BPR 2.0 is a flavor-sector organizing framework built on one boundary equation and two integers, plus a proposed (untested) particle sector. It derives 87 physical quantities with no tuned dimensionless parameters — and documents what failed as carefully as what worked. Open source, reproducible in under 60 seconds.
The Idea
The Standard Model needs about 26 numbers entered by hand — particle masses, force strengths — with no explanation for their values. BPR asks: what if they can be calculated?
The framework's starting point: space is not a smooth fabric but a discrete lattice with a specific mathematical structure, governed by two integers — p = 104,761 (a prime, derived from the strength of electromagnetism) and z = 6 (fixed by the boundary geometry, a 2-sphere).
Write down the simplest boundary equation for that lattice, and electromagnetism, gravity, and quantum mechanics appear as different limits of the same function — not separate theories bolted together.
The 2-sphere boundary is derived, not assumed: it is the unique compact orientable simply-connected surface, and its geometry fixes z = 6 and three fermion generations.
Everything is checked against NIST/CODATA experimental values. With zero adjustable dimensionless parameters, the framework either matches or it doesn't — and the failures are documented as prominently as the successes.
Method
Four steps from two integers to measurable predictions.
A Zp lattice with p = 104,761 and coordination z = 6. These two integers are the only structural inputs the framework ever takes.
The boundary transfer function. Electromagnetism, gravity, and quantum mechanics each appear as different limits of this one function.
67 unit-tested bridge functions chain into end-to-end derivations, from substrate structure to measurable numbers.
Every output is compared with NIST/CODATA values. No tuning after the fact — it matches or it doesn't.
Results
An interactive map of every derivation chain, from (p, z) to each measured constant. Node colors show deviation from experiment.
| Quantity | Result |
|---|---|
| Fine-structure constant α | 0.003% err |
| Weinberg angle sin²θW | exact |
| Electron mass me | 0.11% err |
| Proton radius rp | 0.02% err |
| Muon mass mμ | 1.5% err |
| Dark energy w₀ | 1σ DESI |
LHCb reported a 4σ angular anomaly in B→K*μμ decays (arXiv:2312.09621). BPR derives the required correction δC₉ ≈ −1.0 from substrate mode ratios alone: MZ′ = MZ × √(E₂₆/E₄) = 511 GeV. The same structure predicts exact GIM protection for kaon, Bd, and D-meson decays — matching the pattern of where anomalies are and aren't observed. Testable at HL-LHC.
Where the framework stands
BPR documents its negative results as carefully as its positive ones. A sealed, blind glueball benchmark falsified the original particle sector in 2026 — and the framework was revised, not defended.
The headline claim is no longer "theory of everything." BPR 2.0 is a flavor-sector organizing framework plus a proposed, untested particle sector (gauged dihedral point group, Postulate 0d). Flavor predictions are numerically unchanged; the particle sector is explicitly marked PROPOSED with no spectrum claimed.
Everything determined not to work, in one document: the closed Riemann/GUE line, the falsified glueball sector, refuted retrofits, and formerly fitted coefficients. Reviewers shouldn't have to scrape commit history to find what didn't pan out.
Verify it yourself
The full test suite runs on a laptop. The framework also names the experiments that could rule it out: DESI-II dark energy (w₀ > −0.8 falsifies), next-gen hydrogen 1S–2S spectroscopy, and MEMS Casimir force at 10⁻⁸ sensitivity.
Questions
Not yet — the framework is in open research phase. The mathematics and code are fully public so anyone can check the work now. Formal peer review of the primary paper is in progress.
It's derived from the fine-structure constant: inverting 1/α = [ln p]² + z/2 + γ − 1/(2π) gives p ≈ 104,749, and the nearest prime satisfying the orientability condition (p ≡ 1 mod 4) is 104,761. This gives 1/α = 137.039, matching experiment to 19 parts per million. z = 6 is fixed by the boundary topology, not chosen.
It's derived. A consistent boundary must be compact (discrete masses), orientable (global fermion fields), and simply connected (no free holonomy parameters). The unique compact connected orientable simply-connected 2-manifold is S². Its cubic tiling gives z = 6, and its ℓ=1 Laplacian eigenspace gives exactly three fermion generations.
Named experiments with named thresholds. If DESI-II measures dark energy w₀ above −0.8, BPR is ruled out. If next-generation hydrogen spectroscopy shows no 66.8 Hz shift in the 1S–2S transition, BPR is ruled out. MEMS Casimir experiments at 10⁻⁸ sensitivity test the derived δ = 2 exponent.
It was withdrawn. A sealed, blind glueball benchmark — targets locked before any spectrum was computed — falsified the original particle sector in 2026. The current claim is a flavor-sector organizing framework plus a proposed, untested particle sector. The full history is on the status page and in the negative-findings registry.
Yes. Clone the repo, pip install -e ., then bpr predict --p 104761 --z 6. The 1,225-test suite passes in under 60 seconds on a laptop. A Wolfram Language port is available for Mathematica users.
BPR works in 3+1 dimensions, uses a discrete prime lattice, and makes specific numerical predictions checkable with current experiments. String theory requires extra dimensions with no unique vacuum; LQG quantizes geometry but doesn't derive Standard Model constants. BPR derives its lattice structure rather than assuming it.