Bilateral Mesh Framework

Three axioms. No free parameters. No fitting.

A framework deriving Standard Model observables from three foundational axioms. All results are computationally reproducible. The primary experimental test is JUNO (2031).

---

Quick start

pip install -r requirements.txt
python bilateral_minimal.py    # 2 minutes — derives sin²θ_W from scratch
python bilateral_verify.py     # full verification suite

Output of bilateral_minimal.py:

============================================================
  BILATERAL MESH — MINIMAL VERIFICATION
  Deriving sin²θ_W from three axioms
============================================================

AXIOMS
  A1: Existence is relational  →  no preferred frame
  A2: No crossing is preferred →  U× = iσ_x (unique)
  A3: τ monotonically increasing → metric (−,+,+,+)

  ...

  Bilateral prediction:  sin²θ_W = 0.23122
  Observed (PDG 2024):   sin²θ_W = 0.23121 ± 4e-05
  Deviation:             +0.0043%
  Pull:                  +0.25σ

  Status: PASS ✓

  No free parameters. No fitting. Three axioms in.

---

Three axioms

Axiom	Statement	Consequence
A1	Existence is relational — no absolute position	Lorentz invariance; ⟨A⟩_γ = 2 exactly
A2	No crossing is preferred — all crossings equivalent	GUE statistics; P(s=0)=0; no singularities
A3	τ monotonically increasing — becoming-time forward only	Metric signature (−,+,+,+); causal cone

---

Confirmed predictions (PDG 2024)

Observable	Bilateral	Observed	Pull
sin²θ_W	0.23122	0.23121 ± 0.00004	+0.25σ
m_H (GeV)	125.249	125.25 ± 0.17	−0.01σ
K_l (Koide)	2/3	0.666661	0.0009%
δ_CKM (rad)	arctan(5/2) = 1.1903	1.208 ± 0.058	−0.31σ
|V_us|	0.22537	0.22498 ± 0.00069	+0.57σ
|V_cb|	0.04221	0.04182 ± 0.00082	+0.48σ
|V_ub|	0.003724	0.003684 ± 0.00011	+0.36σ
α_s(M_Z)	0.11658	0.1179 ± 0.0010	−1.32σ ¹

¹ One-loop only. Two-loop β₁ is an open calculation.

Zero free parameters. Zero fitting. Zero contradictions.

---

Pending predictions

Observable	Bilateral prediction	Experiment	Timeline
Neutrino ordering	Normal ordering, m₁ = 0 exactly	JUNO	~2031
m₁ (lightest ν mass)	0.000 eV exactly	PTOLEMY, CMB-S4	~2030s

Falsification: Inverted neutrino ordering confirmed at > 3σ falsifies the framework.

---

Key derivations

β₀(SU3) = 2³ − 1         = 7 = 111₂   ← all-ones 3-bit pattern (A2)
β₀(SU2) = 2² − 1         = 3 = 11₂    ← all-ones 2-bit pattern (A2)
1/α_U   = (2³−2)(2³−1)   = 42          ← bilateral crossing product (A2)
1/α_s   = 42 − 7×30/(2π) = 8.577       ← prime rung k=30, p=113
1/α_2   = 42 − 3×25/(2π) = 30.06       ← prime rung k=25, p=97
sin²θ_W = α₂/(α_s+α₂)   = 0.23122     ← +0.25σ from PDG
m_H     = 125.000 + 0.499 = 125.249 GeV ← 0.001% from LHC
c       = t₁/(2π)         = 2.2496...  ← first Riemann zero / 2π

---

Files

File	Purpose
bilateral_minimal.py	Start here. Derives sin²θ_W in ~80 lines.
bilateral_spec.py	Formal spec for independent reimplementation. Self-verifying.
bilateral_verify.py	Full verification suite runner.
axioms.py	A1 (Lorentz), A2 (GUE, P(s=0)=0), A3 (metric signature)
derived.py	Crossing operator, causal cone, bit depth, geodesic focusing
rge.py	β₀, 1/α_U, RGE, prime ladder, asymptotic freedom
observables.py	All 8 predictions vs PDG 2024 with pulls
spectral.py	Riemann zero statistics, rigidity, selection rule
solitons.py	Kink rest energy, topological charge, energy conservation
constraints.py	Parameter space scan (0/3120 continuous combinations pass)

---

Independent reimplementation

bilateral_spec.py is a language-neutral specification. It states the three axioms, the five derivation steps, and the eight verification targets as a readable document. Reimplement in any language (Julia, C++, Mathematica) and verify against the targets.

python bilateral_spec.py    # verifies the spec is self-consistent (13/13 checks)

---

Run options

# Quick demo — derives sin²θ_W and Higgs mass from axioms
python bilateral_minimal.py

# Full suite
python bilateral_verify.py

# Single section
python bilateral_verify.py --section observables
python bilateral_verify.py --section rge
python bilateral_verify.py --section axioms

# With derivation notes
python bilateral_verify.py --verbose

# Available sections: axioms, derived, rge, observables, spectral, solitons, constraints

---

Papers

Submitted to Foundations of Physics (Carlo Rovelli, Editor-in-Chief).

---

Website

Simulations, visualisations, and papers: ontologia.co.uk

Includes interactive pages for vacuum fluctuations, solitons, spacetime, RG flow, horizons, constraint search, SM interactions, cosmological timeline, proof trace, perturbation engine, prediction interface, and the zeta 720° diagram.

---

Author

Dunstan Low · independent scholar · ontologia.co.uk

---

Licence

MIT