🟢 TFIM/RenyiEntropy/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
bdg, statusexact, reliabilityhigh, refs: Peschel2003 | CalabreseCardy2009 - Free-fermion correlation-matrix Renyi α ≠ 1.
Corroboration
| regime | mechanism | independence | refs | file |
|---|---|---|---|---|
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | second_closed_form | 🟢 structural | TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β | test/models/quantum/TFIM/test_TFIM_entropy_l1_batch.jl |
@sweep | ed_finite_size | 🟢 structural | Renyi-2 from Schmidt spectrum of buildtfim_dense GS: S2 = -log Σ p² | test/models/quantum/TFIM/test_TFIM_renyi.jl |
@sweep | ed_finite_size | 🟢 structural | Renyi-2 from Schmidt spectrum of buildtfim_dense GS: S2 = -log Σ p² | test/models/quantum/TFIM/test_TFIM_renyi.jl |
Test calls
The exact verify(...) call the harness executed for this hub (reconstructed from the test AST):
verify(TFIM(; J = 0.0, 0.5 = 0.5), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 0.5 = 0.5), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 0.5 = 0.5), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 0.5 = 0.5), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 0.5 = 0.5), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 0.5 = 0.5), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 1.0 = 1.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 1.0 = 1.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 1.0 = 1.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 1.0 = 1.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 1.0 = 1.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 1.0 = 1.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 2.0 = 2.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 2.0 = 2.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 2.0 = 2.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 2.0 = 2.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 2.0 = 2.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; J = 0.0, 2.0 = 2.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = 0.0, agree_within = 1.0e-10, refs = ["TFIM J=0 T→0: pure GS ⇒ S_α(ℓ=1) = 0 for any Rényi index"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 0.5 = 0.5, h = 0.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 1.0 = 1.0, h = 0.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(2), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(3), OBC(4); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(2), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(3), OBC(6); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 0.5))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 10.0))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(2), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 2.0 = 2.0, h = 0.0), RenyiEntropy(3), OBC(8); route = :second_closed_form, independent = log(2), agree_within = 1.0e-10, refs = ["TFIM h=0: ρ₁ = I/2 ⇒ S_α(ℓ=1) = log 2 for any Rényi index, any β"], fetch_kw = (; ℓ = 1, beta = 1.0e6))verify(TFIM(; 1.0 = 1.0, 1.0 = 1.0), RenyiEntropy(2), OBC(8); route = :ed_finite_size, fetch_kw = (; 4 = 4, beta = Inf), independent = -(log(sum((LinearAlgebra.svdvals(reshape((LinearAlgebra.eigen(_build_tfim_dense(8, 1.0, 1.0))).vectors[:, 1], (2 ^ 4, 2 ^ (8 - 4)))) .^ 2) .^ 2))), agree_within = 1.0e-8, refs = ["Renyi-2 from Schmidt spectrum of _build_tfim_dense GS: S2 = -log Σ p²"])verify(TFIM(; 1.0 = 1.0, 0.5 = 0.5), RenyiEntropy(2), OBC(8); route = :ed_finite_size, fetch_kw = (; 4 = 4, beta = Inf), independent = -(log(sum((LinearAlgebra.svdvals(reshape((LinearAlgebra.eigen(_build_tfim_dense(8, 1.0, 0.5))).vectors[:, 1], (2 ^ 4, 2 ^ (8 - 4)))) .^ 2) .^ 2))), agree_within = 1.0e-8, refs = ["Renyi-2 from Schmidt spectrum of _build_tfim_dense GS: S2 = -log Σ p²"])Assurance (provisional)
- level: corroborated-at-p 🟢
- cards: 74 · model ED-feasible
- RES not wired — measured residuals / confidence are not shown yet.