All legal base analyses have width three or four

Exact statement

Across all legal reason choices, $F_1$ has maximum analysis width three; for $m\ge2$ , the attainable maximum widths for $F_m$ are exactly $\{3,4\}$ ; every trace of $G_m$ has maximum width three.

StatusProved in the stated all-schedule model

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

Context

The fixed trace in CRD-SAT-13b has width three, but allowing every reason choice exposes a width-four base trace.

Hypotheses and scope

The databases, decision prefix, and legal trace model are those of CRD-SAT-14a.

Proof or evidence

Every intermediate resolvent contains at most the guards $x,y$ and two adjacent path literals, giving width at most four. A mixed-guard reason and conflict at $m=2$ attains width four. The shortcut in $G_m$ keeps all legal traces within width three. The all-trace checker corroborates the spectrum through $m=8$ .

Hostile width audit →

Verification notes

The width-four witness was checked separately from the pivot-count proof. It refines the earlier fixed-trace statement rather than retracting it.

Limitations

This is not a general resolution-width separation.
Width is measured only along the declared first-UIP analyses.

Open work

Keep the width-four mixed-reason witness visible when comparing the fixed-policy and all-schedule statements.