sparse 42: nodes=1000 edges=4557 notes=["potential = HodgeRank-style least-squares ranking (discrete Dirichlet/harmonic extension of the flow); magnetic_gap = normalized magnetic-Laplacian smallest eigenvalue (U(1) gauge flux witness, cousin of spectral_gauge_gap).", "charge γ controls flux sensitivity; very large γ × long cycles can alias past 2π — sweep γ if the gap looks saturated (γ=1 used)."]
clustered 42: nodes=1000 edges=18346 notes=["potential = HodgeRank-style least-squares ranking (discrete Dirichlet/harmonic extension of the flow); magnetic_gap = normalized magnetic-Laplacian smallest eigenvalue (U(1) gauge flux witness, cousin of spectral_gauge_gap).", "charge γ controls flux sensitivity; very large γ × long cycles can alias past 2π — sweep γ if the gap looks saturated (γ=1 used)."]
grid 42: status=422 Unprocessable Entity message=circulation needs >= 2 distinct nodes and >= 1 directed edge (got 1000 nodes, 0 edges)
sparse 1729: nodes=1000 edges=4479 notes=["potential = HodgeRank-style least-squares ranking (discrete Dirichlet/harmonic extension of the flow); magnetic_gap = normalized magnetic-Laplacian smallest eigenvalue (U(1) gauge flux witness, cousin of spectral_gauge_gap).", "charge γ controls flux sensitivity; very large γ × long cycles can alias past 2π — sweep γ if the gap looks saturated (γ=1 used)."]
clustered 1729: nodes=1000 edges=18382 notes=["potential = HodgeRank-style least-squares ranking (discrete Dirichlet/harmonic extension of the flow); magnetic_gap = normalized magnetic-Laplacian smallest eigenvalue (U(1) gauge flux witness, cousin of spectral_gauge_gap).", "charge γ controls flux sensitivity; very large γ × long cycles can alias past 2π — sweep γ if the gap looks saturated (γ=1 used)."]
grid 1729: status=422 Unprocessable Entity message=circulation needs >= 2 distinct nodes and >= 1 directed edge (got 1000 nodes, 0 edges)
sparse 2026: nodes=1000 edges=4548 notes=["potential = HodgeRank-style least-squares ranking (discrete Dirichlet/harmonic extension of the flow); magnetic_gap = normalized magnetic-Laplacian smallest eigenvalue (U(1) gauge flux witness, cousin of spectral_gauge_gap).", "charge γ controls flux sensitivity; very large γ × long cycles can alias past 2π — sweep γ if the gap looks saturated (γ=1 used)."]
clustered 2026: nodes=1000 edges=18444 notes=["potential = HodgeRank-style least-squares ranking (discrete Dirichlet/harmonic extension of the flow); magnetic_gap = normalized magnetic-Laplacian smallest eigenvalue (U(1) gauge flux witness, cousin of spectral_gauge_gap).", "charge γ controls flux sensitivity; very large γ × long cycles can alias past 2π — sweep γ if the gap looks saturated (γ=1 used)."]
grid 2026: status=422 Unprocessable Entity message=circulation needs >= 2 distinct nodes and >= 1 directed edge (got 1000 nodes, 0 edges)
