Marginal capacities discard the decisive correlation

Exact statement

The marginal cap $m_u=\min(N_u^{\mathrm{cap}},W_u)$ records how many guard slots and fixed-weight tails exist, but not which tail occupies which slot or its actual disorder; it is therefore insufficient by itself to resolve the forced-continuation frontier.

StatusSubstantiated as a limitation; the replacement joint statistic remains open

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

Context

Taking the minimum of two marginal counts repairs a simple overcount but erases the matching between arithmetic slots and combinatorial continuations.

Proof or evidence

The LF5 family shows that capacity-one marginals can survive without loss, while C03 identifies actual forced-suffix disorder as the unresolved variable. This establishes the limitation, not a complete impossibility theorem for every refinement.

Why the marginal cap loses the matching →

Verification notes

The page distinguishes a failed abstraction from a theorem that no useful refinement exists.

Limitations

The capped potential remains an exact upper bound and finite pruning tool.
A richer joint refinement may still succeed.

Open work

Track the joint assignment of exact guards to actual forced suffix deficits.