The Universe as a Theorem
A self-guided, interactive introduction to the UGP/GTE theory — from the arithmetic substrate up through particles, forces, quantum mechanics, and cosmology. Every concept illustrated. Every claim verified.
Start at the Foundations →The three nodes of the theory — one substrate, two arms, all connected.
Learning Paths
Eight paths, thirty lessons. Start at Path 1 and follow the sequence, or jump to any path once you have the foundations.
Foundations: The Triangle
The arithmetic substrate, the GTE polynomial, the UWCA, and how all three are the same object viewed differently.
Selection: Why This Polynomial?
How minimum description length uniquely forces GF(7), the 19-bit rule, and the four levels of the theory.
Particles: Kinks, Fields, Masses
The Φ_MDL field, three-tape CMCA, particles as topological kinks, quantum numbers, and mass predictions.
Forces: Gauge Structure from Winding
All four SM interactions from Z₇ winding conservation, the Weinberg angle, strong CP, and the master quadratic.
Spacetime and Gravity
General relativity and quantum gravity emerging from the three-tape CMCA tape geometry.
Quantum Mechanics
Transputation (quantum measurement from MDL) and the Born rule derived as a theorem with zero sorry in Lean 4.
Cosmology
Zero-parameter predictions: Ω_Λ, n_s, baryon asymmetry, hierarchy problem, defect cosmology from topological kinks.
Context and Predictions
Falsifiability, comparison with 8 competing frameworks, and concrete new-physics predictions.
How to Use This Site
Start at Path 1
Follow lessons in sequence. Each lesson answers the question that the previous one leaves open.
Use ← → keys
Arrow keys navigate between lessons. Step-through panels have Previous / Next buttons.
Verify the claims
Every key result links to its Lean 4 machine proof on GitHub and its source paper on Zenodo.
Reading the theory for the first time? Start at Path 1: Foundations. It takes you from "why do the Standard Model parameters have the values they have?" all the way to a complete picture of the arithmetic substrate.
Want a specific topic? Jump to any path — each path landing page lists its lessons and prerequisites so you know exactly what you need first.
Claim-Strength Taxonomy
Every claim in these lessons carries one of the following labels. The labels appear as badges throughout the site. Here is what each means.
This taxonomy follows the certification scheme used in the formal papers. CatAL is the gold standard — the Lean 4 proof compiles on any machine with no gap.
About This Theory
The UGP/GTE framework derives the Standard Model — all particle masses, quantum numbers, and coupling constants — from a single 19-bit arithmetic description. No free parameters are fitted. Every result is either machine-certified in Lean 4 with zero sorry, or carries an explicit confidence label.
The central object is a polynomial p(L,C,R) = C + R − CR − LCR
over GF(7). It is the unique minimum-description-length rule for a 7-state,
radius-1 cellular automaton consistent with the algebraic invariants of the theory.
Author: Nova Spivack
Papers:
novaspivack.com/research
Lean proofs:
github.com/novaspivack/ugp-lean
Preprints:
Zenodo · ugp-physics