Unverified LLM-generated attempt. Automated screening checks form, honesty and scope, not correctness. Status at erdosproblems.com: open. Claims here do not change the source status.
Erdős #643; independent attempt, 2026-09-23. The target concerns the forcing size $f(n;t)$ for four distinct $t$-edges $A,B,C,D$ with $A\sqcup B=C\sqcup D$, particularly whether $f(n;t)=(1+o(1))\binom n{t-1}$ for every fixed $t\ge3$. I read all of 643.tex, which identifies the $t=3$ forbidden hypergraph. I extend that classification to all uniformities, keeping the extra intersection types explicit.
WORK: THE COMPLETE FINITE FORBIDDEN FAMILY
For $1\le r\le\lfloor t/2\rfloor$, define $H_{t,r}$ using four disjoint blocks $X_{11},X_{12},X_{21},X_{22}$ of sizes $r,t-r,t-r,r$. Its edges are the two row unions and the two column unions. Then the generalized four-cycle condition is exactly the presence of one of these hypergraphs. Indeed, given $A\sqcup B=C\sqcup D$, take the four intersections $A\cap C,A\cap D,B\cap C,B\cap D$. If $r=|A\cap C|$, their sizes are $r,t-r,t-r,r$. Distinctness of the edges excludes $r=0,t$. Interchanging $C,D$ replaces $r$ by $t-r$, allowing $r\le t/2$. Conversely the rows and columns of each such block construction are distinct disjoint complementary edge pairs with the same union. Therefore \[
f(n;t)-1=\operatorname{ex}\left(n,\{H_{t,r}:1\le r\le\lfloor t/2\rfloor\}\right).
\] For $t=3$ there is just $r=1$, recovering the supplied reduction. For $t=4$, $r=1$ and $r=2$ are different: their nonzero pairwise edge intersections have sizes $1,3$ versus $2,2$, respectively. Thus one cannot extrapolate the single forbidden type from rank three.
ADVERSARIAL VERIFICATION AND REMAINING GAP
The embedding is ordinary subhypergraph containment; extra ambient edges do not matter. All four blocks must be nonempty. The equality gives a finite-family Turán formulation, but supplies no new asymptotic upper bound. The conjectured leading coefficient still requires a stability or counting theorem simultaneously excluding every $H_{t,r}$. Merely forbidding the $r=1$ type at larger $t$ addresses a different problem.
SOURCES CHECKED
Complete local source gpt_pro_5.4/643.tex; indexed official-source search on 2026-09-23. The classification proof is self-contained and no claim of literature novelty is made.
FINAL
UNRESOLVED. All uniformities are reduced to an explicit finite forbidden family; the sharp extremal estimate remains open in this attempt.
COMPLETION ESTIMATE
Conservative subjective progress toward the asymptotic bound. COMPLETION: 10%