2316 — Black-Box Reachability Cannot Controlize the D(S3) Sector Unitary
Verdict
Uncontrolled access to a unitary U cannot uniformly supply ctrl(U). The
replacement U -> exp(i phi) U is only a global phase for every fixed-query
uncontrolled circuit, but becomes a measurable relative phase between the
two control branches after controlization. Uncontrolled Lie reachability of
the central D(S3) pulse therefore does not derive the controlled powers
needed by sector phase estimation.
An exact source-honest repair is either the conditional Hamiltonian
which implements the powers 1,2,4 in three conditional pulses, or controlled
access to every primitive in a named exact timed word for U. The latter
word and the physical conditional coupling remain unresolved.
Scope
This is a black-box impossibility theorem and a minimal conditional repair, not a no-go for hardware that supplies controlled microscopic interactions. Controlization preserves data support but adds one control system to total support and interaction arity.
Durable verification
- Packet:
research/kitaev/s3-controlled-power-controlization-boundary.md - Checker:
uv run --with sympy python research/kitaev/checkers/check_s3_controlization_boundary.py - Result:
research/kitaev/results/s3-controlization-boundary.json - Exact gates: phase ambiguity, all three conditional powers, controlled-word composition, eight distinct residues, and locality typing
- Epistemic graph:
ev-000000003182-c7704c71-cb0b-4eb7-9e5c-dee0c25aae6a - Ledger allocation:
seqclaim-c36cc44f4813b200aed6a306