🟢 S1Heisenberg1D/YYCorrelation/OBC
Generated by docs/atlas/generate.jl — a pure VIEW over the *_registry.jl claims + the static test/INVENTORY.jsonl AST scan. No test is executed and no src is run; test/INVENTORY.jsonl is regenerated in-place (idempotently) from that static scan; fetch/@register untouched. Assurance labels are PROVISIONAL: residuals / confidence are not shown yet (RES not wired). Badges reflect the committed test AST, not the latest CI run — a hub can read green while its @test is red between regenerations. @sweep = a graceful regime-resolution gap, not card omission.
src claim
- method
dense_ed, statusexact, reliabilityhigh
Corroboration
| regime | mechanism | independence | refs | file |
|---|---|---|---|---|
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
@haldane | second_closed_form | 🟢 structural | S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^αi S^αi⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime) | test/models/quantum/Heisenberg/test_s1heisenberg1d_obc_corr_eqsite_batch.jl |
Test calls
The exact verify(...) call the harness executed for this hub (reconstructed from the test AST):
verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(3); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(3); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(3); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(4); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(4); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(4); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(5); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(5); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(5); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(6); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(6); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(6); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 0.5 = 0.5, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(3); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(3); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(3); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(4); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(4); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(4); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(5); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(5); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(5); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(6); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(6); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(6); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 1.0 = 1.0, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(3); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(3); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(3); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(4); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(4); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(4); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(5); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(5); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(5); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 1.0e6, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(6); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 0.5, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(6); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 10.0, i = 1, j = 1))verify(S1Heisenberg1D(), YYCorrelation(mode = :static), OBC(6); route = :second_closed_form, independent = 2 / 3, agree_within = 1.0e-8, refs = ["S1Heisenberg1D SU(2)-covariance + spin-1 Schur: ⟨S^α_i S^α_i⟩ = ⟨(S^α)²⟩ = (1/3)·S(S+1) = 2/3 at any i, axis α, J, N, β (no ρ_i = I/3 assumption — fails at finite-N OBC edge sites in Haldane regime)"], fetch_kw = (; 2.0 = 2.0, beta = 1.0e6, i = 1, j = 1))Assurance (provisional)
- level: corroborated-at-p 🟢
- cards: 36 · model ED-feasible
- RES not wired — measured residuals / confidence are not shown yet.
← Model: S1Heisenberg1D · Quantity: YYCorrelation · Atlas index