A Discrete Universe Φ
The Standard Model of physics falls out of a single hyperbolic
{3,4,3,4} tessellation in four dimensions, matched across hundreds of
reproducible code experiments here. Physical reality appears to be
basically the thin skin at its edge. Imagine it like a baseball. The
inside is a dense weave of tightly wound fibers, all the way through.
That's 3D, but this is in 4D, and at the base that weave is a perfectly
regular grid, built from a single 24-cell reflecting endlessly like a
mirror, and it is where all experience lives, which is basically all of
reality. The thin skin on the cusp is physical reality, worked from
within like a puppet. Consciousness is the grid. The physical universe
is its projection.
Vibe Theory treats reality as
one thing, a vast growing crystal of experience. The image above is its
simplest face, the hyperbolic {7,3} tessellation, and it is meant
literally. Each tile is a vibe, the smallest unit of experience.
Each vibe carries a ternary tone, its felt charge, shown as a color:
red is pain, green is peace, blue is pleasure. Tiles that touch are
vibes that note (experience) one another, so the edges of the
crystal are the relations of the mesh. There is nothing else in the
model but this.
To hold it at a glance: a single tile is one quantum of experience, a patch of tiles is a thing or a mind, and the whole crystal is the universe, growing forever at its ever-receding edge, which is the present. The geometry is hyperbolic because that is the shape roomy enough to grow without end and with no preferred direction, so it respects relativity. Everything we call physical, space and time and matter and force and gravity, and everything we call inner, sensation and emotion and thought, is a large-scale pattern in this one colored, growing mesh of feeling.
The flat {7,3} picture is the easy-to-draw two-dimensional face. The
committed substrate is another member in the same family of regular
hyperbolic honeycombs, the four-dimensional {3,4,3,4}, whose cells are
24-cells and whose 24 directions form the D4 root system that carries
spin. Its flat three-dimensional cusp is the physical space we live in,
and time is its growth. The three-dimensional {5,3,4} and the
two-dimensional {7,3} are the lower faces used to build intuition,
since {3,4,3,4} cannot be drawn directly. The dimension is not a free
choice. Regular hyperbolic honeycombs run out by the fifth dimension,
and {3,4,3,4} is the one that is at once crystallographic,
spinor-carrying, and three-dimensional where physics lives.
The base of the model is settled, the discrete substrate and its single local rule. From it the architecture of physics is derived: the particles and their charges, the gauge group, the Higgs, the shape of the mass hierarchy, and the emergent laws of relativity, gravity, the quantum, holography, and cosmology. The absolute masses and couplings are free, exactly the parameters the Standard Model leaves free, each now identified with a specific geometric origin. The larger aim is to derive space, matter, gravity, the quantum, cosmology, and mind from the one rule, and to be clear at every step about what is solid, what is free, and what is still open. The companion papers are snapshots of that work.
The base model of reality is settled here pretty much, next is to explore the elaborations/implications.
Here are the key notes:
- Short audio overview of things
- A Discrete Universe: The Standard Model from the octonions on a hyperbolic 24-cell mesh
- Vibe Theory: A Discrete Hyperbolic Substrate for the Emerging Conscious Universe
@cluesurf/vibe is a finite, discrete, reproducible simulator that
turns the theory into runnable measurements. It is the bench where the
model is built, stress-tested, and checked against known physics. It
generates the discrete substrate (the mesh), runs the one local rule
over it in discrete beats, and measures what emerges, so each question
becomes a concrete experiment that either works or does not.
Everything is finite and deterministic, so every result is exactly
reproducible. The base never relies on randomness. Real numbers appear
only as measured outputs (coordinates, eigenvalues, dimensions), never
as the base, in keeping with the discreteness principle. Much of this
code was written with AI assistance, which changes nothing about
trusting it. It is deterministic and reproducible, so you can run it and
verify every result yourself. Each question is one experiment in
test/experiment/<category>/, a single experiment that returns a
structured verdict (status, metrics, control, claim) graded by an honest
depth level, from L0 circular through L1 known math and L2 known
physics to L3 emergent and novel. The standard the experiments are
held to is in
note/experimental-methodology.md,
and the code and test layout is in
note/architecture.md.
test/catalog.csv is the full index of every
experiment in the suite, one row per registered experiment. It is
generated from the registry itself (npx tsx test/catalog.ts, or
pnpm call test/catalog.ts), so the code and the catalog are always the
same source of truth, and it is sorted strongest-first, by depth, then
id. It is the fastest way to see, at a glance, everything the model has
been asked and how strongly each result holds. Regenerate it any time
the registry changes.
