Covering finite handles

The existing record is in ../PROBLEM.md. This leaf was reconstructed on 2026-09-10. The current request reopens covering-code constructions beyond the settled OK37 partition obstruction.

Leaf	Campaign	Status	Finite handle / outcome
radius2-r10-n49-block	q9	residue	Single quotient-block replacements left undecided cases; no 49-column matrix.
radius2-r10-n49-aut	q10	residue	Odd-order exclusions leave the 2-group case; no 49-column matrix.
radius2-fibered	q11	residue	Fibered-family searches leave r=9, n=38 unresolved; no improvement.
radius3-ok37-p17	q12	residue	Min (3,0)-partition of OK37 is p=18 (Cadical); all p≤17 UNSAT; no dependent triples ⇒ ℓ≥1 impossible. QM_4^3 m=4 needs p≤17 for n=607 — does not apply.
radius3-r44-qm43-from817	q13	certified	$\ell_2(44,3)\le52351<52415$ : the inherited 34-block $(3,0)$ -partition and its 65-block refinement cover all $2^{26}$ seed syndromes; the QM $_4^3$ identity is checked column by column.
radius2-r10-n49-local-switch	q14	residue	All 1,194,375 two-delete/one-add candidates have at least 9 holes; no three-delete/two-add switch covers all syndromes. Local to the 50-set; $n=49$ remains open.
radius3-r41-qm43-merge817	q16	certified	Two of 561 block pairs merge validly; the (7,31) merge gives a 33-block $(3,0)$ -partition and $\ell_2(41,3)\le26175<26238$ (31 below the notebook's 26206). Full $2^{26}$ seed sweep and independent lift identity check.
radius3-r26-delete817	q16	blocked	All 817 columns are essential: each occurs in a unique representation of some syndrome, both for the 33-block partition and without block restrictions. No one-column deletion can retain radius 3.
radius3-r24-small-seed	q16	open	Search a new $r=12$ radius-3 seed with a $p\le17$ $(3,0)$ -partition and $n\le37$ ; the settled OK37 seed cannot meet $p\le17$ .
radius2-r10-n49-two-block	q16	open	Test simultaneous replacements of two quotient blocks of the certified 50-set, outside q9's single-block replacement family.
radius3-r47-qm43-from817	q15	certified	A 129-block refinement of the 817-column seed gives $\ell_2(47,3)\le104703<104831$ (paper). Output matrix checked column by column; seed covered by a full $2^{26}$ sweep. The companion $\ell_2(41,3)\le26175$ via merge 15+24 coincides with q16.

Earlier certified constructions and their replays remain indexed in ../PROBLEM.md; their campaign directories predate this leaf.