The pentagon twist has a six-state reachable expression realization

Exact statement

For the optional-once five-cycle expression, the useful component-prefix product has 11 states and the natural prefix automaton has 16. Synchronizing it with the copy relabelled by $i\mapsto2i\pmod5$ has only six reachable natural-prefix states; its five noninitial last-signature pairs are exactly $\{(i,2i):i\in\mathbb Z_5\}$ , a nonrectangular independent set of size five in $C_5^{\boxtimes2}$ .

StatusExplicit expression, exact state/transition counts, and executable audit

External reviewNo documented external or specialist review of these FPRD results is recorded.

Context

The calibration asks whether a prefix expression can see the twisted section, not whether tensor supports already contain five code letters.

Proof or evidence

The two copies have 16 natural-prefix states each, but synchronization and the complementing relabelling leave only the initial state and five correlated one-event states. Both coordinate projections have size five, so the section is not a rectangle.

Reachable pentagon twist →

Verification notes

The verifier checks the 11/16 one-layer counts, all 15 transitions, the ambient 256-state square, the six reachable states, five projected signatures, and the equivalent flat ten-participant construction.

Limitations

This realizes the classical C5 code and does not improve Shannon capacity.
The construction lists five macro-events; its importance is semantic calibration, not asymptotic compression.

Open work

Use this as calibration while defining a nonvacuous succinct-generator resource.