🟢 RiceMele/MassGap/Infinite
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
analytic, statusexact, reliabilityhigh, refs: RiceMele1982 - "min_k E₊(k) = √((|v|−|w|)² + Δ²), Fermi level to band edge; the band gap is 2×. " * "SSH's convention, to which it reduces at Δ = 0. Never zero for Δ ≠ 0."
Corroboration
| regime | mechanism | independence | refs | file |
|---|---|---|---|---|
@sweep | second_closed_form | 🟢 structural | Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊ | test/models/quantum/misc/test_ricemele.jl |
@sweep | second_closed_form | 🟢 structural | Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊ | test/models/quantum/misc/test_ricemele.jl |
@sweep | second_closed_form | 🟢 structural | Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊ | test/models/quantum/misc/test_ricemele.jl |
@sweep | second_closed_form | 🟢 structural | Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊ | test/models/quantum/misc/test_ricemele.jl |
@sweep | second_closed_form | 🟢 structural | Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊ | test/models/quantum/misc/test_ricemele.jl |
@sweep | second_closed_form | 🟢 structural | Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊ | test/models/quantum/misc/test_ricemele.jl |
Test calls
The exact verify(...) call the harness executed for this hub (reconstructed from the test AST):
verify(RiceMele(; 0.75, 0.25, 0.1), MassGap(), Infinite(); route = :second_closed_form, independent = minimum((sqrt(0.75 ^ 2 + 0.25 ^ 2 + 2 * 0.75 * 0.25 * cos(k) + 0.1 ^ 2) for k = range(-π, π; length = 400001))), agree_within = 1.0e-9, refs = ["Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊"])verify(RiceMele(; 0.25, 0.75, 0.1), MassGap(), Infinite(); route = :second_closed_form, independent = minimum((sqrt(0.25 ^ 2 + 0.75 ^ 2 + 2 * 0.25 * 0.75 * cos(k) + 0.1 ^ 2) for k = range(-π, π; length = 400001))), agree_within = 1.0e-9, refs = ["Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊"])verify(RiceMele(; 1.0, 1.0, 0.3), MassGap(), Infinite(); route = :second_closed_form, independent = minimum((sqrt(1.0 ^ 2 + 1.0 ^ 2 + 2 * 1.0 * 1.0 * cos(k) + 0.3 ^ 2) for k = range(-π, π; length = 400001))), agree_within = 1.0e-9, refs = ["Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊"])verify(RiceMele(; -0.5, 0.7, 0.2), MassGap(), Infinite(); route = :second_closed_form, independent = minimum((sqrt((-0.5) ^ 2 + 0.7 ^ 2 + 2 * -0.5 * 0.7 * cos(k) + 0.2 ^ 2) for k = range(-π, π; length = 400001))), agree_within = 1.0e-9, refs = ["Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊"])verify(RiceMele(; 0.6, -1.0, -0.4), MassGap(), Infinite(); route = :second_closed_form, independent = minimum((sqrt(0.6 ^ 2 + (-1.0) ^ 2 + 2 * 0.6 * -1.0 * cos(k) + (-0.4) ^ 2) for k = range(-π, π; length = 400001))), agree_within = 1.0e-9, refs = ["Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊"])verify(RiceMele(; 1.0, 0.0, 0.5), MassGap(), Infinite(); route = :second_closed_form, independent = minimum((sqrt(1.0 ^ 2 + 0.0 ^ 2 + 2 * 1.0 * 0.0 * cos(k) + 0.5 ^ 2) for k = range(-π, π; length = 400001))), agree_within = 1.0e-9, refs = ["Rice & Mele 1982: E₊(k) = √(v²+w²+2vw cos k + Δ²), gap = min_k E₊"])Assurance (provisional)
- level: corroborated-at-p 🟢
- cards: 6 · model ED-feasible
- RES not wired — measured residuals / confidence are not shown yet.