The project

The papers

• sg het — Spectral Geometry of Vacuum Entanglement on the Cube and Prism. The bond coordinate, the gauge couplings and induced gravity on the cube and prism, and the vacuum scales from the descent relation, the vacuum expectation value, the string tension, and the glueball, with the three neutrino Yukawa couplings from the vertex operator.
• Lepton Yukawa Couplings — Spectral Geometry of Vacuum Entanglement on the Cube and Prism: Lepton Yukawa Couplings. The three charged-lepton Yukawa couplings as derivatives of the vacuum functional D_ω that gives the neutrinos, each step taken against the Yukawa coupling of the heavier lepton's doublet neutrino.
• Lepton Flavour — Spectral Geometry of Vacuum Entanglement on the Cube and Prism: Lepton Flavour. Both lepton Yukawa matrices built from link chains on the prism, their six singular values the prism Yukawa couplings, and the lepton mixing matrix compared with NuFIT 6.0 and split into U_e and U_ν.
• Up-Type Quark Yukawa Couplings — Spectral Geometry of Vacuum Entanglement on the Cube and Prism: Up-Type Quark Yukawa Couplings. Each up-type quark the neutrino of its generation with the vacuum functional removed, times the cells of the prism and the propagator weight of the colour string.
• Down-Type Quark Yukawa Couplings — Spectral Geometry of Vacuum Entanglement on the Cube and Prism: Down-Type Quark Yukawa Couplings. Each down-type quark the charged lepton of its generation times a factor built from the same cells and the same colour string, with the Georgi–Jarlskog factors appearing in the generation steps.

sg het (PDF)

Status of this work

Harmonic Entanglement Theory is a proposed theory and is being worked on at this time. No claim is made for the validity of these works. The results set out here are the output of the construction described in the paper, and the verification script checks the internal consistency of that construction, that the geometry built from NetworkX with the paper's stated rules reproduces the matrices in the text and that those reproduce every derived number. It does not establish that the underlying physics is correct. The agreement with measured values reported on this site is presented as it stands, without a claim that the framework is established.

About the author

Acknowledgement

Anthropic's Claude (Opus versions 4.6–4.8) was used for computational combinatorics and algebraic derivations, Python scripting, and manuscript editing carried out interactively, and PocketCAS for iOS and NetworkX with NumPy in Google Colab to independently verify the matrix calculations. Theoretical direction was provided by the author.