2329 — A Lower-Arity D(S3) Sector Bus Still Needs Three Charge Predicates and Four-Edge Support
Verdict
Gauge-invariant phases on the existing six-level holonomy bus are class
functions and force the collision blocks A/B/C, D/E, and F/G/H. A
one-shot clean bus for eight distinct sector phases needs dimension at least
eight.
Sequential qubit reuse needs three binary rounds. Exhaustion of all 40,320 three-bit labelings shows that every coordinate splits a flux class, so all three predicates require charge-sensitive information. No relabeling moves one round onto a holonomy-only interface.
Every exact labeler must also touch all four boundary edges. A standard clean compute--phase--uncompute bus therefore starts at four forward and four reverse edge interactions plus one phase gate, before charge overhead.
Durable verification
- Packets:
research/kitaev/s3-holonomy-bus-versus-sector-label.md,research/kitaev/s3-sequential-charge-predicate-lower-bound.md, andresearch/kitaev/s3-sector-bus-four-edge-support-bound.md - Exact checker results: six class/ancilla gates, five exhaustive labeling gates, and five edge-support gates
- Epistemic graph:
ev-000000003192-5c8ef1d1-4479-420c-9146-9624adf7785c - Ledger allocation:
seqclaim-496cfaf8a87801087000578f