A Discrete Universe Φ

This codebase 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.

The base model of reality is settled here pretty much, next is to explore the elaborations/implications.

Here are the key notes:

• Short high-level 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

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 one primitive is the vibe, a unit of experience. It carries a ternary tone (its felt charge: pain, peace, pleasure) and it notes (experiences) its neighbors. Everything else is arrangements of vibes and one rule for how their tones update. That the base genuinely is experience, that the tone is felt and not merely a label on a number, is the model's one axiom. Like every axiom, it is unfalsifiable. No lab reading distinguishes a universe whose base is felt from an identical universe whose base is only structure. We hold it as a frame, not a result. The experiments here never confirm it. They confirm structure.

Under that frame sits a concrete discrete dynamical system, and it is highly falsifiable: a fixed geometry (the {3,4,3,4} honeycomb, a 24-direction coin), a ternary state, and one reversible charge-conserving local rule. The physics is derived from that fixed base as measured consequences, and the whole method is built to try to make them come out wrong. Every deep claim carries a control, a case where the answer should be no, and a test that cannot fail is graded L0 and counts for nothing. Negatives are kept, not hidden. The spinor that appears on the {3,4,3,4} coin and provably fails to appear on the {5,3,4} control, the area-law exponent that had to land near 2 and not near 3, the Lorentz isotropy that could have stayed anisotropic: each could have killed its claim and did not.

So "vibe theory is unfalsifiable" is half right and half wrong, and the two halves must be kept apart. The axiom "experience is the base" is unfalsifiable, which is what an axiom is. The physics built under it is falsifiable, is being falsification-tested with controls and published failures, and is the opposite of a theory that fits anything. The reading is that the experiments do not prove the base is felt. They show that a single discrete rule, framed as felt, recovers a large amount of physics as results that could have come out otherwise.

The structures the one base rule holds fixed, each measured with a control that could have failed. An invariant is anything that stays put: a conserved quantity, a structure the rule is forced to keep, or a number that survives when the substrate is varied. These are also the structures that keep recurring across other physics theories built from different starting points, worked out in note/triangulating-invariants.md with the per-theory maps in note/link/.

Each is a measured consequence of the base rule, not an input. The first four are the invariants the rest are built on.

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 a plain 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, and the code and test layout is in note/architecture.

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.

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.

As of the latest run the catalog holds 810 experiments across 18 categories, graded by the depth rubric:

The largest categories are selves, quantum, foundations, gauge, gravity, and cosmology. The standing depth audit regrades overclaimed depths down, and new derivations measured straight off the substrate's own dynamics and walk-operator spectrum (zitterbewegung, Klein tunneling, Bloch oscillations, Aubry-Andre localization, the Jackiw-Rebbi bound state, the topological winding number, 2D cyclotron confinement, and the bulk-boundary correspondence) raise the L3 count.

test/catalog.csv is the flat, machine-generated index, one sorted row per experiment. For a human-navigable walk through the whole suite, read the experiment map. There are hundreds of experiments and no one is going to read them all, so the map is the way in.

It groups every experiment into its arena (selves, gauge, foundations, quantum, gravity, and the rest), and each arena doc distills every experiment by sub-theme in one line. The top of the map carries the full coverage matrix (which arenas are deep, which are thin, where there is no control-gated result yet), a concepts cross-index for finding an idea across arenas, curated reading paths for diving in cold, and a guide for adding your own experiment. Start there to see the full scope and reach any single result without piecing it together from the files.

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 a scientific negative.

• substrate: regular {p,q,...} hyperbolic honeycombs through the Coxeter engine, including the {3,4,3,4} cell graph with O(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 D4 and F4 root 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 experiment per 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 in test/.

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).
• The math catalog lists every piece of math the library runs: what each module implements, what it depends on, and which experiments use it.
• 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 negatives.
• Open problems are the negatives written up in full. The hardest is spacelike Bell correlations: what Bell's theorem actually proves, why a deterministic theory can still match quantum mechanics (it drops measurement independence, not determinism), the price vibe pays for that, and the measured shared-past collapse that makes it hard.
• Cross-tessellation experiments is how to write an experiment that runs against every regular hyperbolic tessellation at once.
• Reference data and verification is the measuring stick: the real physics numbers the experiments are checked against, and the live cross-check of each.

The experiments are only as good as the numbers they are compared to, so those numbers live in one cited place: note/data/reference/.

• What we gathered. Every external value an experiment must match or use as a comparison: the fundamental constants, the full Standard Model particle table, the roughly 26 free Standard Model parameters, the CKM and PMNS mixing matrices, the cosmological parameters, and the geometric and group-theory targets the model derives (the ternary 3, the 24 of the cell, the octonion ceiling 8, F4 order 1152, sin^2(theta_W) = 3/8, the Tsirelson bound, the Born exponent, and so on).
• What it contains. Structured CSV plus a machine-readable reference.json, with a prose readme and a bibliography. Every single row carries a source tag and a verified date. The empirical values were fetched from and reconciled against their primary sources on 2026-06-24 (CODATA 2022, PDG 2024, NuFIT 6.0, Planck 2018).
• How we used it. The verification folder runs the comparison-bearing experiments live and diffs each measured number against the reference value, recording a status per experiment in cross-check.csv. This is the double-and-triple-check rule applied to the data: it confirmed the genuine matches (the quantum bounds, the 3/8 angle, F4, the warp factor, the area law) and caught real problems (two mismapped experiments, one circular result whose number was hardcoded, and one result that is actually stronger than the table recorded).

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.