feat(QuantumInfo): cyclic symmetry for Bargmann invariant and phase#1133
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jstoobysmith merged 1 commit intoMay 29, 2026
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Add `bargmannInvariantThree_cyclic` and `bargmannPhaseThree_cyclic`, proving that cyclic permutation of the three states preserves both the Bargmann invariant and its geometric phase. Also fix unused `DecidableEq` section variable warnings across all existing lemmas and drop the unused non-zero hypothesis from `bargmannPhaseThree_reverse`. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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This looks good - approved
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Summary
bargmannInvariantThree_cyclic: cyclic permutation(ψ₂, ψ₃, ψ₁)preservesΔ₃, proved byringbargmannPhaseThree_cyclic: cyclic permutation preserves the geometric phase, via rewriteDecidableEqsection variable warnings on all existing lemmas (omit [DecidableEq d] in)hfrombargmannPhaseThree_reverse—Complex.arg_conj_coe_angledoes not require itContext
Cyclic invariance is a fundamental property of the Bargmann invariant: since
Δ₃ = ⟨ψ₁|ψ₂⟩ · ⟨ψ₂|ψ₃⟩ · ⟨ψ₃|ψ₁⟩is a cyclic product, permuting(1,2,3) → (2,3,1)is an algebraic identity. Together with the existing_reverselemma (anti-cyclic order conjugates), this completes the symmetry group of the three-vertex invariant.Build
Zero warnings, zero errors on
lake build QuantumInfo.Finite.GeometricPhase.BargmannInvariant.🤖 Generated with Claude Code