Vela
✦ 5 frontiers

Campaign · dogfooding

The Erdős campaign.

1,217 problems mapped · 84 worked · OEIS A309370 adopted

OEIS records approved 9 · gate-verified records 88 · ledger records 219

All 1,217 problems →

The campaign sky.

gate-verifiedobstruction / null

number theory — 52 worked of 498number theory498 problems · 52 touchedgraph theory — 7 worked of 217graph theory217 problems · 7 touchedadditive combinatorics — 15 worked of 142additive combinatorics142 problems · 15 touchedramsey theory — 3 worked of 105ramsey theory105 problems · 3 touchedgeometry — 2 worked of 98geometry98 problems · 2 touchedanalysis — 2 worked of 74analysis74 problems · 2 touchedother — 3 worked of 44other44 problems · 3 touchedcombinatorics36 problems · 0 touchedset theory3 problems · 0 touched#458#488#1#7#14#30#39#41#44#100#124#153#155#158#254#273#313#321#324#326#329#340#342#346#348#357#361#489#567#881#885#1113#1056#409#535#971#930#377#463#477#417#33#387#931#949#319#213#108#272#740#10#184#1062#85#359#1150#595#188#306#267#510#302#307#295#312#148#242#396704#396705#301#699#700#23#1093#1094#376#366#203#993#647#470#684#686#396#30 · Sidon (A309370): 9 records approved#993 · forest unimodality: frontier extension

The semantic constellation.

