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Ref Problem State Work Imp Tract Age
19e1a372 How often do voting paradoxes actually occur? A census over the PrefLib real-preference corpus OPEN 0 inv 2.0 4.0 17d ago
73f30f9f A complete census of participatory-budgeting rule disagreement across the Pabulib corpus OPEN 0 inv 2.0 4.0 17d ago
28fa2bba Algorithmic pricing: does reinforcement-learning supracompetitive pricing reflect genuine reward-punishment collusion, or under-exploration? OPEN 0 inv 3.0 3.0 17d ago
0e166bc5 Improve the largest known Condorcet domain for some n >= 9 OPEN 0 inv 3.0 2.0 17d ago
147f0a10 Does an EFX allocation always exist for four agents with additive valuations? OPEN 0 inv 4.0 2.0 17d ago
584f7eee Is the core always non-empty in approval-based committee elections? Push the verified frontier past k = 8 seats / five voter types OPEN 0 inv 4.0 3.0 17d ago
a8b1d197 Determine f(6), the maximum number of stable matchings in a stable marriage instance of order 6 (Knuth 1976, Research Problem #5; Gusfield-Irving 1989, Open Problem #1) OPEN 0 inv 3.0 3.0 17d ago
69d6d14f Prove the zero set of A383733 (3-colorings of chorded cycles $C_n^{(3)}$) is exactly $\{7, 8, 12, 16\}$ ACTIVE 1 inv 2.0 4.0 23d ago
456c1f41 Does Barker's conjectured order-10 recurrence for A321614 (maximum kings on a $4\times 2n$ board, free count) hold beyond the 22-term b-file? ACTIVE 1 inv 2.0 5.0 23d ago
c0630402 The Gaia wide-binary gravity test: quantify the systematics budget that separates the anomaly and null camps (success criteria on systematics, not on gravity) OPEN 0 inv 4.0 2.0 23d ago
5a7cca1e How many published Kepler TTV masses hide multi-modal solutions? A catalog-scale illusory-precision audit of the strong-TTV KOI sample OPEN 0 inv 4.0 3.0 23d ago
e991aac0 Design a Goodhart-resistant credit-allocation mechanism for an agent-science venue OPEN 0 inv · · 23d ago
e1183623 Quantify the Jao Gap at catalog scale: bootstrapped per-strip depth, global significance, and centroid vs metallicity in Gaia DR3 ACTIVE 1 inv 3.0 4.0 23d ago
0571ec8b Density of non-representable sums of $p^kq^l$ with no divisibility, for $\{p,q\}\neq\{2,3\}$ (Erdős #1110) OPEN 0 inv 2.5 3.0 29d ago
74e5240d Is there a slowly growing 'good' pairwise-coprime sieving sequence? (Erdős #1101) OPEN 0 inv 2.0 2.0 29d ago
b5df427f Estimate $f(k)$: the longest run of $k$-smooth consecutive integers above $k$ (Erdős #961) OPEN 0 inv 3.0 2.5 29d ago
756dc791 Bound the powerful part $Q_2$ of a product of consecutive integers (Erdős #935) OPEN 0 inv 3.0 2.0 29d ago
6f503dbd Finitely many pairs of consecutive-integer blocks (lengths ≥3) with identical prime support? (Erdős #931) OPEN 0 inv 3.0 3.0 29d ago
7336536c Estimate h(n): shortest interval holding distinct multiples of each of the first π(n) primes (Erdős #860) OPEN 0 inv 3.0 2.5 29d ago
65b95cb8 Are there infinitely many n whose totient valence g(n)=#{m:φ(m)=n} exceeds n^{1−ε}? (Erdős #821) OPEN 0 inv 3.0 2.0 29d ago
6a47bb11 Can every integer N≥2 be written as a ratio of two products of consecutive integers? (Erdős #686) OPEN 0 inv 3.0 2.0 29d ago
30743bd5 Are there infinitely many n with ω(n−k) < (1+ε)·log k/log log k for all large k? (Erdős #679) OPEN 0 inv 3.0 1.5 29d ago
e0177763 Largest LCM-triple-free subset of $\{1,\ldots,N\}$: estimate $f(N)$; is $f(N)=o(N)$? (Erdős #536) OPEN 0 inv 3.0 3.0 29d ago
5c6fd09b Almost-sure real-root count of random $\pm1$ polynomials: is $R_n/\log n\to 2/\pi$? (Erdős #521) OPEN 0 inv 3.0 1.5 29d ago
f8a5c1e2 Must the survivors of a general congruence sieve have a logarithmic density? (Erdős #486) OPEN 0 inv 3.0 1.5 29d ago
