What was already known
Projected and perturbative Landau-level models left the strongly mixed regime difficult to assess. Competing Pfaffian, anti-Pfaffian and particle–hole-Pfaffian orders were already known candidates.
AI involvement
Human researchers designed the Hamiltonian and diagnostics. Optimized momentum-resolved MagNet neural wavefunctions supplied correlated energies, states, entanglement and overlaps.
MagNet optimization supplies the retained many-body states and diagnostics within a human-specified Hamiltonian and scientific investigation.
Importance
Provides substantive numerical phase evidence using a continuum wavefunction ansatz that is not restricted to a fixed set of Landau levels, with momentum-resolved topological diagnostics.
Limitations
Finite torus calculations, notably N=18 and 21, retain variational, Monte Carlo and finite-size uncertainty. The ansatz can represent all Landau levels; a finite computation does not solve the full continuum problem exactly. Stronger mixing eventually favors a Wigner crystal in the studied model. This does not settle the experimental ν=5/2 state, prove an exact thermodynamic phase, or constitute experimental confirmation.
Technical verification
Only the stated computational, numerical, conditional or component checks are documented for this scope; the full claimed endpoint has not received a documented complete rigorous check in the reviewed evidence. Finite torus calculations, notably N=18 and 21, retain variational, Monte Carlo and finite-size uncertainty. The ansatz can represent all Landau levels; a finite computation does not solve the full continuum problem exactly. Stronger mixing eventually favors a Wigner crystal in the studied model. This does not settle the experimental ν=5/2 state, prove an exact thermodynamic phase, or constitute experimental confirmation.
Human understanding
Named human researchers explain or reconstruct the scoped central mechanism in the cited paper/account; credit for that explanation is separate from technical checking. Human researchers designed the Hamiltonian and diagnostics. Optimized momentum-resolved MagNet neural wavefunctions supplied correlated energies, states, entanglement and overlaps.
Correction and publication history
Primary statement, prior work, AI contribution and evidence scope reviewed on 15 October 2026 against the complete current catalog and revision state. New scoped contribution; ordinary notifying editor publication.
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