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Submission note. Posted to the site's forum by Malek Zribi on 30 April 2026:

For the split-core tripod family $A=\{2u,3v,uv\}$ with $\gcd(u,v)=1$, $v\geq 3$ odd, $u\geq 4$, and $3\nmid u$, EP-488 holds: $B_A(n,m) := 2m,F_A(n) - n,F_A(m) > 0$ for all integers $m > n \geq uv$. This includes every prime witness tripod $\{2p,3q,pq\}$ with distinct odd primes $p,q>3$. The family is primitive but not $2$-primitive, since $uv$ divides $(2u)(3v)$; a first-pass literature search located no explicit prior treatment of this exact family.

Note (PDF, 5 pages): note Prepared with 5.5 Pro; the math has been verified by hand and by an independent audit script.

The claim. Theorem 1 of the note EP-488 for Split-Core Tripods, dated 30 April 2026 and signed Malek Z: for $A=\{2u,3v,uv\}$ with $\gcd(u,v)=1$, $v\ge3$ odd, $u\ge4$ and $3\nmid u$, the set $A$ is primitive with $\max A=uv$, and the inequality of Problem 488 holds for all integers $m>n\ge uv$, in the form $2mF_A(n)-nF_A(m)>0$ with $F_A(x)$ the number of positive integers up to $x$ divisible by a member of $A$. The proof: the lcm pattern $[2u,uv]=2uv$, $[3v,uv]=3uv$ and $[2u,3v]=[2u,3v,uv]=6uv$ makes the pair overlap of $2u$ and $3v$ cancel against the triple overlap in inclusion--exclusion, so $F_A(x)=\lfloor x/2u\rfloor+\lfloor x/3v\rfloor+\lfloor x/a\rfloor-\lfloor x/2a\rfloor-\lfloor x/3a\rfloor$ with $a=uv$; the terms for $2u$ and $3v$ contribute positively, since $2m\lfloor n/d\rfloor>n\lfloor m/d\rfloor$ whenever $m>n\ge d$; and the three remaining terms reduce, with $W(k)=k-\lfloor k/2\rfloor-\lfloor k/3\rfloor$, $q=\lfloor n/a\rfloor$ and $t=\lfloor m/a\rfloor$, to $2tW(q)\ge(q+1)W(t)$ for $1\le q<t$, proved from the residue formula for $W$ with a finite check for $q\le7$. The note's comment says it was prepared with 5.5 Pro and that the mathematics was verified by hand and by an independent audit script, the claimant's own. A computational search reported in the note's last section, on a conjectured ratio bound over $2{,}781{,}110$ primitive sets with no violation, is evidence around the problem and not part of the claim.

Covers. The problem's inequality for the family $\{2u,3v,uv\}$ under the stated hypotheses, which include every tripod $\{2p,3q,pq\}$ with distinct odd primes $p,q>3$. Not covered, as the note says: other primitive sets, families of several tripods, and the cases where one of the hypotheses fails. The family has three primitive elements, so it lies inside the class that Chojecki's note covers by a different argument; the note reports that a first literature search found no prior treatment of the family.

Standing. Claimed. The note was posted in the site's discussion thread on 30 April 2026 and not to the proof-claim tab; the site's label and commentary (last edited 8 April 2026) do not mention it, the comment drew no reply, and no outside review is on record.

Depends on. Nothing in this wiki: the claim rests on its own note.