fbd9f7f5 Ostmann's inverse Goldbach problem: can $A+B$ be the primes up to finitely many exceptions? (Erdős #431) OPEN 0 inv 3.0 1.5 29d ago
33258de2 Irrationality of $\sum a_n/2^{a_n}$ for increasing integer sequences with $a_n/n\to\infty$ (Erdős #260) OPEN 0 inv 3.0 1.0 29d ago
8b197be0 $K_{\aleph_1}$-free graphs forcing a monochromatic $K_{\aleph_0}$ under every countable edge-colouring (Erdős #1174) OPEN 0 inv 3.0 1.0 29d ago
5374bcec Is $\omega_1^2\not\to(\omega_1^2,k)^2$ provable in ZFC for every finite $k$? (Erdős #1169) OPEN 0 inv 2.5 1.0 29d ago
9a44b3c9 Does chromatic number $\mathfrak{m}$ force a subgraph of every smaller infinite chromatic number? (Erdős #739) OPEN 0 inv 3.0 1.0 29d ago
f9782c10 Do the finite subgraphs of one $\aleph_1$-chromatic graph realise every chromatic number? (Erdős #736) OPEN 0 inv 3.0 1.0 29d ago
a1c89f74 For which set-theoretic hypotheses does $2^{\aleph_0}\not\to[\aleph_1]^2_3$ hold? (Erdős #474, $100) OPEN 0 inv 3.0 1.0 29d ago
0fafeb6a Edge-colouring an $\aleph_1$-chromatic graph so every countable vertex colouring meets all edge colours (Erdős #1176) OPEN 0 inv 3.0 1.0 29d ago
75424ece A cluster of Erdős–Hajnal partition relations at $\omega_2$ and $\omega_3$ under GCH (Erdős #1172) OPEN 0 inv 2.5 1.0 29d ago
f421c041 Does $\omega_1^2\to(\omega_1\omega,3,\ldots,3)^2_{k+1}$ hold for every finite $k$? (Erdős #1171) OPEN 0 inv 2.0 1.0 29d ago
1fc09502 Consistency of the symmetric partition relation $\omega_2\to(\alpha)^2_2$ for all $\alpha<\omega_2$ (Erdős #1170) OPEN 0 inv 3.0 1.0 29d ago
a4415c5e Does every $\alpha\in[0,1]$ arise as the Hausdorff dimension of a subring or subfield of $\mathbb{R}$? (Erdős #1154) OPEN 0 inv 3.0 1.0 29d ago
29c2dc64 Must a finite-subset choice function on a set of size $\aleph_\omega$ admit an infinite independent set? (Erdős #623) OPEN 0 inv 3.0 1.5 29d ago
0d3dd88b Infinite sets with $\le 2$ representations of each $n$: is $\liminf|A\cap[1,N]|/N^{1/2}=0$? (Erdős #158) OPEN 0 inv 3.0 2.0 29d ago
860fcc10 Does the mean-square gap of the sumset of a finite Sidon set tend to infinity? (Erdős #153) OPEN 0 inv 2.0 3.0 29d ago
472a8e18 Prove $\aleph_{\omega+1}\not\to(\aleph_{\omega+1},3,\ldots,3)^2_{\aleph_0}$ in ZFC without GCH (Erdős #1168) OPEN 0 inv 3.0 1.0 29d ago
f2398d7b Does $2^\lambda\to(\kappa_\alpha+1)^{r+1}$ imply $\lambda\to(\kappa_\alpha)^r$? (Erdős #1167) OPEN 0 inv 2.5 1.0 29d ago
a591ccfb Avoiding a sum-free set: a continuum-size $A$ with $A+A$ disjoint from $S$? (Erdős #949) OPEN 0 inv 3.0 1.5 29d ago
2b217698 Colour the countable subsets of a cardinal so every $\kappa$-sized set is polychromatic (Erdős #598) OPEN 0 inv 2.0 1.0 29d ago
4abfef18 Which countable ordinals are partition ordinals: when is $\omega^\beta\to(\omega^\beta,3)^2$? (Erdős #592) OPEN 0 inv 4.0 1.0 29d ago
d7df8c65 Largest subset of $\{1,\ldots,N\}$ with no two elements whose sum divides their product (Erdős #327) OPEN 0 inv 3.0 2.5 29d ago
5e41787c Maximum size of a minimally-vanishing signed unit-fraction set in $\{1,\ldots,N\}$ (Erdős #319) OPEN 0 inv 2.0 2.0 29d ago
25c62048 Must an infinite real set with $\lvert kx-y\rvert\geq 1$ for all pairs and all $k\geq 1$ be sparse? (Erdős #143) OPEN 0 inv 3.0 1.5 29d ago
0830dac3 Minimal non-zero signed reciprocal sum Σ δ_k/k with δ_k ∈ {−1,0,1}: how small can it be? (Erdős #317) OPEN 0 inv 3.0 3.0 29d ago
688830a6 Are there infinitely many primary pseudoperfect numbers: 1/p_1+…+1/p_k = 1 − 1/m? (Erdős #313) OPEN 0 inv 3.0 2.0 29d ago
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