Weak synchronization needs backward memory

Exact statement

The published weak synchronized location construction records forward memory $\Delta,\Lambda$ for solo synchronized letters since the last joint event. A prefix construction based on last events instead needs a dual receipt describing allowable solo synchronized letters until the next joint event; reusing the forward memory does not by itself define that automaton.

StatusRequirement discharged by the proved reversal-dual construction

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

Context

Weak synchronization lies between strong and arbitrary behavior, but its automaton state carries directional history.

Proof or evidence

The location construction asks what has happened since the previous synchronization; the prefix recursion asks what may happen before the next synchronization. These are dual questions and require an explicit conversion proof.

Weak-synchronization boundary →

Verification notes

The subsequent reversal construction supplies the missing conversion and the exact unary checker confirms the induced three-state receipt discipline.

Limitations

This record states the prerequisite, not the completed construction and classification recorded separately on this page.
The resolved boundary still prevents forward memory from being reused without the reversal-dual proof.

Open work

Retain the directionality distinction when extending the receipt beyond the unary family.