2425 — Nonlinear Source Dynamics Explains the Logical D(S3) Capability Boundary
Verdict
The source-authorized capability principle now has a generative D(S3) instance. Independently declared occupation interactions generate the missing record phases, while a conditional qutrit exchange pulse generates controlled inversion exactly. A three-body occupation pulse independently generates CCZ, hence Toffoli and the same controlled inversion through a binary embedding.
Hostile sources with unchanged Hilbert-space support but erased controls, wrong pulse angles, or missing label couplings fail the exact target operations. The explanation therefore depends on source dynamics rather than restating that the gates are unavailable in the stabilizer theory.
The direct physical lift is nevertheless falsified on the frozen five-rail codes. The hybrid exchange, controlled-T, and controlled-S transversal pulses have maximum codespace leakage norms (0.99344398), (0.66487330), and (0.95491635). Rail-local fault spread is not code preservation. The logical capability is source-explained; the full physical compiler remains conditional on verified encoded injection or an explicit code-switch intertwiner.
Scope
This is a proper generative explanation of the logical capability boundary, not a completed magic factory or executable five-rail fault-tolerance theorem.
Durable verification
- Packet:
research/kitaev/dpc-source-generated-d-s3-capability.md - Consolidated checker:
research/kitaev/checkers/check_s3_dpc_explanation_audit.py - Consolidated result:
research/kitaev/results/s3-dpc-explanation-audit.json - Component checkers replayed: 4
- Graph claim:
claim:ff518eb5a5c72ef3a36f - Graph admission:
ev-000000003315-8d630deb-f2c2-4990-af4a-21da43959fd5 - Ledger allocation:
seqclaim-1214a86c45b3be34302bf2cd