Four-state binary actions had an n-minus-one pattern

Exact statement

Exhaustive enumeration of unordered pairs of distinct transformations on $n=2,3,4$ states found maximum shortest-word diameters $1,2,3$ , respectively, among the binary L-trivial semiautomata that admit a minimal DFA final set.

StatusFinite exhaustive evidence through four states; the inferred pattern is refuted at five states

External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

The observed pattern motivated an n-minus-one conjecture. The five-state classification in FPRD-LT-E02 refutes that extrapolation while preserving the exact smaller counts.

Hypotheses and scope

Exactly two distinct complete generators are used.
A semiautomaton is retained only when some final-state set makes the resulting DFA minimal.

Proof or evidence

Each generated monoid, its principal left ideals, candidate final sets, and breadth-first distances from the identity were checked by exact finite tuple operations.

Enumeration method and results →

Verification notes

The stored report gives the exhaustive method and aggregate counts but does not identify a separately preserved executable output for independent reproduction.

Limitations

The search stops at four states and does not cover variable alphabet size.
The n-minus-one pattern does not continue to five states.

Open work

Retain these counts as the completed four-state baseline; use FPRD-LT-E02 for the five-state classification.