Every experiment self-grades by what it actually establishes, not by whether it prints PASSED.
| level | meaning |
|---|---|
| L3 | emergent and novel. One base rule produces the result as a measured consequence, with a control, ideally a quantitative prediction that could be wrong. The genuine target. |
| L2 | known physics. Reproduces a known construction on the substrate (a Dirac quantum walk, lattice gauge theory, a ballistic light cone). |
| L1 | known math. Correctly confirms an established mathematical fact (the 24-cell is the binary tetrahedral group, a 2pi rotation gives minus one). |
| L0 | circular. The answer is put in by hand, so it proves nothing on its own. Kept only as a consistency note, never as evidence. |
So L3 is the real prize, L1 and L2 are groundwork, and L0 is a marker of
what is assumed rather than derived. Most results in a young program are
L1 and L2, and that is fine as long as they are labeled as such. The
full rubric and the rules the runner enforces (an L3 claim must carry a
control, for instance) are in
note/experimental-methodology.md.
As of the latest run the catalog holds 574 experiments across 17
categories: 72 at L3 (emergent and novel), 362 at L2 (known
physics reproduced), 126 at L1 (known math confirmed), and 14 at L0
(circular), with 376 of them backing a specific claim in the papers. The
largest categories are selves, gauge, foundations, cosmology, spin,
gravity, and relativity.
pnpm install
pnpm test # the full experiment registry plus the conformance battery
Every experiment lives in test/experiment/<category>/<name>.ts as one
experiment, and the suite runner (test/run.ts) imports them all and
runs the registry. The shared library they import is in code/, and the
named batteries (conformance, paper) are in test/suite/. The build
fails only on a code crash or a conformance failure, never on an honest
scientific negative.
- substrate: regular
{p,q,...}hyperbolic honeycombs through the Coxeter engine, including the{3,4,3,4}cell graph withO(log n)addressing, plus hyperbolic random graphs, regular lattices, Minkowski and curved sprinklings, and classical sequential growth. - tone: the ternary alphabet and the directional fill carried on each cell.
- rule: synchronous, asynchronous, reversible, rewriting, and gauge updates.
- operator: graph Laplacian, Kahler-Dirac and overlap fermions, the gauge-covariant Dirac, the cellular-automaton Hamiltonian, and the gauge index.
- algebra: quaternions and the binary tetrahedral 24-cell, the
D4andF4root systems, spinor and vector rotation, Clifford and exterior calculus, and the linear-algebra kernels (Lanczos lowest eigenvalues, the kernel-polynomial method, Bethe resolvents). - measure: dimension, distance, curvature, manifold-likeness, Lorentz isotropy, streaming BFS shells, navigation, CHSH, locality, integration, Wilson loops, and Aharonov-Bohm phase.
- dynamics: the Benincasa-Dowker action, uniform-measure and Wang-Landau sampling, parallel tempering, coarse graining, and the Wilson heat bath.
- control: the negative controls that make a positive result mean something (the substrate or rule where the answer must be no).
- draw, render, and viz: renderers and figures for the bulk, the cusp, gliders, gravity, and the nesting tower.
- test/experiment: one
experimentper question, grouped by category (foundations, geometry, relativity, spin, gauge, gravity, cosmology, holography, quantum, renormalization, selves, computation, addressing, substrate-survey, data-structure), run by the suite runner intest/.
All docs live in note/. The entry points:
- The library guide is how to USE the
code/library. It opens with a features-at-a-glance page (what the library solves for in one scannable set of tables) and an overview of how it all fits together. Under that are per-domain API guides (substrate, tone-and-rule, operator, measure, dynamics, algebra, model, tool, computing-and-data-structures, draw-and-render) and engine deep dives explaining how each engine works inside (the Coxeter tessellation engine, the reversible rule, the Kahler-Dirac fermion, the spinor coin, the spectral methods, the causal-set sampler, the unitary evolution, the lattice gauge engine, the coarse-graining and selves engine, and the associative memory engine). - Architecture is where code and tests live, and how to add an experiment.
- Experimental methodology is the standard every experiment is held to, the depth rubric, the control requirement, determinism, and the honest negatives.
- Cross-tessellation experiments is how to write an experiment that runs against every regular hyperbolic tessellation at once.
MIT. Open for science: use, modify, and build on it freely, with attribution. See LICENSE. The written results and figures are shared under CC-BY-4.0 (attribution).
Made by ClueSurf, meditating on the universe ¤. Follow the work on YouTube, X, Instagram, Substack, Facebook, and LinkedIn, and browse more of our open-source work here on GitHub.