105 draft edges · unverified
#30 related #43 (conf 0.92) — Both define the maximum size of a Sidon set in {1,...,N} (h(N) in P30, f(N) in P43) — the same extremal quantity under different names.#30 related #44 (conf 0.9) — P44 asserts the explicit upper bound (max Sidon set size in {1,...,N} ≤ 2√N) on exactly the quantity h(N) that P30 defines and studies.#30 related #155 (conf 0.9) — P155's F(N) (size of the largest Sidon subset of {1,...,N}) is the same extremal function as P30's h(N).#30 generalizes #241 (conf 0.78) — P241 is the B_3 analogue (all triple sums a+b+c distinct) of the B_2/Sidon (pairwise-sum-distinct) extremal problem P30 studies, generalizing distinct-pairwise-sums to distinct-triple-sums.#30 related #39 (conf 0.7) — P39 asks for an infinite Sidon set of density N^{1/2-ε}, the infinite analogue of the finite maximal-Sidon-size question in P30, both governed by the √N Sidon bound.#14 shares_technique #30 (conf 0.6) — Both concern the representation function of a Sidon/B_2 set in {1,...,N}; P14's count of non-uniquely-representable integers and P30's max Sidon size both hinge on bounding 1_A*1_A.#43 related #44 (conf 0.88) — P44 states the 2√N upper bound on precisely the extremal Sidon function f(N) that P43 defines.#9 specializes #10 (conf 0.85) — P10 (numbers expressible as a prime plus at most k powers of 2) generalizes the k=2 case; P9 is its complement asking which odd numbers are NOT a prime plus two powers of 2.#9 related #16 (conf 0.82) — P16 (odd integers not of form 2^k+p, i.e. prime + one power of 2) and P9 (not prime + two powers of 2) are consecutive cases of the same prime-plus-powers-of-2 representation question.#10 specializes #16 (conf 0.8) — P16 (odd integers not of form 2^k+p) is the k=1 instance of P10's general prime-plus-at-most-k-powers-of-2 representation.#10 specializes #9 (conf 0.82) — P9's 'two powers of 2' case is the k=2 instance of P10's prime-plus-at-most-k-powers-of-2 framework.#7 related #273 (conf 0.72) — Both ask whether a covering system exists with moduli restricted to a special form — P7 odd moduli, P273 moduli of the form p-1 — variants of the restricted-modulus covering-system question.#11 shares_technique #9 (conf 0.55) — Both ask whether all odd n admit an additive decomposition involving a power of 2 (P11: squarefree + power of 2; P9: prime + two powers of 2), studied via the same powers-of-2 covering/density machinery.#28 related #326 (conf 0.55) — Both concern additive bases / the representation function 1_A*1_A: P28 on whether A+A cofinite forces unbounded representations, P326 on thinning a basis of order 2 to a sub-basis, both about basis representation multiplicity.#28 related #66 (conf 0.6) — Both study the asymptotic behaviour of the representation function 1_A*1_A(n): P28 on its limsup being infinite for cofinite sumsets, P66 on whether 1_A*1_A(n)/log n can tend to a nonzero limit.#3 depends_on #219 (conf 0.6) — P3 (does divergent reciprocal sum force arbitrarily long APs) applied to the primes yields long prime APs (P219), the famous special case resolved by Green-Tao.#17 related #855 (conf 0.5) — Both are statements about prime differences/counting: P17 (cluster primes representing even n as a prime difference) and P855 (Segal π(x+y)≤π(x)+π(y)) concern the additive distribution of primes.#44 specializes #30 (conf 0.85) — Problem 44 asserts the explicit upper bound (max Sidon set in {1,...,N} is at most 2√N), which is a specific quantitative bound on exactly the function h(N) that Problem 30 studies.#44 related #155 (conf 0.8) — Both concern the maximum size of a Sidon subset of {1,...,N} (44 states the ≤2√N bound, 155 names this maximum F(N)), so 44 is a bound on 155's quantity.#41 generalizes #44 (conf 0.8) — Problem 41 (sets whose n-fold sums are all distinct, i.e. B_n sets) is the order-n generalization of Sidon sets (B_2), and Problem 44 is the n=2 Sidon size bound.#41 generalizes #30 (conf 0.75) — B_n sets (distinct n-tuple sums) in Problem 41 generalize Sidon sets, whose maximum size h(N) is the subject of Problem 30; the n=2 case recovers 30.#41 specializes #241 (conf 0.78) — Problem 241 studies the maximum size of B_3 sets (distinct triple sums) in {1,...,N}, the n=3 instance of the general distinct-n-fold-sum (B_n) condition of Problem 41.#39 shares_technique #30 (conf 0.6) — Both rely on counting-function bounds for Sidon sets in {1,...,N}; the infinite-density question of 39 is governed by the same h(N) ~ √N upper bound estimated in 30.#39 depends_on #44 (conf 0.6) — The N^{1/2-ε} density ceiling for an infinite Sidon set in 39 is forced by the finite Sidon upper bound (≈√N) asserted in 44, so 39's obstruction depends on that bound.