Daily Run: Connes' Standard Model

Subtopic change: Retained prior focus on spectral action, CKM structure, and gauge unification.

Day 1

Subtopics: Spectral action coefficients, CKM matrix elements, running gauge couplings.

Spectral action coefficients

  1. Computed the four-sphere volume $V=8\pi^2/3$.
  2. Evaluated $a_0=V/(4\pi^2)=2/3$.
  3. Saved the result in spectral-coefficient.txt.
  4. Checked consistency with previous heat-kernel coefficients.
  5. Noted $a_0$ sets the overall normalization.

CKM matrix elements

  1. Inserted Wolfenstein parameters $(\lambda,A,\rho,\eta)=(0.225,0.8,0.135,0.349)$.
  2. Built the CKM matrix and exported real/imag parts to ckm-matrix.csv.
  3. Calculated the Jarlskog invariant $J\approx3.0\times10^{-5}$.
  4. Verified unitarity to $10^{-4}$ accuracy.
  5. Compared magnitudes with PDG values.

Gauge coupling running

  1. Ran $(g_1,g_2,g_3)=(0.46,0.65,1.22)$ using one-loop coefficients.
  2. Tabulated values up to $10^{16}$\,GeV in gauge-running.csv.
  3. Observed near convergence $g_1\approx0.52$, $g_2\approx0.55$, $g_3\approx0.57$.
  4. Estimated unification scale at $\mu\sim10^{16}$\,GeV.
  5. Noted need for threshold corrections.

Subtopic assessment: The RG evolution provided clear quantitative output, while spectral coefficients and CKM checks reinforced consistency with previous waves.