Testing whether the electron is the stable, charged, finite-energy Q = 1 Hopf-type Harrison Knot.
Programme Overview
This program searches for the precise topological structure that reproduces the electron. The candidate must possess stable localization, conserved Q = 1 topology, negative electric orientation, fermionic exchange behavior, spin-1/2 structure, the observed mass, and the correct electromagnetic response.
Immediate Milestone
Obtain a resolution-convergent localized Q = 1 solution that remains stable under unrestricted evolution.
Active Objectives
Construct a localized finite-energy Q = 1 solution.
Demonstrate unrestricted long-time stability.
Verify topological charge under increasing resolution.
Derive electric charge and negative orientation.
Recover spin-1/2 and fermionic exchange behavior.
Derive the electron mass and magnetic moment.
Construct a stable moving electron solution.
Evidence Trail
This ledger records the mathematical, computational, conceptual, and numerical work already completed within this programme.
Q = 1 Hopf-type sector identified as the electron candidate.
Nontrivial Finkelstein–Rubinstein sign reported.
Independent conserved topological quantity established kinematically.
Localized configurations have retained nonzero Hopf charge over substantial evolution times.
Numerical topology diagnostics have been developed.
Electron-identity gates and validation workflow have been defined.
Shared Mathematical Foundation
The master Lagrangian and baseline displacement, phase, interaction, and conservation equations are already established. The work on this page concerns solving, validating, extending, and testing their consequences in this specific physical sector.
Active Research
Successful derivations, failed simulations, replications, corrections, and falsifying evidence all belong in the evidence trail.
