Infinite`

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 analytic, status exact, reliability high, refs: Giamarchi2003
K = π / (2(π − arccos Δ)) for -1 < Δ ≤ 1.

Corroboration

regime	mechanism	independence	refs	file
`@free_fermion`	`second_closed_form`	🟢 structural	Jordan-Wigner free fermion: K=1 at Delta=0	`test/models/quantum/XXZ/test_XXZ1D.jl`
`@su2`	`limiting_case`	🟡 asserted	Luther-Peschel 1975: K=1/2 at the SU(2) isotropic point	`test/models/quantum/XXZ/test_XXZ1D.jl`
`@sweep`	`ed_finite_size`	🟢 structural	"Independent sparse-ED bipartite-fluctuation extraction at N ∈ $([8, 10, 12, 14]), 1/N-extrapolated (Rachel-LeHur 2012; Song-Rachel-LeHur 2010) — cross-checks the Bethe-ansatz closed form K(Δ) = π / (2(π − arccos Δ))"	`test/verification/heisenberg_xxz/test_xxz_luttinger_ed.jl`
`@sweep`	`ed_finite_size`	🟢 structural	"Independent sparse-ED bipartite-fluctuation extraction at N ∈ $([8, 10, 12, 14]), 1/N-extrapolated (Rachel-LeHur 2012; Song-Rachel-LeHur 2010) — cross-checks the Bethe-ansatz closed form K(Δ) = π / (2(π − arccos Δ))"	`test/verification/heisenberg_xxz/test_xxz_luttinger_ed.jl`
`@sweep`	`ed_finite_size`	🟢 structural	"Independent sparse-ED bipartite-fluctuation extraction at N ∈ $([8, 10, 12, 14]), 1/N-extrapolated (Rachel-LeHur 2012; Song-Rachel-LeHur 2010) — cross-checks the Bethe-ansatz closed form K(Δ) = π / (2(π − arccos Δ))"	`test/verification/heisenberg_xxz/test_xxz_luttinger_ed.jl`
`@sweep`	`second_closed_form`	🟢 structural	Haldane 1980: K = π / (2(π - arccos Δ)) for the critical XXZ chain	`test/verification/heisenberg_xxz/test_xxz_luttinger_ed.jl`
`@sweep`	`second_closed_form`	🟢 structural	Haldane 1980: K = π / (2(π - arccos Δ)) for the critical XXZ chain	`test/verification/heisenberg_xxz/test_xxz_luttinger_ed.jl`
`@sweep`	`second_closed_form`	🟢 structural	Haldane 1980: K = π / (2(π - arccos Δ)) for the critical XXZ chain	`test/verification/heisenberg_xxz/test_xxz_luttinger_ed.jl`
`@sweep`	`second_closed_form`	🟢 structural	Haldane 1980: K = π / (2(π - arccos Δ)) for the critical XXZ chain	`test/verification/heisenberg_xxz/test_xxz_luttinger_ed.jl`

Test calls

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

verify(XXZ1D(; J = 1.0, Δ = 0.0), LuttingerParameter(), Infinite(); route = :second_closed_form, independent = 1.0, agree_within = 1.0e-12, refs = ["Jordan-Wigner free fermion: K=1 at Delta=0"])

verify(XXZ1D(; J = 1.0, Δ = 1.0), LuttingerParameter(), Infinite(); route = :limiting_case, independent = 0.5, agree_within = 1.0e-12, refs = ["Luther-Peschel 1975: K=1/2 at the SU(2) isotropic point"])

verify(XXZ1D(; J = 1.0, -0.5 = -0.5), LuttingerParameter(), Infinite(); route = :ed_finite_size, independent = K_inf, agree_within = 0.03, at = ["Δ=$(-0.5)", "Ns=$([8, 10, 12, 14])"], refs = ["Independent sparse-ED bipartite-fluctuation extraction at N ∈ $([8, 10, 12, 14]), 1/N-extrapolated (Rachel-LeHur 2012; Song-Rachel-LeHur 2010) — cross-checks the Bethe-ansatz closed form K(Δ) = π / (2(π − arccos Δ))"])

verify(XXZ1D(; J = 1.0, 0.0 = 0.0), LuttingerParameter(), Infinite(); route = :ed_finite_size, independent = K_inf, agree_within = 0.03, at = ["Δ=$(0.0)", "Ns=$([8, 10, 12, 14])"], refs = ["Independent sparse-ED bipartite-fluctuation extraction at N ∈ $([8, 10, 12, 14]), 1/N-extrapolated (Rachel-LeHur 2012; Song-Rachel-LeHur 2010) — cross-checks the Bethe-ansatz closed form K(Δ) = π / (2(π − arccos Δ))"])

verify(XXZ1D(; J = 1.0, 0.5 = 0.5), LuttingerParameter(), Infinite(); route = :ed_finite_size, independent = K_inf, agree_within = 0.12, at = ["Δ=$(0.5)", "Ns=$([8, 10, 12, 14])"], refs = ["Independent sparse-ED bipartite-fluctuation extraction at N ∈ $([8, 10, 12, 14]), 1/N-extrapolated (Rachel-LeHur 2012; Song-Rachel-LeHur 2010) — cross-checks the Bethe-ansatz closed form K(Δ) = π / (2(π − arccos Δ))"])

verify(XXZ1D(; J = 1.0, -0.5 = -0.5), LuttingerParameter(), Infinite(); route = :second_closed_form, independent = π / (2 * (π - acos(-0.5))), agree_within = 1.0e-9, refs = ["Haldane 1980: K = π / (2(π - arccos Δ)) for the critical XXZ chain"])

verify(XXZ1D(; J = 1.0, 0.0 = 0.0), LuttingerParameter(), Infinite(); route = :second_closed_form, independent = π / (2 * (π - acos(0.0))), agree_within = 1.0e-9, refs = ["Haldane 1980: K = π / (2(π - arccos Δ)) for the critical XXZ chain"])

verify(XXZ1D(; J = 1.0, 0.5 = 0.5), LuttingerParameter(), Infinite(); route = :second_closed_form, independent = π / (2 * (π - acos(0.5))), agree_within = 1.0e-9, refs = ["Haldane 1980: K = π / (2(π - arccos Δ)) for the critical XXZ chain"])

verify(XXZ1D(; J = 1.0, 1.0 = 1.0), LuttingerParameter(), Infinite(); route = :second_closed_form, independent = π / (2 * (π - acos(1.0))), agree_within = 1.0e-9, refs = ["Haldane 1980: K = π / (2(π - arccos Δ)) for the critical XXZ chain"])

Assurance (provisional)

level: corroborated-at-p 🟢
cards: 9 · model ED-feasible
RES not wired — measured residuals / confidence are not shown yet.

← Model: XXZ1D · Quantity: LuttingerParameter · Atlas index

🟢 XXZ1D/LuttingerParameter/Infinite

src claim

Corroboration

Test calls

Assurance (provisional)

🟢 `XXZ1D/LuttingerParameter/Infinite`

`src` claim