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Programme Overview

The UGP Physics programme derives the Standard Model of particle physics — its gauge structure, particle spectrum, and all known parameters — from a single 19-bit polynomial over GF(7), selected by Minimum Description Length applied to a self-referential system. Starting from Perfect Self-Containment (PSC) as the foundational axiom, the framework derives over 170 quantitative observables across 15 prediction sectors with zero free parameters. Every major result is cross-sector: the same arithmetic that selects the gauge group determines particle masses, which determine nuclear structure, which constrains the cosmological constant — with no inter-sector parameter tuning. 56 papers (P00–P55). Machine-certified in Lean 4, more than 400 modules, all results independently verifiable.

Additional Flagship Results

Papers

All 56 papers are published on Zenodo with permanent DOIs. The programme survey guide (P00) provides one-paragraph summaries of all 49 companion papers with a thematic grouping and reading paths for different backgrounds — it is the recommended entry point for new readers. Papers marked are book-length monographs.

• P00 — Survey and Reader’s Guide to UGP Physics
• P01 — A Deterministic Number-Theoretic Framework for the Standard Model Parameter Spectrum
• P02 — The GTE Particle Spectrum at n=10
• P03 — GTE Coordinates as Nuclear Descriptors
• P04 — The Dynamics and Universality of the Universal Generative Principle: Attractors and Emergent Thermodynamics
• P05 — The Uniqueness of the Universal Generative Principle
• P06 — The Algebraic and Geometric Foundations of the Universal Generative Principle: A Derivation of the Standard Model Gauge Group
• P07 — UGP/GTE as an Organizing Principle for Nine Meta-Laws of Physics
• P08 — From UGP to GTE: Prime-Locked Universes, Minimality, and the Emergence of Our World (Foundational Monograph)
• P09 — The Architecture of a Computable Universe: Structural Principles of the Universal Generative Principle
• P10 — Reflexive Reality and Self-Defining Physical Law
• P11 — Ontological Dissonance Minimization as the Generative Meta-Law: Discovery and Validation in PR-0
• P12 — Unified Rigidity Theorem for PSC/UGP Universes
• P13 — Mathematical Foundations of Reflexive Reality: A Unified Formalism of Self-Defining Systems, Transputation, and the Geometry of Coherence (Monograph)
• P14 — Formal and Computational Concordance on PSC-Selected Standard Model Structure: Axiomatic Closure Theorems and Finite Universe Enumeration
• P15 — The Information Profit Principle
• P16 — Black Hole Unitarity via Reflexive Unitarity
• P17 — The Topology of the Standard Model from First Principles: A Derivation of the Canonical Braid Atlas
• P18 — The Koide Relation as a Cyclotomic-12 Closed Form
• P19 — Cyclotomic-12 Structure in the Charged-Fermion Mass Spectrum
• P20 — Mathematical Foundations of Reflexive Reality: A Survey
• P21 — Neutrino Mass-Squared Ratio from the Braid Atlas
• P22 — UGP Interaction Skeleton Theorem
• P23 — Substrate Depth and Self-Generated Mass: The c-Component of the UGP Canonical Triple Predicts Reflexive Closure across the Standard Model Spectrum
• P24 — The Arithmetic Uniqueness of the Standard Model: Asymptotic Sparsity, Galois Structure, and the Positive-Root Theorem
• P25 — Structural Admissibility and Biological Viability Uniquely Select the Standard Genetic Code
• P26 — A General Theory of Selection
• P27 — The Self-Referential Renormalization Group: A Universal Framework for Physical Constants
• P28 — Computational Universality and the Standard Model: Rule 110, Z5 Rings, and Mod-7 Structure in the Universal Generative Principle
• P29 — The Mirror Branch Braid Atlas: A Parameter-Free Dark Sector Classification from the Universal Generative Principle
• P30 — Machine-Certified Formalization of Cook’s Rule 110 Universality Theorem in Lean 4
• P31 — Arithmetic Derivation of the Electroweak Mixing Angle from Rule 110 Orbit Arithmetic
• P32 — The CKM Wolfenstein Parameters from Generative Triple Evolution Orbit Arithmetic
• P33 — Deeper Consequences of Arithmetic Universality in the Standard Model
