The symbolic C7 compiler does not improve the Shannon-capacity bound

Exact statement

The table-free base reconstruction, constant-template product DAG, and 192,771-state canonical symbolic lowering give a complete path-language presentation of Gao's known 200-dimensional code. They do not improve $\Theta(C_7)$ , prove DFA minimality, or realize the code as a small last-signature image. Further minimization of this presentation is not presently a literature-recognized open problem.

StatusExact scope boundary recorded

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

Context

A compact compiler explains the presentation cost of a known finite code; it does not by itself change the unresolved Shannon capacity of C7.

Proof or evidence

The compiler denotes Gao's code exactly, while the current stronger lower bound belongs to Buys, Polak, and Zuiddam. Cardinality separately prevents sub-output last-signature compression.

C7 compiler stopping boundary →

Verification notes

Public statements separate known construction, FPRD presentation cost, unproved minimality, and the external numerical record.

Limitations

This is a stopping decision, not a mathematical impossibility theorem for every automata model.

Open work

Study exact XCC algorithms parameterized by support-family diversity.