FPRD LabShare an approach

← Claims

Counterexample · scheduling obstruction

CRD-SAT-F14

An available shortcut need not be used

Exact statement

Retaining the absorbed shortcut LL does not guarantee that every legal propagation and reason schedule realizes the one-pivot conflict analysis.

StatusRefuted by a legal long trace in the augmented family
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

Adding a shorter reason path changes the trace space but does not delete the original long path.

Hypotheses and scope

  • The augmented database GmG_m and legal trace model are those of CRD-SAT-14a.

Proof or evidence

A legal schedule can postpone both endpoint clauses, propagate v0,v1,…,vmv_0,v_1,\ldots,v_m along the original forward chain, and then select the old conflict. This produces the same m+1m+1-pivot analysis available in FmF_m, even though one-pivot traces also exist.

Delayed-shortcut countertrace →

Verification notes

The countertrace is included in the exact spectrum proof and preserves the distinction between minimum and maximum cost.

Limitations

  • The result does not say that practical heuristics usually ignore the shortcut.
  • It concerns guaranteed cost over all legal schedules, not the existence of a shorter proof.

Open work

Do not translate best available proof work into a guaranteed runtime improvement without a policy theorem.