• P34 — The GTE-Möbius Architecture: Arithmetic Unification of Computation and Transputation in the Universal Generative Principle
• P35 — GTE Unification: A Bidirectional Correspondence between Rule 110 Orbit Arithmetic and the Standard Model Electroweak Sector
• P36 — Emergent Gravity from Rule 110 Cellular Automaton
• P37 — Quantum Mechanics from Rule 110: Hilbert Space, Hamiltonian, and Born Rule
• P38 — Emergent Gravity from the Phi_MDL Field: Einstein Equations, Kink Sources, and Quantum Gravity Scale
• P39 — QCD Structure from the Generative Triple Evolution Substrate: Asymptotic Freedom, Confinement, and Hadron Spectroscopy from F₂₁ ⊂ SU(3)
• P40 — Algebraic Characterization of Rule 110 over GF(7) and Finite NAND Functional Completeness
• P41 — The Three-Layer Chiral Minkowski Cellular Automaton: A Unified Discrete Spacetime Model from First Principles
• P42 — The Phi_MDL Field: Quantum Structure, Born Rule, and Continuum Completion of the Chiral Minkowski CA
• P43 — The Complete Phi_MDL Framework: Algebraic Necessity, Quantum Mechanics, Emergent Gravity, and Uniqueness
• P44 — Quantum Gravity in the GTE/Phi_MDL Framework: Functional Completeness
• P45 — The Three-Tape Chiral Minkowski Cellular Automaton: Spacetime, Particles, and Gravity from a Shared Clock Protocol
• P46 — The GTE Polynomial as Unified Field Theory: One 19-Bit Description for Spatial Dynamics, Gauge Coupling, Gravity, Entanglement, and Baryon Number
• P47 — Cosmological Predictions of the GTE/Phi_MDL Framework: Dark Energy, the CMB Spectral Tilt, and Gravitational Signatures from First Principles
• P48 — The Complete GTE Framework: Standard Model, Gravity, Quantum Mechanics, and Cosmology from Φ_MDL (Complete Synthesis Monograph — capstone of the UGP Physics programme)
• P49 — MDL Selects the Wolfram Rule: Z₇ Dynamics, Algebraic Structure, and Standard Model Encoding of the GTE Polynomial
• P50 — The Spin-7 Lattice Model: Phase Transitions and Statistical Mechanics of the GTE Polynomial
• P51 — The Polynomial Certificate of Transputation: MDL Unification, Quantum Measurement, and the SRRG Fixed Point
• P52 — The PSL(2,7) Algebraic Structure of the Generative Triple Evolution Framework — Seven CatAL machine-certified theorems proving PSL(2,7) unifies the Fibonacci–Möbius map, F₁ gauge skeleton, and Eisenstein integers as facets of one group. Klein quartic genus = N  = 3 (CatAL). more than 400 modules.
• P53 — The GTE Framework: A Comparative Assessment — Assesses GTE against a 11-dimension rubric comparing it to 10 competing frameworks. GTE is the only programme with a derived selection principle, zero free dimensionless parameters, machine-certified proofs (Lean 4, zero sorry, more than 400 modules), cross-sector predictions, and named falsifiers. ∼40 zero-parameter predictions, ∼37 within 1σ of PDG 2024/NuFIT 6.0/Planck 2018.
• P54 — The Fire in the Equations: Consciousness, Physics, and the Primordial Ground — A formal essay arguing that the GTE and NEMS programmes together provide a theorem-backed answer to the observer problem in quantum mechanics and the hard problem of consciousness. Dissolves the measurement problem via PSC-forced transputation; unifies mind and physics without reducing either to the other; locates experience in the same principle that selects physical law. Two questions remain genuinely open: the intrinsic character of specific qualia and the empirical inventory of conscious systems.
• P55 — The Octonionic Shadow of GF(7): Color, Chirality, and Three Generations from a Quadratic-Residue Difference Set — Proves that the UGP/GTE arithmetic programme and the octonion/division-algebra programme are facets of a single finite structure: QR(7) = {1,2,4} ⊂ F₇* is the common anchor. Six-link machine-verified derivation chain derives N_c = 3 from the Fano plane, certifies PSL(2,7) ≅ GL(3,2) by Todd–Coxeter, proves der(O) = g₂ and Stab_G2(apex) = su(3) dimension-exact (39 Lean theorems), establishes equivariant triality isomorphism to UGP flavor, and places the Koide mass ladder at 7 ppm (PDG). Normal neutrino ordering predicted (Δm²₂₁ and Δm²₃₁ within 1% of NuFIT 6.0 IC24 NH, JUNO-falsifiable). 11 Lean modules, 174 theorems, zero sorry. more than 400 modules in ugp-lean.

