Open registry federation
59 source-grounded records. Verification labels remain separate from source authentication and publication status.
Imported from VibeMathed under CC BY 4.0. Each record links to its registry entry and named primary source. Registry verification is preserved verbatim.
VibeMathed records this result as “Erdős Problem #948.” The registry entry and named primary source contain the available statement and scope.
A monic prime $P$ of $\mathbb{F}_q[T]$ is a $c$-Wieferich prime if $\rho_P(1) \equiv 1 \bmod P^2$ for the Carlitz module $\rho$. On limited data and proofs in degrees $2$ and $3$, Thakur suggested in 2015 that in odd characteristic every $c$-Wieferich prime has degree divisible by $p$. It is false: an explicit irreducible $c$-Wieferich prime has degree not divisible by $p$, and the resulting common factor has a cl…
VibeMathed records this result as “Erdős Problem #858.” The registry entry and named primary source contain the available statement and scope.
The question as posed was implicit in Davenport–Erdős (1951); the AI result settles Tenenbaum's open variant negatively
VibeMathed records this result as “Erdős Problem #152.” The registry entry and named primary source contain the available statement and scope.
VibeMathed records this result as “Erdős Problem #690.” The registry entry and named primary source contain the available statement and scope.
For two qubits, the paper considers $\rho=\frac12|\Phi^+\rangle\langle\Phi^+|+\frac12|01\rangle\langle01|$, where $|\Phi^+\rangle=(|00\rangle+|11\rangle)/\sqrt2$. This rank-2 state has no global supporting affine functional for Entanglement of Formation. Setting $\rho_t=(1-t)\rho+t|10\rangle\langle10|$, Wootters’ formula gives $C(\rho_t)=\frac12-\sqrt{2t}+O(t)$. Consequently, $\lim_{t\to0^+}[E_F(\rho)-E_F(\r…
VibeMathed records this result as “Erdős Problem #888.” The registry entry and named primary source contain the available statement and scope.
VibeMathed records this result as “Erdős Problem #1202.” The registry entry and named primary source contain the available statement and scope.
VibeMathed records this result as “Erdős Problem #1153.” The registry entry and named primary source contain the available statement and scope.
What is the largest $A\subseteq\{1,\dots,N\}$ such that all subset sums $\sum_{n\in S}1/n$ (over $S\subseteq A$) are distinct?
VibeMathed records this result as “Erdős Problem #960.” The registry entry and named primary source contain the available statement and scope.
VibeMathed records this result as “Erdős Problem #543.” The registry entry and named primary source contain the available statement and scope.
VibeMathed records this result as “Erdős Problem #1217.” The registry entry and named primary source contain the available statement and scope.
The target-free clique conjecture asserts that the supports of stable fixed points of a nondegenerate combinatorial threshold-linear network are exactly its target-free cliques, the bidirected cliques no outside vertex receives an edge from every member of. An explicit six-neuron counterexample refutes it.
Donner proved in 1992 that the list color function $P_\ell(G,k)$ equals the chromatic polynomial $P(G,k)$ once $k$ is large. Kaul and Mudrock asked whether the analogue holds for Hanlon's unlabeled chromatic polynomial, and could not settle even the edgeless graph, which they posed as a conjecture. The conjecture is true, and it implies that a disconnected graph satisfies the unlabeled analogue of Donner's result…
Proves Haglund's Conjecture 4 for $k=1$: every non-real first-quadrant zero of $\Phi_1+t\Phi_2$ is simple with strictly decreasing imaginary part, no branch escapes forward, and every finite-multiplicity real collision stays real afterwards. The cases $k\ge2$ remain open. Two readings worth separating: Conjecture 4 asserts the monotone descent alone, so the no-escape and stays-real statements are this paper's own…
The dihedral case only, for every $a \ge 4$ and $b \ge 1$; the substance is the upper bound, which the source paper's own computations could not reach. Together with the sibling a = 3 entry this proves Conjecture 4.9's claim $1+(a-1)(b-1)$ for all $a \ge 3$; the conjecture's trivial a = 1, 2 cases are unaddressed by either entry, and the cyclic analogue $R_{cyc}(P_a^{alt}, K_b)$ for $a \ge 4$ remains open. The eng…
Nineteen individual exact values, each decided by SAT certificate: unsatisfiable at the claimed $n$, witnessed satisfiable at $n-1$. They close cells in DD26's Tables 3-13 but settle no infinite family - the sibling entries do that for the $K$ column. The three overlap cells are $R_{dih}(P_4^{alt},K_6)=16$, $R_{dih}(P_3^{alt},K_9)=17$ and $R_{dih}(P_9^{alt},K_3)=17$, each an instance of a sibling theorem; the rema…
The a = 3 slice is settled outright. The parent conjecture's dihedral side has since been resolved for every a >= 4 as well (see the related entry), so Conjecture 4.9's claim 1 + (a-1)(b-1) now stands proved for all a >= 3; the trivial a = 1, 2 cases and the cyclic analogue for a >= 4 remain formally unaddressed.
The evenly-divided reading of WOWII Conjecture 72 holds: $ \lceil(A + L)/3\rceil \le t, $ where $ t = $ tree($ G $) (order of a largest induced tree), $ A = $ average eccentricity and $ L = $ maximum neighbourhood independence number. A stronger reading that divides only $ L $ by three is false. The argument rests on two elementary observations (a diametral path is chordless and therefore induces a t…
Nothing in the paper's proof is affected. At the witness, inequality (4) holds with slack +27.0, inequality (5) holds with equality (f is inner), and the theorem itself holds with slack 2 - kappa = +0.80. Only the shortcut Remark 2 floats is refuted.
Answered in full: for every $k\ge4$, a target with exactly two nonadjacent zero digits has $F_k(t)=(k+23)3^{k-4}$, independently of the distance between the zeros. Exact at every width, no error term, no hypothesis on $k$ (Theorem 1.1). This is an evaluation, not an extremal result, and the paper is explicit about the difference: the plateau value is not maximal. At $k=12$ it reads $35\cdot3^8=229{,}635$ while $F_…