OBC`

Provisional v2 view — RES not wired

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.

Assurance level: corroborated-at-p

Independently corroborated. See the cards below.

`src` claim

method dense_ed, status exact, reliability high
Pass subsystem length ℓ; β=Inf gives ground-state EE.

Corroboration

regime	mechanism	independence	refs	file
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`
`@sweep`	`second_closed_form`	🟢 structural	XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β	`test/models/quantum/XXZ/test_xxz1d_obc_entropy_l1_batch.jl`

Test calls

The exact verify(...) call the harness executed for this hub (reconstructed from the test AST):

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 0.5 = 0.5, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 1.0 = 1.0, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 1.0 = 1.0, 2.0 = 2.0, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(3); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(5); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 1.0e6))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 0.5))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 10.0))

verify(XXZ1D(), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["XXZ1D U(1) × Z₂^x symmetry (Z₂ from e^{iπΣS^x}): ρ₁ = I/2 ⇒ S_vN(ℓ=1) = log 2 for all J, Δ, N, β"], fetch_kw = (; 2.0 = 2.0, -0.5 = -0.5, ℓ = 1, beta = 1.0e6))

Assurance (provisional)

level: corroborated-at-p 🟢
cards: 48 · model ED-feasible
RES not wired — measured residuals / confidence are not shown yet.

← Model: XXZ1D · Quantity: VonNeumannEntropy · Atlas index

🟢 XXZ1D/VonNeumannEntropy/OBC

src claim

Corroboration

Test calls

Assurance (provisional)

🟢 `XXZ1D/VonNeumannEntropy/OBC`

`src` claim