living Crystal
The popular telling — thirty-three chapters, no equations required. Book
Get the PDFDistilled Edition
The compact technical core: axioms to cosmology in minimal pages. Technical
Get the PDFDownload links are wired at deployment — PDFs will be hosted alongside this page.