The Standard Model of particle physics correctly predicts the behavior of subatomic particles to twelve decimal places. Yet it contains approximately nineteen numbers — particle masses, force strengths, mixing angles — that it cannot derive. It measures them from experiment, writes them down, and moves on. The theory is silent on why these numbers take the values they do.
Two deeper problems compound this. The hierarchy problem: gravity is 10³⁸ times weaker than electromagnetism, and no principle in physics explains this ratio. The cosmological constant problem: quantum field theory predicts a vacuum energy density 10¹²² times larger than astronomers observe — the worst numerical mismatch in the history of science. The standard assumption is that some unknown mechanism cancels the QFT contributions to 122 decimal places. No such mechanism has been found.
These are not gaps at the edges of knowledge. They are holes at its center.
This repository is the computational companion to projectiveprocessmonism.com. The theory and full derivations live there. What lives here are three notebooks — one shows the headline numbers, one lets you break and fix the framework interactively, and one reproduces every equation.
Every prediction computed live. No sliders, no preamble — just the numbers.
| Prediction | Formula | PPM | Observed | Error |
|---|---|---|---|---|
| 1/α | Twisted heat trace at t*=1/32 | 137.257 | 137.036 | 0.16% |
| δ_CP | π(1 − 1/φ) = π/φ² | 68.5° | 68.4 ± 3° | within 1σ |
| H₀ | 1/T_universe | 70.9 km/s/Mpc | 67.4–73.0 | splits tension |
| sin²θ_W | 3/8 (Pati-Salam) | 0.375 | 0.375 | 0.13% |
| Generations | CP³ topology | 3 | 3 | exact |
| θ_strong | RP³ non-orientability | 0 | < 10⁻¹⁰ | exact |
Fast to scroll. 33 cells. Full scorecard at the end.
Narrative-driven with FloatSliders at each stage. Move parameters off their geometric values and watch multiple observables break simultaneously. Voila-compatible.
| Section | Slider | What breaks when you change it |
|---|---|---|
| Hierarchy | g (5.0–7.8) | Move g off 2π → masses diverge |
| EWSB | k_EWSB (43–46) | Higgs, top, τ, μ all move |
| α | log₁₀(t) | Twisted heat trace ratio vs t |
| Cosmology | log₁₀(N) (78–86) | G and Λ curves cross at N_cosmic |
Every claim in the paper that involves a number, reproduced with intermediate steps. 44 cells covering all 22 sections from CP³ spectral data through cosmological predictions. For physicists checking the math.
Projective Process Monism (PPM) proposes that physical reality has a discrete, hierarchical structure. Energy scales sit on a ladder indexed by a dimensionless integer k, with rung spacing set by a single geometric constant g. The ladder is anchored at one measured scale: the pion mass.
E(k) = m_π × g^((k_ref − k) / 2)
where m_π = 140 MeV is the experimental anchor, k_ref = 51 is the confinement level, and
g = 2π is derived from topology. The derivation: the elementary discrete symmetry of the vacuum
is Z₂ × Z₂ — the simplest non-trivial product of inversions. The natural geometric arena for
a Z₂ × Z₂-invariant process in 3+1 dimensions is the real projective space RP³ ≅ SO(3), with
volume π² in the natural SU(2) metric:
g² = |Z₂ × Z₂| × Vol(RP³) = 4 × π² = 4π² → g = 2π
No particle mass enters this calculation. That single formula — one measured input, step size from geometry — predicts particle masses across 30 orders of magnitude, and the same constant fixes the strength of electromagnetism, the weakness of gravity, the cosmological constant, and the temperature at which biological processes are possible.
With g = 2π established, every subsequent quantity follows without new free parameters.
Particle spectrum. E(k) spans from the Planck scale (k ≈ 0) to the thermal energy of a
living cell. Every major Standard Model particle has a k-assignment that reproduces its mass.
Particles with topology-derived prefactors sit above the bare curve: the Higgs VEV
v = 2√2(2π)^(1/4) × E(44.5) = 246.2 GeV (observed: 246.2 GeV) and the top quark
m_t = π × E(44.5) = 172.7 GeV (observed: 173.0 GeV). The prefactors come from SU(2) → U(1)
geometry, not fitting.
Electroweak sector. The level at which electroweak symmetry breaks is fixed by the RP³
emergence condition at k_EWSB = 44.5. The lepton mass hierarchy — spanning six orders of
magnitude with no Standard Model explanation — emerges as a Z₂-quantized tower above this level.
Fine structure constant. The framework's formulas for G and Λ both contain α. The observed Λ fixes N (no free parameters); then the observed G and N determine α:
α = G_obs · m_π² · √N / (16π⁴ ħc) = 1/(137.6 ± 1.3)
Central error 0.4%; the observed value 1/137.036 lies within the 1σ band from Λ_obs uncertainty. This is a consistency prediction using zero free parameters.
Newton's constant and the cosmological constant. Both follow from the same holographic count with different exponents:
G = 16π⁴ ħc α / (m_π² √N_cosmic) → G ∝ N^(−1/2)
Λ = 2(m_π c²)² / ((ħc)² N_cosmic) → Λ ∝ N^(−1)
Because the exponents differ, only one value of N_cosmic satisfies both simultaneously. That
value is N ≈ 10⁸². Gravity is weak because the universe is old and large — G is diluted by the
square root of the holographic count. The cosmological constant is small because Λ falls faster.
Neither requires fine-tuning; both are consequences of the universe's age.
Phase coherence and body temperature. At each rung k, two phase contributions compete —
thermal phase (large at high energy, decreasing) and Berry phase (small at low energy,
increasing). They cross at exactly one point. At n = 5/6 — the crossing falls at k_cross ≈ 75.354, corresponding to T = 310 K. Human body
temperature is not a separate prediction. It is an automatic consequence of the value of n
established by electromagnetism.
