Quantum Foundations
Derive why identical electron knots cannot occupy the same complete quantum state and recover the many-electron exclusion structure from topology, exchange, and orbital corridors.
The Problem
HGUT proposes that electrons are topological Q=1 structures moving through physically organized orbital corridors in the Graviton Mesh. The open problem is to derive the full Pauli principle from the field theory, including the fermionic exchange sign, occupancy rules, opposite-spin pairing, shell structure, and the distinction between spatial antibunching and exclusion from a complete quantum state.
Scientific Importance
Pauli exclusion is responsible for atomic structure, chemistry, degeneracy pressure, and the stability of ordinary matter. A visual corridor picture is not enough; the observed rule must follow mathematically from the electron sector and many-body dynamics.
Progress Ledger
The Q=1 electron sector carries a reported nontrivial Finkelstein-Rubinstein sign.
The Streets of the Mesh picture supplies a candidate mechanical interpretation of orbital corridors.
Electron antibunching and full Pauli exclusion have been distinguished conceptually.
A complete many-electron derivation and atomic occupancy calculation remain open.
Pass-or-Fail Structure
Every gate must be addressed before this problem can be considered closed. Partial success does not establish the complete identification.
Establish the fermionic sign for the completed electron configuration space.
Derive why two identical electrons cannot share every quantum label.
Recover two-electron occupation of one spatial orbital with opposite spin.
Derive the effective antisymmetric state structure and occupation counting.
Recover shell, subshell, and periodic occupancy consequences.
Recover macroscopic fermionic pressure from the same mechanism.
Definition of Success
This problem closes only when the following conditions are satisfied together.
The exchange sign is derived for physically allowed electron paths.
Complete-state exclusion follows from the field configuration space.
Opposite-spin orbital pairing is recovered.
Many-electron occupation numbers and shell structure agree with observation.
Antibunching, exchange correlations, and Pauli exclusion emerge consistently.
The model reproduces degeneracy pressure and ordinary-matter stability.
Prerequisites
Open Collaboration
Connected Research
Matter and Particle Closure
Determine whether a stable, charged, finite-energy Q=1 Hopf-type Harrison Knot reproduces the complete physical identity of the electron.
Atomic Structure
Derive how electron knots change atomic orbitals, exchange discrete energy, obey selection rules, and produce the observed spectral lines within the Graviton Mesh.
Quantum Foundations
Derive definite outcomes, detector capture, basis selection, Born frequencies, entangled correlations, and causal post-measurement evolution without adding collapse as an independent rule.
The Question Remains Open
Successful arguments, failed attempts, independent simulations, corrections, and falsifying evidence all move the research program forward.
