The Pauli Algebra Closes
Theorem.The Pauli Algebra Closes.
Proof.The operator algebra closes: with the associative product (gateMul), the Lie bracket (commutator), the Jordan product (anticommutator), the trace and the adjoint, the Pauli defining relations all hold exactly — σ_i² = I, {σ_i,σ_j} = 2δ_ij I, [σ_i,σ_j] = 2i ε_ijk σ_k, σ_i† = σ_i, tr σ_i = 0 — so su(2) ⊂ M₂(ℂ) is a complete, self-verifying *-algebra, not just a product and a bracket.
Checked by exact arithmetic over the stated finite range — a verified witness, evidence toward the claim, not a ∀-proof.
src/9/1 pauliAlgebraCloses/index.ts#pauliAlgebraCloses
1 · Classification
bounded-witness — morph from sealed card/discovery fold
2 · Provenance
cardScientificPaperRows ← src/9/1 pauliAlgebraCloses
Acknowledgment
"The Pauli Algebra Closes" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation pauliAlgebraCloses.
- Prior art
- documented mathematics — the original proof is the prior art this re-derivation acknowledges
- Novelty
- not new to humanity — a re-derivation (humanityNovel = false)
- Contribution
- a reproducible computation (pauliAlgebraCloses @ src/9/1 pauliAlgebraCloses) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem
3 · Reproducibility
recompute pauliAlgebraCloses · npm run quantum:card-paper-links · paperRoute=/theorems/pauli-algebra-closes