Lean Formalizations

The core derivations of the UGP Physics programme are machine-certified in Lean 4 with a strict zero-sorry, zero-custom-axiom policy. All Lean libraries are published on Zenodo and browsable on GitHub.

• ugp-lean — more than 400 modules, more than 400 Lean 4 modules — all results independently machine-verifiable. The primary formalization library for UGP Physics: the ridge sieve, prime-lock criterion, GTE update map, canonical orbit, Quarter-Lock identity, Turing universality, Braid Atlas, Koide theorem, gauge coupling derivations, interaction skeleton, and all machine-certified results throughout the programme corpus. GitHub.
• ugp-physics-lean — Formalization paper documenting the Lean 4 proofs across the UGP Physics programme, providing a curated index of all theorem-grade results and their Lean proof names. GitHub.
• srrg-lean — Lean 4 formalization of the Self-Referential Renormalization Group (P27): fixed-point structure, SRRG monotonicity, Vieta no-third-zero certificate, and the β-function algebraic uniqueness results. GitHub.
• rule110-lean — Lean 4 formalization of Cook’s Rule 110 universality theorem (P30): infinite-tape semantics, ether stability, cyclic tag system evaluation, glider overlays, and the structured partial discharge of Cook’s bridge lemmas. GitHub.

Tutorial Series

Companion tutorial documents — accessible worked examples for each major result of the UGP Physics programme.

