C3 MEASURED: positional chirality is Sidon-invariant for powers-of-2
labels. CRT embedding is redundant when input is already Sidon.
BUT: the framework is modular BECAUSE different stages are optimal
in different regimes. The encode engine is a MODULE, not a universal
preprocessor:
- Already-Sidon input: skip CRT, use direct check (redundant)
- Non-Sidon input: CRT wrapping CREATES Sidon (primary value)
- Geometric regime: use dual quaternion products (different filter)
- Quantum regime: use COUCH tractability (not Sidon-based)
The octagon principle requires regime matching: match the spectral
embedding to the regime, then filter. Forcing all inputs through
one pipe is the failure mode.
New conjecture C11: test CRT wrapping on non-Sidon input at scale.
If wrapping creates Sidon → engine is needed for that regime.
If not → wrapping doesn't work at scale.
