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๐ŸŸข TFIM/VonNeumannEntropy/OBC

Provisional v2 view โ€” RES not wired

Generated by docs/atlas/generate.jl โ€” 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 โ€” 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 bdg, status exact, reliability high, refs: Peschel2003
  • Free-fermion correlation-matrix method; pass subsystem length โ„“.

Corroboration

regimemechanismindependencerefsfile
@orderedlimiting_case๐ŸŸก assertedt=0: quench EE equals the initial ground-state entanglementtest/models/quantum/TFIM/test_tfim_quench_entanglement.jl
@sweeped_finite_size๐ŸŸข structuralSchmidt-SVD of buildtfim_dense GS (Calabrese-Cardy c=1/2 at h=J)test/models/quantum/TFIM/test_TFIM_cft_entanglement.jl
@sweeped_finite_size๐ŸŸข structuralSchmidt-SVD of buildtfim_dense GS (Calabrese-Cardy c=1/2 at h=J)test/models/quantum/TFIM/test_TFIM_cft_entanglement.jl
@sweeped_finite_size๐ŸŸข structuralDirect Schmidt-SVD of the buildtfim_dense ground statetest/models/quantum/TFIM/test_TFIM_entanglement.jl
@sweeped_finite_size๐ŸŸข structuralDirect Schmidt-SVD of the buildtfim_dense ground statetest/models/quantum/TFIM/test_TFIM_entanglement.jl
@sweeped_finite_size๐ŸŸข structuralDirect Schmidt-SVD of the buildtfim_dense ground statetest/models/quantum/TFIM/test_TFIM_entanglement.jl
@sweepsecond_closed_form๐ŸŸข structuralTFIM J=0 Tโ†’0: GS is pure product state+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0
@sweepsecond_closed_form๐ŸŸข structuralTFIM J=0 Tโ†’0: GS is pure product state+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0
@sweepsecond_closed_form๐ŸŸข structuralTFIM J=0 Tโ†’0: GS is pure product state+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0
@sweepsecond_closed_form๐ŸŸข structuralTFIM J=0 Tโ†’0: GS is pure product state+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0
@sweepsecond_closed_form๐ŸŸข structuralTFIM J=0 Tโ†’0: GS is pure product state+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0
@sweepsecond_closed_form๐ŸŸข structuralTFIM J=0 Tโ†’0: GS is pure product state+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0
@sweepsecond_closed_form๐ŸŸข structuralTFIM J=0 Tโ†’0: GS is pure product state+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0
@sweepsecond_closed_form๐ŸŸข structuralTFIM J=0 Tโ†’0: GS is pure product state+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0
@sweepsecond_closed_form๐ŸŸข structuralTFIM J=0 Tโ†’0: GS is pure product state+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,
@sweepsecond_closed_form๐ŸŸข structuralTFIM h=0: (a) Tโ†’0 cat-state ofโ†‘..โ†‘โŸฉ,

