The 367-word C7 base code has a table-free three-bit compiler

Exact statement

The published 367-word independent set in $C_7^{\boxtimes5}$ can be reconstructed without storing its vectors. The cyclic 382-word precursor and conflict filter leave 327 words. The 71-vertex, 85-edge extension graph has exactly eight maximum independent sets of size 40: they share a 37-word core and differ by one endpoint choice on each of three disjoint conflict edges. Three selector bits recover the published extension.

StatusIndependent reconstruction and exact maximum-set enumeration pass

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

Context

This result replaces a stored table of 367 five-letter words by an exact arithmetic generator and three binary choices, making the published base code reproducible as a path language.

Proof or evidence

Exact arithmetic generates 382 distinct words, the published conflict rule leaves 327, and an exhaustive coloring-bound clique search proves that every maximum 40-word extension is the common 37-word core plus three binary choices.

Table-free 367-code compiler →

Verification notes

The verifier visits 383 exact clique-search nodes, finds all eight maximum extensions, and reconstructs the published code with SHA-256 a8d96cb1593aa03058e781c819a5254895ccae4dfc05f35a4ef3e89e6566c9e4.

Limitations

This is a compact presentation of the published code, not a larger independent set or a new Shannon-capacity bound.
The compiler is a path-language generator; it does not realize 367 tuples as one-step last signatures of fewer than 367 states.

Open work

Treat the generated typed package, rather than a 367-vector input file, as the leaf of Gao's recursive compiler.