#66 related #28 (conf 0.65) — Both concern the asymptotic behavior of the representation function 1_A*1_A(n) for additive sets; 28 bounds its limsup when A+A is cofinite, 66 asks whether 1_A*1_A(n)/log n can tend to a nonzero limit.#33 shares_technique #32 (conf 0.55) — Both ask for thin sets A that additively complement a fixed sparse set (the squares for 33, the primes for 32) so that the sumset covers all large integers, i.e. additive-complement constructions.#74 depends_on #75 (conf 0.6) — Problem 75 asks about subgraphs whose minimum number of edges to delete to make them bipartite is constrained, which is exactly the bipartite-edit quantity defined in Problem 74.#74 shares_technique #23 (conf 0.65) — Problem 74 defines the number of edge deletions needed to make a graph bipartite, which is precisely the quantity bounded in Problem 23's make-triangle-free-graph-bipartite result.#75 related #750 (conf 0.55) — Both ask whether graphs of large (uncountable/infinite) chromatic number must contain finite subgraphs of prescribed chromatic complexity as a function of size.#64 related #108 (conf 0.5) — Both are forcing problems for cycle lengths from a degree/chromatic hypothesis — 64 forces a cycle of length 2^k from min degree 3, 108 forces cycles of given girth/length from large chromatic number.#98 specializes #89 (conf 0.75) — Problem 98's h(n) is the minimum number of distinct distances under the general-position (no three collinear) restriction, a special case of the unrestricted distinct-distances lower bound asked in 89.#98 related #1082 (conf 0.7) — Both ask for a lower bound on the number of distinct distances determined by n points under a general-position-type hypothesis (no three collinear), with 1082 conjecturing the explicit bound floor(n/2).#98 related #982 (conf 0.6) — Problem 982's claim that some vertex of a convex n-gon realizes at least floor(n/2) distinct distances is a convex-position instance of the general-position distinct-distance question quantified in 98's h(n).#89 related #1082 (conf 0.6) — Both are distinct-distance lower-bound problems for n planar points; 1082 strengthens the bound to floor(n/2) under the no-three-collinear hypothesis whereas 89 asks the unrestricted n/sqrt(log n) bound.#91 depends_on #98 (conf 0.7) — An 'optimal' set in 91 is defined as one achieving the minimum distinct-distance count, which is exactly the function h(n) studied in 98, so 91's definition is parasitic on that minimum.#91 related #89 (conf 0.55) — Problem 91's notion of a distance-count-minimizing optimal configuration is the extremal object underlying the distinct-distances lower bound problem 89.#96 specializes #1085 (conf 0.65) — Problem 96 counts unit distances among the vertices of a convex n-gon, a convex-position restriction of the maximum-unit-distances problem 1085 for n points in R^d.#97 related #653 (conf 0.55) — Problem 97's count of points equidistant from a point p is the multiplicity structure dual to 653's R(x_i), the number of distinct distances from x_i, since many equidistant points means a repeated distance value.#108 shares_technique #750 (conf 0.6) — Both concern forcing high-girth subgraphs inside graphs of large (here infinite) chromatic number, using the same Erdős high-girth high-chromatic-number probabilistic/construction machinery.#123 related #32 (conf 0.55) — Both are additive-completeness problems asking that every sufficiently large integer be represented as a sum from a set (distinct elements in 123, p+a complements to primes in 32).#124 shares_technique #406 (conf 0.55) — Both involve restricted base-d digit representations of integers (sums of distinct powers d^i in 124, powers of 2 with only digits 0,1 in base 3 in 406), relying on the same base-representation combinatorics.#128 related #566 (conf 0.6) — Both ask whether a local edge-density condition on every small/medium subgraph (n^2/50 edges on half-sets in 128; at most 2k-3 edges on k-sets in 566) forces or forbids a triangle/short cycle, the same extremal local-density-vs-triangle question.#142 related #139 (conf 0.85) — Both concern r_k(N), the largest AP-free subset of {1,...,N}; 139 states the bound problem while 142 asks specifically for an asymptotic formula for the same quantity.#142 related #138 (conf 0.55) — 142 is the density (Szemeredi) version of avoiding k-term APs while 138 is the coloring (van der Waerden) version of forcing monochromatic APs, two faces of the same arithmetic-progression Ramsey phenomenon.#138 related #645 (conf 0.65) — 645 (any 2-colouring of N yields a monochromatic 3-term AP) is a special low-length, two-colour instance of the monochromatic-AP guarantee that 138 quantifies via van der Waerden numbers.#138 related #142 (conf 0.55) — 138 counts N forcing monochromatic APs (van der Waerden) whereas 142 measures the largest AP-free set (Szemeredi density), the partition and density formulations of the same AP-avoidance problem.