All predictions use g = 2π (topology) and m_π = 140 MeV (one experimental anchor).
No other free parameters.
| Observable | Formula | Prediction | Observed | Error |
|---|---|---|---|---|
| Higgs VEV | 2√2(2π)^(1/4) × E(44.5) |
246.2 GeV | 246.2 GeV | < 0.01% |
| Top quark | π × E(44.5) |
172.7 GeV | 173.0 GeV | 0.2% |
α⁻¹ |
Consistency: Λ_obs → N → α | 137.6 ± 1.3 | 137.036 | 0.4% |
G |
16π⁴ħcα / (m_π² √N) |
~6.5×10⁻¹¹ | 6.674×10⁻¹¹ | ~4% |
Λ |
2m_π² / ((ħc)² N) |
~1.0×10⁻⁵² m⁻² | ~1.1×10⁻⁵² m⁻² | ~9% |
T_bio |
Phase coherence crossing at n = 5/6 |
310 K | 310 K | exact |
α_w |
1/(3π²) from RP³ geometry |
1/29.6 |
1/29.9 |
~1% |
α_s |
Confinement condition at k = 51 |
1/3 |
1/3 |
exact |
δ_CP |
Berry phase: π(1 − 1/φ) |
1.200 rad | 1.20 ± 0.08 rad | 0.0% |
sin²θ₂₃ |
Tribimaximal from Z₂ × 3D topology | 1/2 (exact) |
0.546 ± 0.021 | 8.4% |
H₀ |
1/T_universe (CMB age: 13.797 Gyr) |
70.9 km/s/Mpc | 69.8 (TRGB) | ~1.5% |
G(t)/G₀ |
N_cosmic ∝ (1+z)^{-3} causal volume |
5–36× at z=10 | 3–100× (JWST) | overlaps |
The framework has one experimental anchor (m_π = 140 MeV) and one topology-derived constant
(g = 2π). Every other quantity follows by calculation — and the sequence closes on itself:
topology: Z₂ × Z₂
│ Vol(RP³) = π²
▼
g = 2π ◄─────────────────────────────────────────────────────┐
│ │
│ E(k) = m_π · g^((51−k)/2) │
│ │
┌────┴──────────────────┐ │
▼ ▼ │
k = 44.5 k = 51 │
EW sector anchor: m_π = 140 MeV │
Higgs, top, τ, μ, e │
│ │
▼ │
n = 5/6 (CP³ phase space: 5 of 6 dims projected by Z₂) │
│ │
▼ │
Λ_obs → N_cosmic = 10⁸² │
│ │
├──► G, Λ, H₀ │
├──► α = 1/(137.6 ± 1.3) (consistency prediction from G, N) │
│ │
▼ │
T_bio = 310 K │
│ │
└── k_c ≈ 75.4 · E(k_c) = k_B × 310 K · on E(k) above ───┘
Topology fixes g. Geometry fixes k_EWSB and n. Holography fixes N_cosmic. The consistency
of G and Λ with framework geometry determines α. Phase coherence fixes T_bio. No step adjusts
a previous result to fit a new observation. The endpoint — 310 K —
lands back on the same E(k) ladder the chain began with.
ppm-framework/
├── ppm/ # Core computational package (14 modules, ~3,100 lines)
│ ├── constants.py # Physical and framework constants
│ ├── hierarchy.py # E(k) hierarchy formula, particle table
│ ├── alpha.py # Fine-structure constant (three routes)
│ ├── gauge.py # Gauge structure, sin²θ_W, generations
│ ├── higgs.py # Higgs quartic, top Yukawa, τ-involution
│ ├── instanton.py # S=30π, zero modes, T² partition function
│ ├── spectral.py # Heat kernel, zeta functions, det(Δ)
│ ├── cosmology.py # G, Λ, H₀, G(z) evolution
│ ├── golden_ratio.py # Pyramidal numbers, A₅ decomposition
│ ├── berry_phase.py # CKM matrix, δ_CP from Berry phase
│ ├── neutrino.py # PMNS, θ_strong, sterile ν brackets
│ ├── predictions.py # Master prediction table (23 PRED + derived)
│ └── verify.py # Run-all checker (22/22 PASS)
│
├── notebooks/
│ ├── predictions.ipynb # Sizzle Reel — headline numbers
│ ├── explorer.ipynb # Interactive Explorer — sliders + narrative
│ └── derivations.ipynb # Technical Derivations — every equation
│
├── notebooks/archive/ # Old notebooks (preserved)
└── ppm_old/ # Old ppm/ package (preserved)
pip install -e .Requirements: Python 3.9+, NumPy, Matplotlib, ipywidgets, Jupyter.
jupyter notebook notebooks/predictions.ipynb
jupyter notebook notebooks/explorer.ipynb
jupyter notebook notebooks/derivations.ipynbVerify the computational core:
python -c "import ppm; ppm.verify.print_report()"pytest tests/test_all.py -v@article{ppm-framework-2026,
title = {Projective Process Monism: Deriving Physical Constants
from Z2 x Z2 -> RP3 Topology},
author = {Jeff Wozniak},
year = {2026},
url = {https://projectiveprocessmonism.com}
}bash dev/run.shStarts two servers — no Python environment setup required:
- Jupyter Lab (code visible):
http://localhost:8888 - Voilà (rendered app, code hidden):
http://localhost:8889
Custom ports: bash dev/run.sh ppm 8888 8889. dev/ contains Dockerfile, requirements-dev.txt, and start.sh if you prefer to build manually.
MIT