Test calls

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

verify(TFIM(; J = 1.0, h = 0.5), VonNeumannEntropy(:quench), OBC(8); route = :limiting_case, fetch_kw = (; initial = TFIM(; J = 1.0, h = 2.0), 4 = 4, t = 0.0), independent = QAtlas.fetch(TFIM(; J = 1.0, h = 2.0), VonNeumannEntropy(), OBC(8); 4 = 4, beta = Inf), agree_within = 1.0e-8, refs = ["t=0: quench EE equals the initial ground-state entanglement"])
verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), VonNeumannEntropy(), OBC(8); route = :ed_finite_size, fetch_kw = (; 4 = 4, beta = Inf), independent = -(sum((s->begin p = s ^ 2 if p > 1.0e-15 p * log(p) else 0.0 end end), LinearAlgebra.svdvals(reshape((LinearAlgebra.eigen(_build_tfim_dense(8, 1.0, 1.0))).vectors[:, 1], (2 ^ 4, 2 ^ (8 - 4)))))), agree_within = 1.0e-8, refs = ["Schmidt-SVD of _build_tfim_dense GS (Calabrese-Cardy c=1/2 at h=J)"])
verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), VonNeumannEntropy(), OBC(8); route = :ed_finite_size, fetch_kw = (; 4 = 4, beta = Inf), independent = -(sum((s->begin p = s ^ 2 if p > 1.0e-15 p * log(p) else 0.0 end end), LinearAlgebra.svdvals(reshape((LinearAlgebra.eigen(_build_tfim_dense(8, 1.0, 0.5))).vectors[:, 1], (2 ^ 4, 2 ^ (8 - 4)))))), agree_within = 1.0e-8, refs = ["Schmidt-SVD of _build_tfim_dense GS (Calabrese-Cardy c=1/2 at h=J)"])
verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), VonNeumannEntropy(), OBC(8); route = :ed_finite_size, fetch_kw = (; 4 = 4, beta = Inf), independent = -(sum((s->begin p = s ^ 2 if p > 1.0e-15 p * log(p) else 0.0 end end), LinearAlgebra.svdvals(reshape((LinearAlgebra.eigen(_build_tfim_dense(8, 1.0, 1.0))).vectors[:, 1], (2 ^ 4, 2 ^ (8 - 4)))))), agree_within = 1.0e-8, refs = ["Direct Schmidt-SVD of the _build_tfim_dense ground state"])
verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), VonNeumannEntropy(), OBC(8); route = :ed_finite_size, fetch_kw = (; 4 = 4, beta = Inf), independent = -(sum((s->begin p = s ^ 2 if p > 1.0e-15 p * log(p) else 0.0 end end), LinearAlgebra.svdvals(reshape((LinearAlgebra.eigen(_build_tfim_dense(8, 1.0, 0.5))).vectors[:, 1], (2 ^ 4, 2 ^ (8 - 4)))))), agree_within = 1.0e-8, refs = ["Direct Schmidt-SVD of the _build_tfim_dense ground state"])
verify(TFIM(; 1.0 = 1.0, 2.0 = 2.0), VonNeumannEntropy(), OBC(8); route = :ed_finite_size, fetch_kw = (; 4 = 4, beta = Inf), independent = -(sum((s->begin p = s ^ 2 if p > 1.0e-15 p * log(p) else 0.0 end end), LinearAlgebra.svdvals(reshape((LinearAlgebra.eigen(_build_tfim_dense(8, 1.0, 2.0))).vectors[:, 1], (2 ^ 4, 2 ^ (8 - 4)))))), agree_within = 1.0e-8, refs = ["Direct Schmidt-SVD of the _build_tfim_dense ground state"])
verify(TFIM(; J = 0.0, 0.5 = 0.5), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 Tโ†’0: GS is pure product state |+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; J = 0.0, 0.5 = 0.5), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 Tโ†’0: GS is pure product state |+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; J = 0.0, 0.5 = 0.5), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 Tโ†’0: GS is pure product state |+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; J = 0.0, 1.0 = 1.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 Tโ†’0: GS is pure product state |+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; J = 0.0, 1.0 = 1.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 Tโ†’0: GS is pure product state |+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; J = 0.0, 1.0 = 1.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 Tโ†’0: GS is pure product state |+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; J = 0.0, 2.0 = 2.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 Tโ†’0: GS is pure product state |+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; J = 0.0, 2.0 = 2.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 Tโ†’0: GS is pure product state |+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; J = 0.0, 2.0 = 2.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 Tโ†’0: GS is pure product state |+โŸฉ^N โ‡’ ฯโ‚ pure โ‡’ S_vN(โ„“=1) = 0"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; 0.5 = 0.5, h = 0.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 0.5))
verify(TFIM(; 0.5 = 0.5, h = 0.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 10.0))
verify(TFIM(; 0.5 = 0.5, h = 0.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; 0.5 = 0.5, h = 0.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 0.5))
verify(TFIM(; 0.5 = 0.5, h = 0.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 10.0))
verify(TFIM(; 0.5 = 0.5, h = 0.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; 0.5 = 0.5, h = 0.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 0.5))
verify(TFIM(; 0.5 = 0.5, h = 0.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 10.0))
verify(TFIM(; 0.5 = 0.5, h = 0.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; 1.0 = 1.0, h = 0.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 0.5))
verify(TFIM(; 1.0 = 1.0, h = 0.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 10.0))
verify(TFIM(; 1.0 = 1.0, h = 0.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; 1.0 = 1.0, h = 0.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 0.5))
verify(TFIM(; 1.0 = 1.0, h = 0.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 10.0))
verify(TFIM(; 1.0 = 1.0, h = 0.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; 1.0 = 1.0, h = 0.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 0.5))
verify(TFIM(; 1.0 = 1.0, h = 0.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 10.0))
verify(TFIM(; 1.0 = 1.0, h = 0.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; 2.0 = 2.0, h = 0.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 0.5))
verify(TFIM(; 2.0 = 2.0, h = 0.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 10.0))
verify(TFIM(; 2.0 = 2.0, h = 0.0), VonNeumannEntropy(), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; 2.0 = 2.0, h = 0.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 0.5))
verify(TFIM(; 2.0 = 2.0, h = 0.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 10.0))
verify(TFIM(; 2.0 = 2.0, h = 0.0), VonNeumannEntropy(), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))
verify(TFIM(; 2.0 = 2.0, h = 0.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 0.5))
verify(TFIM(; 2.0 = 2.0, h = 0.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 10.0))
verify(TFIM(; 2.0 = 2.0, h = 0.0), VonNeumannEntropy(), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: (a) Tโ†’0 cat-state of |โ†‘..โ†‘โŸฉ,|โ†“..โ†“โŸฉ or (b) finite-T Zโ‚‚-symmetric ensemble โ‡’ ฯโ‚ = I/2 โ‡’ S_vN(โ„“=1) = log 2 for any ฮฒ"], fetch_kw = (; โ„“ = 1, beta = 1.0e6))

Assurance (provisional)

  • level: corroborated-at-p ๐ŸŸข
  • cards: 42 ยท model ED-feasible
  • RES not wired โ€” measured residuals / confidence are not shown yet.

โ† Model: TFIM ยท Quantity: VonNeumannEntropy ยท Atlas index