#160 related #138 (conf 0.6) — Both study colourings of {1,...,n} with respect to arithmetic progressions: 160 asks the fewest colours so no 4-AP is monochromatic, 138 asks when a monochromatic AP is unavoidable.#143 generalizes #1196 (conf 0.55) — 1196 defines primitive sets where no element divides another; 143's condition |kx-y|>=1 for all integer k>=1 is a real-valued strengthening/generalization of the no-multiple (primitivity) divisibility condition to A in (1,infty).#155 related #30 (conf 0.9) — F(N) (largest Sidon subset of {1,...,N}) in 155 is the same extremal quantity as h(N) (max size of a Sidon set in {1,...,N}) in 30, stated under a different name.#155 related #43 (conf 0.9) — 155's F(N) and 43's f(N), both the maximum size of a Sidon set in {1,...,N}, are literally the same function.#155 specializes #44 (conf 0.8) — 44 asserts the specific upper bound F(N) <= 2*sqrt(N) for exactly the largest-Sidon-set quantity F(N) that 155 defines, so 44 is a concrete bound on 155's object.#158 generalizes #155 (conf 0.8) — B_2[g] sets in 158 generalize Sidon sets (the g=1 case), so the extremal size questions in 158 generalize the largest-Sidon-subset quantity F(N) studied in 155.#158 generalizes #30 (conf 0.75) — A Sidon set is a B_2[1] set, hence 158's B_2[g] maximum-size problem strictly generalizes 30's maximum Sidon set size in {1,...,N}.#153 shares_technique #152 (conf 0.85) — 153 and 152 use the identical construction f(n) = minimum over Sidon sets A of size n of a functional of the gap/structure of A+A, differing only in which statistic of A+A is minimized.#153 related #155 (conf 0.55) — 153 minimizes a gap-statistic of A+A over Sidon sets while 155 maximizes Sidon-set size; both are extremal problems over the same family of Sidon sets and their sumsets.#172 related #1199 (conf 0.7) — 1199 asks for an infinite monochromatic A+A under 2-colouring; 172 asks for arbitrarily large A with all sums and products monochromatic under finite colouring, the same Hindman-type monochromatic-sumset Ramsey question with products added.#172 related #645 (conf 0.5) — Both are partition-regularity (Ramsey) statements over finite colourings of N seeking monochromatic additive structure (sums in 172, 3-term APs in 645).#195 specializes #196 (conf 0.9) — 196 (must every permutation of N contain a monotone 4-term AP) is the k=4, ground-set-N special case of 195's question on the largest guaranteed monotone k-term AP in any permutation of Z.#195 related #197 (conf 0.7) — Both concern monotone arithmetic progressions inside permutations of the integers; 197's 2-colouring/permutation construction is exactly the kind of avoidance argument used to bound the k in 195.#196 related #197 (conf 0.65) — 197 (partition N into two AP-3-avoidable-permutation sets) is the natural lower-bound companion to 196's existence question about monotone APs in a single permutation.#200 related #3 (conf 0.6) — Both ask about arithmetic progressions among a sparse density-zero set (primes for 200, general sum-of-reciprocals-divergent sets for 3); the prime case is the canonical instance motivating Erdős's general AP conjecture.#203 shares_technique #7 (conf 0.75) — Both are resolved by constructing covering systems of congruences; 203 needs a covering of the exponents (k,l) of 2^k·3^l·m+1, exactly the covering-system machinery that 7 studies in the odd-modulus case.#203 shares_technique #1113 (conf 0.8) — 203 asks for m making 2^k·3^l·m+1 never prime; 1113's covering-set framework for k·2^n+1 (Sierpiński numbers) is the same prime-blocking-by-covering construction extended to two exponents.#203 shares_technique #279 (conf 0.65) — Both rely on choosing congruence classes a_p mod p (covering congruences) to force every relevant integer into a prescribed residue, the shared covering-system method.#236 related #9 (conf 0.85) — 236 counts representations n=p+2^k while 9 is precisely the set of odd n with zero such representations; 9 is the support of {n: f(n)=0} for 236's counting function.#236 related #10 (conf 0.75) — Both study representability of integers as a prime plus powers of 2; 10 generalizes the single power-of-2 in 236's n=p+2^k to a prime plus at most k powers of 2.#213 related #212 (conf 0.7) — Both concern point sets in the plane with rational/integral pairwise distances; 213's finite no-3-collinear-no-4-concyclic integral-distance configurations are the structured finite analogue of 212's dense rational-distance set.#241 specializes #41 (conf 0.85) — 241 (max A with all triple sums a+b+c distinct, a B_3 set) is the h=3 case of 41's general B_h condition that all n-tuple sums be distinct up to trivial coincidences.