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🟢 Kitaev1D/TopologicalInvariant/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 pfaffian, status exact, reliability high, refs: Kitaev2001 | AsbothOroszlanyPalyi2016
  • ν = sgn[Pf A(k=0)·Pf A(k=π)] = sgn(μ² - 4t²); ν=-1 topological, +1 trivial.

Corroboration

regimemechanismindependencerefsfile
@sweepsecond_closed_form🟢 structural"Kitaev 2001; Asboth-Oroszlany-Palyi 2016: ν = sgn(μ²-4t²) " * "(-1 topological, +1 trivial)"test/models/quantum/misc/test_kitaev1d.jl
@sweepsecond_closed_form🟢 structural"Kitaev 2001; Asboth-Oroszlany-Palyi 2016: ν = sgn(μ²-4t²) " * "(-1 topological, +1 trivial)"test/models/quantum/misc/test_kitaev1d.jl
@sweepsecond_closed_form🟢 structural"Kitaev 2001; Asboth-Oroszlany-Palyi 2016: ν = sgn(μ²-4t²) " * "(-1 topological, +1 trivial)"test/models/quantum/misc/test_kitaev1d.jl
@sweepsecond_closed_form🟢 structural"Kitaev 2001; Asboth-Oroszlany-Palyi 2016: ν = sgn(μ²-4t²) " * "(-1 topological, +1 trivial)"test/models/quantum/misc/test_kitaev1d.jl
@sweepsecond_closed_form🟢 structural"Kitaev 2001; Asboth-Oroszlany-Palyi 2016: ν = sgn(μ²-4t²) " * "(-1 topological, +1 trivial)"test/models/quantum/misc/test_kitaev1d.jl
@sweepsecond_closed_form🟢 structuralKitaev 2001 Pfaffian Z2: ν = sgn(μ² − 4t²) on the gapped phasestest/models/quantum/misc/test_kitaev1d.jl
@sweepsecond_closed_form🟢 structuralKitaev 2001 Pfaffian Z2: ν = sgn(μ² − 4t²) on the gapped phasestest/models/quantum/misc/test_kitaev1d.jl
@sweepsecond_closed_form🟢 structuralKitaev 2001 Pfaffian Z2: ν = sgn(μ² − 4t²) on the gapped phasestest/models/quantum/misc/test_kitaev1d.jl
@sweepsecond_closed_form🟢 structuralKitaev 2001 Pfaffian Z2: ν = sgn(μ² − 4t²) on the gapped phasestest/models/quantum/misc/test_kitaev1d.jl

Test calls

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

verify(Kitaev1D(; 0.0 = 0.0, 1.0 = 1.0, 1.0 = 1.0), TopologicalInvariant(), Infinite(); route = :second_closed_form, independent = sign(0.0 ^ 2 - 4 * 1.0 ^ 2), agree_within = 1.0e-12, refs = ["Kitaev 2001; Asboth-Oroszlany-Palyi 2016: ν = sgn(μ²-4t²) " * "(-1 topological, +1 trivial)"])
verify(Kitaev1D(; 1.5 = 1.5, 1.0 = 1.0, 1.0 = 1.0), TopologicalInvariant(), Infinite(); route = :second_closed_form, independent = sign(1.5 ^ 2 - 4 * 1.0 ^ 2), agree_within = 1.0e-12, refs = ["Kitaev 2001; Asboth-Oroszlany-Palyi 2016: ν = sgn(μ²-4t²) " * "(-1 topological, +1 trivial)"])
verify(Kitaev1D(; -1.5 = -1.5, 1.0 = 1.0, 0.5 = 0.5), TopologicalInvariant(), Infinite(); route = :second_closed_form, independent = sign((-1.5) ^ 2 - 4 * 1.0 ^ 2), agree_within = 1.0e-12, refs = ["Kitaev 2001; Asboth-Oroszlany-Palyi 2016: ν = sgn(μ²-4t²) " * "(-1 topological, +1 trivial)"])
verify(Kitaev1D(; 3.0 = 3.0, 1.0 = 1.0, 1.0 = 1.0), TopologicalInvariant(), Infinite(); route = :second_closed_form, independent = sign(3.0 ^ 2 - 4 * 1.0 ^ 2), agree_within = 1.0e-12, refs = ["Kitaev 2001; Asboth-Oroszlany-Palyi 2016: ν = sgn(μ²-4t²) " * "(-1 topological, +1 trivial)"])
verify(Kitaev1D(; -2.5 = -2.5, 1.0 = 1.0, 1.0 = 1.0), TopologicalInvariant(), Infinite(); route = :second_closed_form, independent = sign((-2.5) ^ 2 - 4 * 1.0 ^ 2), agree_within = 1.0e-12, refs = ["Kitaev 2001; Asboth-Oroszlany-Palyi 2016: ν = sgn(μ²-4t²) " * "(-1 topological, +1 trivial)"])
verify(Kitaev1D(; 0.0 = 0.0, 1.0 = 1.0, 1.0 = 1.0), TopologicalInvariant(), Infinite(); route = :second_closed_form, independent = -1, agree_within = 0, refs = ["Kitaev 2001 Pfaffian Z2: ν = sgn(μ² − 4t²) on the gapped phases"])
verify(Kitaev1D(; 0.5 = 0.5, 1.0 = 1.0, 1.0 = 1.0), TopologicalInvariant(), Infinite(); route = :second_closed_form, independent = -1, agree_within = 0, refs = ["Kitaev 2001 Pfaffian Z2: ν = sgn(μ² − 4t²) on the gapped phases"])
verify(Kitaev1D(; 3.0 = 3.0, 1.0 = 1.0, 1.0 = 1.0), TopologicalInvariant(), Infinite(); route = :second_closed_form, independent = 1, agree_within = 0, refs = ["Kitaev 2001 Pfaffian Z2: ν = sgn(μ² − 4t²) on the gapped phases"])
verify(Kitaev1D(; -3.0 = -3.0, 1.0 = 1.0, 0.5 = 0.5), TopologicalInvariant(), Infinite(); route = :second_closed_form, independent = 1, agree_within = 0, refs = ["Kitaev 2001 Pfaffian Z2: ν = sgn(μ² − 4t²) on the gapped phases"])

Assurance (provisional)

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

← Model: Kitaev1D · Quantity: TopologicalInvariant · Atlas index