2519 — CDFG Has an Exact Lockstep Interface Normal Form
Exact reordering theorem
The CDFG interaction layer has 21 Boolean-predicate-controlled (Z_4^c) terms. All are diagonal in the common three-bit data and four-pointer residue basis. Exact enumeration of all (2^3 4^4=2048) basis states gives zero phase residual modulo four between compiler, reverse, predicate-grouped, and odd/even-grouped orders.
Therefore all CDFG interactions admit one synchronized digit-exposed window. The ideal circuit algebra itself authorizes the two-state lockstep selector orbit; mixed native/binary configurations are not required by interaction ordering.
Correction and surviving boundary
Ledger 2518's 16-state and four-bit lower bound applies when port switching must be independent. The exact CDFG layer does not impose that requirement. What remains unresolved is physical: the synchronized interface is a joint channel on four encoded pointer blocks, with a common-cause fault root and no derived cost or exRec. Native (F_4) layers are not commuted through the interaction window.
Scope
This is an ideal-unitary scheduling normal form. It neither constructs the four-block code switch nor makes the conditional (83T)-equivalent interface allowance executable.
Durable verification
- Packet:
research/kitaev/s3-lockstep-interface-normal-form.md. - Checker:
uv run python research/kitaev/checkers/check_s3_lockstep_interface_normal_form.py. - Result:
research/kitaev/results/s3-lockstep-interface-normal-form.json. - Result SHA256:
6822F9D9283E24292E442C8F2836829971EDDAED85A2FFD365C0A368DF19D265. - Graph admission:
ev-000000003489-14d9df04-462e-431b-8cd1-65479299c759. - Ledger allocation:
seqclaim-f8df6cb678a0b7a9ccff44de.