• The Born Rule as a Theorem, Not a Postulate: Quantum Measurement in the GTE Framework — Quantum mechanics says a particle can be in a superposition — in two states at once.
• The Cosmological Constant: Why It Isn’t Zero But Nearly So — The cosmological constant — Einstein’s lambda — is the most famous fine-tuning problem in physics: its observed value is roughly 10^120 times smaller than any naive quantum field theory estimate.
• Z_7 Defect Cosmology: Domain Walls, Phase Transitions, and the Zero-Relic Prediction — As the early universe cooled, it underwent phase transitions — just like water freezing into ice.
• The Master Quadratic: One Equation, Two Crown Jewels — From the Diagonal of the GTE Polynomial to the Higgs Boson and Rule 110 — Setting all three inputs of the GTE polynomial equal (L = C = R = x) reveals a hidden quadratic: the master quadratic m(x) = x^2 + x – 1.
• Gravity from Description-Length Minimization: The MDL-Lovelock Principle and the GTE Derivation of General Relativity — Every other force in nature is described by a quantum field theory; gravity alone is still described by a classical theory, and the two are mathematically incompatible at the highest energies.
• The Levels of the Theory: Coarse, Fine, and the Role of the Algebraic Certificate — The UGP Physics / GTE derivation tower spans multiple levels of description — from the discrete arithmetic substrate of the GTE polynomial up through cellular automaton dynamics, continuum field theory, and finally the Standard Model particle content and parameters.
• How MDL Selects the 19-Bit Polynomial: The Five-Step Elimination — The MDL (Minimum Description Length) principle selects the GTE polynomial p(L,C,R) = C + R – CR – LCR mod 7 from 7^343 approximately 10^290 candidates by running a five-step elimination chain.
• The Phi_MDL Field: From Discrete Certificate to Continuum Physics — From a single polynomial — p(L,C,R) = C + R – CR – LCR mod 7 — that updates a row of cells in seven possible states, the masses of all elementary particles, the structure of spacetime, and the gauge couplings of the Standard Model can be derived.
• The GTE Polynomial: A Step-by-Step Cheat Sheet — From Cellular Automata to the Standard Model — A concise reference tutorial on the GTE (Generative Triple Evolution) polynomial p(L,C,R) = C + R – CR – LCR mod 7 and the complete derivation chain from this single arithmetic rule to the Standard Model of particle physics.
• Perfect Self-Containment and MDL: Why the Universe Has to Select Itself — Why do the laws of physics have the specific values they do? The Standard Model of particle physics is the most precise physical theory ever constructed, but it cannot explain its own parameters — it requires approximately 25 free constants that must be measured and inserted by hand.
• How the Standard Model Quantum Numbers Emerge from Z_7 x Z_3: A Tutorial on Winding Numbers, Ground States, and Generations — A quantum number is a permanent label attached to a particle — like a barcode that no physical process can change.
• Why the Strong CP Problem Is Solved: theta_QCD = 0 from F_21 Group Theory — The strong CP problem is one of the deepest mysteries in particle physics: the QCD Lagrangian contains a term proportional to theta_QCD that would generically cause the strong force to violate CP symmetry (the combined symmetry of charge conjugation and parity).
• The Three-Tape CMCA: How 3+1D Spacetime Emerges from Three 1D Rules — A single 1D cellular automaton rule operates on a line — but how do you get three-dimensional space from a one-dimensional rule? This tutorial explains the Three-Tape Chiral Minkowski Cellular Automaton (CMCA), the key construction in the UGP Physics framework for deriving 3+1D spacetime from the GTE polynomial.
• Transputation: Quantum Measurement at Turing Degree Exactly 0-prime — This tutorial explains one of the most surprising results in the GTE framework: quantum measurement has a precise location in the mathematical hierarchy of computational difficulty.
• From the Arithmetic Substrate to Particle Masses: The GTE Cascade and the Nine Charged-Fermion Masses — The Universal Generative Principle (UGP) is a number-theoretic sieve that, starting from a single integer ridge level n, severely restricts which starting triples are internally self-consistent — and identifies our universe as the unique self-consistent solution.
• Computational Universality of the Substrate: Undecidability, Self-Reference, and Why the Universe Can’t Know Itself Completely — The substrate of the universe is computationally universal — it can, in principle, simulate any computation.
• How the UWCA Works: A Step-by-Step Explanation of the Universal Windowed Cellular Automaton — A regular cellular automaton (like Rule 110) updates every cell at once using a lookup table.
• The Weinberg Angle, Fine-Structure Constant, and Gauge Couplings from the Polynomial — A gauge coupling is a number that tells you how strongly particles interact via one of the three non-gravitational forces.
• The CMB, the Baryon Asymmetry, and Why There Was No Inflation Field — The cosmic microwave background (CMB) is the afterglow of the early universe. This tutorial explains how GTE derives the spectral tilt and tensor-to-scalar ratio without free parameters, and how it explains the baryon asymmetry without invoking an inflation field.
• Falsifiability: How to Test the GTE Framework — With zero free parameters, every output of GTE is a prediction that could in principle be falsified. This tutorial is the experimentalist’s guide: the complete prediction and falsification register, organized by sector, with named experiments and explicit criteria.
• The Forces: How SU(3)×SU(2)×U(1) Emerges from the Polynomial — In the Standard Model, the gauge group is an assumption. In GTE it is a theorem. This tutorial explains how the three non-gravitational forces emerge from the symmetry structure of the GTE polynomial, including the left-handedness of the weak force.
• The Hierarchy Problem Dissolved: Deriving the Higgs Mass and Electroweak Scale from the GTE Polynomial — The electroweak scale is 17 orders of magnitude below the Planck scale with no explanation in the Standard Model. This tutorial explains how the GTE framework dissolves the hierarchy problem: the electroweak scale is a fixed point of the polynomial’s own arithmetic.
• New Physics Predictions: What GTE Predicts Will and Won’t Be Found — The LHC has found no new physics beyond the Higgs boson. GTE is designed differently: any structure not forced by the 19-bit certificate is absent. This tutorial catalogs what GTE forbids, what it predicts, and how near-future experiments can test it.
• Particles as Topological Kinks: From the Phi-MDL Field to the Standard Model Spectrum — In GTE there is only one object: the Phi-MDL field. Particles are not added separately — they emerge as localised topological kink solitons. This tutorial explains how the Standard Model particle spectrum emerges from the topology of the Phi-MDL field.
• The Problem of Physics: Why the Standard Model Needs an Explanation — The Standard Model requires 19 to 28 free parameters inserted by hand. This foundational tutorial explains why those parameters are not explanations, and how GTE addresses this gap by deriving all SM parameters from a single 19-bit algebraic certificate with zero free parameters.
• GTE Polynomial and Rule Selection: Z₇ Algebraic Structure — MDL selects the unique k=7 cellular automaton rule p(L,C,R) = C+R−CR−LCR (mod 7) from all candidates. Explains the Z₇ algebraic structure underlying this selection, the polynomial’s invariant subsets, and why Rule 110 is the maximal proper invariant sub-CA — providing a selection certificate for the physical rule.

Links

• ← Back to Full Research Program
• → Blog: “The Standard Model Is Not a Coincidence”
• → Complete Corpus Hub on Zenodo (DOI: 10.5281/zenodo.20168144)