The site's wording quantifies over every $m\ge1$ and fails at $m=2$. Here $R(G)$ is the least $N$ such that every $2$-coloring of the edges of $K_N$ contains a monochromatic copy of $G$, the diagonal graph Ramsey number the site and the formalization use. For $m=2=\binom22+1$, $n=2$, $t=1$ and $H=P_3$, the path with two edges, and $R(P_3)=3$: two of the three edges of $K_3$ share a color and any two edges of $K_3$ share a vertex, while $K_2$ has one edge. The graph $G=2K_2$, two disjoint edges, has two edges, no isolated vertex and $R(2K_2)=5$: coloring a triangle of $K_4$ red and the three edges at the fourth vertex blue leaves no two disjoint edges of one color, and in any $2$-coloring of the ten edges of $K_5$ one color has at least five edges, while a graph whose edges pairwise share a vertex is a star or a triangle, with at most four edges on five vertices. So $R(G)=5>3=R(H)$ at $m=2$. The same coloring gives $m=3$: in $K_7$, a red $K_5$ and blue edges at the other two vertices contain no monochromatic $3K_2$, so $R(3K_2)\ge8>6=R(K_3)$. The site's discussion thread records failures for $2\le m\le5$ and $7\le m\le9$, all from the matchings $mK_2$, with $R(mK_2)=3m-1$ (Cockayne and Lorimer 1975, as the comments cite them) against values of $R(H)$ from Radziszowski's survey and a written argument in the thread; at $m=6$ the comparison holds by Burr's 1989 table, as the curator reports. Every recorded failure lies at $m\le9$, and a matching cannot fail for large $m$, since $3m-1$ grows linearly while $R(H)\ge R(K_n)>2^{n/2}$; these are boundary failures. The change inserts the words "for all sufficiently large $m$," after "That is,"; nothing else changes. No source gives a threshold for general $t$, so the form is the one used when boundary failures are treated as exceptions by the poser's framing and the site's commentary. [ErGr75] p. 526 asks the case $t=0$ as an example of an asymptotic question, "Among all such graphs, which have the fastest growing values of $r(G_n;k)$?", and its range "$k\ge1$, $n\ge1$" is the natural domain, not a print that blocks the change. Its two-color case already fails at $n=3$ (the instance $m=3$ above), so for $t=0$ the defect is in the poser's text and the site inherits it. Burr and Erdős restate that case with $k\ge4$ ([BuEr76] p. 257), which removes the failures with $t=0$ and says nothing about $t\ge1$. The general $t$ comes from Chung's problem collection, whose condition $n\ge4$, as the thread reports it, still fails at $m=7$ to $9$, so it is not the form. The site's commentary records the small-$m$ failures under the label OPEN, and the formal-conjectures statement takes all sufficiently large $m$; it counts with the site. The form rests on these sources alone; no result settles it. A disproof of the corrected Statement needs failures for infinitely many $m$. The results about the site's wording are thread comments of 28 October 2025 at erdosproblems.com/forum/thread/545: the account Adenwalla's failure at $m=2$; the account LouisD's failures at $m=3,4,5,7,8,9$, which the site's commentary credits, on a rejected claim page (LouisD, 2025); and the curator T. F. Bloom's check that $m=6$ holds. They are credited here. The failures answer the site's wording (every $m$), not the corrected Statement (all sufficiently large $m$), so they do not count toward the problem's standing, which judges the corrected Statement.