Quantum Vacuum Geometry (QVG)

Author: Bertrand Jarry
Preprint: Quantum Vacuum Geometry: Spectral Derivation of the Standard Model Parameters, the Cosmological Constant, and the CMB Temperature (2026)
Repository: github.com/berjarry71/QVG

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Overview

QVG derives the physical constants of the Standard Model from five algebraic axioms (C1–C5) applied to a non-commutative spectral triple. The finite algebra A_F = ℂ ⊕ ℍ ⊕ M₃(ℂ) forces N_F = 96 fermion modes; the spectral free energy functional F_ρ[T] has a unique maximum-entropy fixed point ρ* = 1/96 from which all SM parameters emerge.

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Results: Three Levels of Certainty

Level 1 — Algebraically proven (exact, from axioms C1–C5)

Result	Value	Derivation
Fermion modes N_F	96	dim(H_F) from A_F
Hypercharge invariant Tr_F(Y²)	10	Trace over H_F
Weinberg angle sin²θ_W at Λ_GUT	3/8	Tr_F(T₃²)/Tr_F(Y²)_GUT
Off-diagonal curvature K_ij	0	Algebraic proof
Loop closure condition	g* = N_F/e at T = 149 MeV	From 4π³g*/(45N_F) = 1

Level 2 — Numerically established (computed, reproducible)

Result	QVG	Observed	Deviation
ρ* = 1/96 (fixed point)	1/96 exact	—	✓ Machine precision
T_CMB	2.709 K	2.7255 K	0.61%
Λ_cosmo	0.990×10⁻⁵² m⁻²	1.089×10⁻⁵² m⁻²	9%
sin²θ_W (numerical RGE)	0.37569	3/8 = 0.37500	0.18%
Koide K (emergent)	0.666661	2/3 = 0.666667	4×10⁻⁶

Level 3 — Demonstration models (illustrate conjectures, not full proofs)

Script	What it does	Key limitation
fixed_point.py	Demonstrates ρ → 1/N_F convergence	M-step simplified; masses depend on random seed
true_qvg_solver.py	FSS O(1/N) scaling toy model	PDG masses injected as targets — tautological
rge_2loop_solver_corrected.py	2-loop RGE Runge-Kutta	GUT-normalised α₁ has Landau pole; results unreliable
spectral_anomaly.py	Trace anomaly h(T) peak at 155 MeV	m_gap = ms√π injected, not derived
mcmc_lattice.py	Lattice NCG MCMC prototype	Structural prototype; does not produce SM masses

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The Single Open Frontier

One calculation remains to close the theoretical loop:

Derive ⟨a₄(D_ext, T)⟩_KMS from M₃(ℂ) during confinement — without injecting any phenomenological mass parameter.

If proven, this derives E₀ = 3.2 meV from the axioms alone and closes:

R_H ↔ E₀ ↔ Λ_cosmo ↔ R_H

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Falsifiable Prediction

QVG predicts w = −1 exactly. DESI DR3 (2026–2027) is the experimental verdict.
Current status: DESI DR2 (March 2025) shows 2.8–4.2σ preference for w ≠ −1.

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Repository Structure

core/
  fixed_point.py                    # Demonstrates ρ*=1/96 (M-step simplified)
  rge.py                            # 1-loop RGE running
  seeley_dewitt.py                  # a₄, Caldeira-Leggett, T_CMB
  observables.csv                   # QVG vs PDG 2024

research/
  spectral_anomaly.py               # h(T) proof-of-concept (m_gap injected)
  rge_2loop_solver_corrected.py     # 2-loop prototype (see limitations)
  mcmc_lattice.py                   # Lattice NCG prototype
  true_qvg_solver.py                # FSS toy model (PDG targets injected)
  theory_notes.md                   # Full theoretical derivations

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Running

pip install numpy scipy matplotlib
python core/fixed_point.py        # ρ* = 1/96 convergence
python core/seeley_dewitt.py      # T_CMB = 2.709 K
python research/spectral_anomaly.py  # h(T) peak at 155 MeV

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Citation

Jarry, B. (2026). Quantum Vacuum Geometry. viXra. github.com/berjarry71/QVG