The infinite-dimensional unit ball, descended to four dimensions, is indistinguishable from our universe.
One hypothesis. Zero free parameters. No choices.
The series derives — from this alone — the cosmological constant, quantum mechanics, general relativity at d=4 with Lorentzian signature, the Standard Model gauge group and its symmetry breaking, three fermion generations, particle masses and couplings, and the cosmological parameters including a Planck-compatible Hubble constant (incompatible with SH0ES).
Read another way: the universe is the asymptotic resolution of
Structural (forced by uniqueness theorems):
- Spacetime dimension d = 4 with Lorentzian signature (−,+,+,+)
- Gauge group SU(3) × SU(2) × U(1) with SU(2) broken
- Exactly three fermion generations
- Dark energy equation of state w = −1 exactly
- Strong CP phase θ_QCD = 0
- No supersymmetric partners · No dark matter particles · No extra Higgs bosons · No axion · No gravitons
Precision numerics (closed within experimental error, zero fitted parameters):
| Observable | Predicted | Observed | Match |
|---|---|---|---|
| ρ_Λ / M⁴_Pl,red (Gram-corrected) | 7.14 × 10⁻¹²¹ | 7.15 × 10⁻¹²¹ | −0.07% |
| α_s(M_Z) | 0.11792 | 0.1179 ± 0.0009 | +0.02σ |
| m_τ / m_μ | 16.8173 | 16.8170 ± 0.0011 | +0.24σ |
| sin²θ_W | 0.23123 | 0.23121 ± 0.00004 | +0.40σ |
| m_μ / m_e | 206.50 | 206.77 | +0.13% |
| H₀ (Gram-corrected) | ≈67.5 km/s/Mpc | Planck: 67.4 ± 0.5 | Planck-compatible |
| T_CMB | 2.642 K | 2.7255 K | −3.1% (descent-dependent) |
| Universe age | 13.88 Gyr | 13.80 ± 0.02 | +0.6% |
See PREDICTIONS.md for the full tiered table (structural results, all precision derivations, frontier experimental predictions, and provisional items with known gaps).
| File | Title |
|---|---|
cascade-series-cover-sheet.tex |
Cover Sheet — The Thought Experiment, Hypothesis, and Series Overview |
cascade-series-prelude.tex |
Prelude — Why Nothing Has Structure |
cascade-series-part0.tex |
Part 0 — Scale Variance from Orthogonality: How the Unit Ball Generates 10^120 Orders of Magnitude |
cascade-series-part0.0.tex |
Part 0 Supplement — Inter-Layer Coupling and the Independent-Step Correction |
cascade-series-part1.tex |
Part I — The Cosmological Constant from the Observer's Frame |
cascade-series-part2.tex |
Part II — Quantum Mechanics from the Cascade: Effective Theory of a 4-Dimensional Observer in the Sphere-Area Geometry |
cascade-series-part3.tex |
Part III — General Relativity, Four Dimensions, and Lorentzian Signature from the Cascade |
cascade-series-part2-equals-3.tex |
Part II = III — Quantum Gravity without Quantising Gravity: Why the Quantum and Gravitational Projections of the Cascade Are the Same Theorem |
cascade-series-part4a.tex |
Part IVa — The Standard Model from the Cascade: Gauge Group, Symmetry Breaking, and Three Generations from Bott Periodicity and Hairy Ball Zeros |
cascade-series-part4b.tex |
Part IVb — The Standard Model from the Cascade: Masses, Couplings, and Precision Predictions from the Geometric-Topological Factorization |
cascade-series-part5.tex |
Part V — Cosmology from the Cascade: ΛCDM Parameters, the Hubble Constant, and the DESI BAO Observations |
cascade-series-part6.tex |
Part VI — Tower Growth, Inflation, and the Pre-Big-Bang from the Cascade (speculative extension; Tier 5) |
A GitHub Actions workflow automatically compiles all .tex files into PDFs on every push. PDFs are available as build artifacts.
To build locally, run:
cd src
latexmk -pdf cascade-series-cover-sheet.texOr compile all files at once:
cd src
latexmk -pdf *.texEvery numerical claim in the series is backed by a script in tools/. The scripts are organised by role (generators, verifiers, closures, model checks) and share a single source of truth for cascade primitives in tools/cascade_constants.py.
See tools/README.md for the full index — which script backs which LaTeX citation, how to run each one, and which results it reproduces.
This work is licensed under CC BY 4.0.
See CITATION.cff for citation information.