Escape from every compact core characterizes failed sewing

Exact statement

For an increasing compact exhaustion $S_{r,t}\uparrow S_r$ , exact membership in a core is equivalent to infinite escape modulus, while feasibility through every horizon is equivalent to unbounded escape moduli across the cores. Thus finite-horizon fitting fails to sew exactly at resource $r$ precisely when every core is excluded at some finite horizon but those exclusion horizons are unbounded.

StatusProved and internally audited

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

Context

Compact cores turn the abstract failure of quantifier exchange into a measurable escape pattern.

Definitions

$e_x(r,t)=\min\{N:q_N(x)\notin q_N(S_{r,t})\}$ , with value $\infty$ if no such horizon exists.

Hypotheses and scope

The compact cores are target-independent, increasing in t, and exhaust S_r.
Observation maps are compatible across horizons.

Proof or evidence

Compact sewing applies inside each core. Taking the union over cores yields the equivalences; a horizon-fitting sequence must permanently leave a fixed core once it passes that core's escape horizon.

Escape characterization →

Verification notes

The proof and an independent reconstruction were reconciled. Review corrected the scope from arbitrary sequences to sequences that actually fit progressively deeper horizons.

Limitations

The eventual-departure conclusion does not apply to arbitrary sequences of presentations.
Demand divergence across different bounds is not itself a fixed-bound sewing defect.

Open work

Find natural presentation classes with a genuine fixed-resource sewing defect, rather than demand that merely diverges across resource bounds.

Notes

The eventual-departure conclusion applies to presentations fitting progressively deeper horizons. It is not asserted for arbitrary sequences, and a failed compiler or bounded computation is not evidence.