#241 shares_technique #30 (conf 0.7) — Both are extremal problems for the maximum size of an additive-distinctness set in {1,...,N}; 241's B_3 sets and 30's Sidon (B_2) sets are bounded by the same counting/representation-function arguments.#218 related #234 (conf 0.6) — Both are statistical questions about consecutive prime gaps d_n=p_{n+1}-p_n: 218 on the density of indices where the gap increases, 234 on the limiting distribution of normalized gaps, sharing the same gap-distribution heuristics.#233 related #234 (conf 0.6) — Both concern the fine distribution of prime gaps d_n relative to log n: 233 on the second moment sum of d_n, 234 on the distribution function of d_n/log n, governed by the same Cramér-type gap model.#274 generalizes #7 (conf 0.6) — Problem 274's exact coverings of a group generalize covering systems of congruences (the integers with subgroups nZ), of which 7's odd-moduli covering is a special instance.#274 related #275 (conf 0.55) — Both concern exact/disjoint covering systems of congruences, with 274 lifting the disjoint-covering notion to general groups.#279 shares_technique #7 (conf 0.6) — Both are covering-system questions over residues; constructing the a_p mod p covering of all large integers in 279 uses the same covering-congruence machinery as building covering systems in 7.#279 shares_technique #273 (conf 0.55) — Both ask for covering systems with prime-indexed moduli (a_p mod p in 279, moduli p-1 in 273), built via the same residue-covering constructions.#288 related #289 (conf 0.7) — Both study sums of reciprocals over finite intervals hitting target rational values; 288 asks finiteness for two intervals while 289 asks existence for k intervals, the same interval-reciprocal framework.#289 depends_on #295 (conf 0.7) — Problem 295 is stated as a helper lemma producing a run n_1<...<n_k of integers above N with reciprocal sum a prescribed value, the existence ingredient needed to build the k intervals in 289.#295 reduction #289 (conf 0.6) — The dense Egyptian-representation lemma 295 supplies the building block that reduces the interval-construction question 289 to packing such reciprocal runs.#304 specializes #242 (conf 0.7) — Erdős–Straus 242 (4/n as three distinct unit fractions) is the special case a/b=4/n, k=3 of the general question 304 of which k admit a/b as a sum of k distinct unit fractions.#306 specializes #304 (conf 0.6) — Problem 306 asks for Egyptian-type representations of a/b restricted to denominators that are products of two distinct primes, a constrained variant of representing a/b as a sum of unit fractions (304).#319 related #317 (conf 0.6) — Both concern signed sums of reciprocals (delta_k in {-1,0,1} or {-1,1}) approximating/avoiding values; 319 asks for the largest such set while 317 asks for a uniform smallness constant, sharing the signed-reciprocal framework.#321 related #319 (conf 0.55) — Both ask for the largest A in {1,...,N} with a distinctness/signed-sum condition on subset reciprocal sums, the same extremal subset-sum-of-reciprocals setup.#323 related #325 (conf 0.6) — Both count/characterize integers expressible as sums of fixed numbers of kth powers; 325's sum-of-three-kth-powers predicate is the m=3 instance of the counting function f_{k,m} studied in 323.#364 related #366 (conf 0.82) — Both ask about consecutive runs of powerful (k-full) numbers: 364 forbids three consecutive 2-full numbers while 366 asks for a 2-full n adjacent to a 3-full n+1, the same consecutive-powerful-numbers circle attacked via ABC/Pell methods.#366 related #364 (conf 0.8) — 366 (a 2-full n with 3-full n+1) is the adjacent-pair analogue of 364's nonexistence of three consecutive 2-full numbers, both reducing to gaps between powerful numbers.#373 related #390 (conf 0.6) — Both concern representing n! as a product of other factors: 373 as a product of smaller factorials and 390 as a product of distinct integers exceeding n, the same multiplicative-decomposition-of-n! theme.#373 related #398 (conf 0.55) — Both are Diophantine equations in factorials (373: n!=a_1!...a_k!; 398: Brocard's n!+1=m^2), studied with the same prime-factorization-of-n! tools, but neither reduces to the other.#390 related #373 (conf 0.6) — 390 (smallest m so n! is a product of distinct integers >n) and 373 (n! as a product of smaller factorials) are companion problems on multiplicative decompositions of n!.#376 related #377 (conf 0.78) — Both study which primes divide the central binomial coefficient C(2n,n): 376 asks for n with C(2n,n) coprime to 105 (no prime 3,5,7), 377 sums reciprocals of primes <n not dividing C(2n,n).#377 related #376 (conf 0.78) — 377 (reciprocal sum over primes not dividing the central binomial coefficient) and 376 (n with C(2n,n) coprime to 105) both concern the set of primes missing from C(2n,n)'s factorization.#376 related #396 (conf 0.55) — Both are divisibility questions about the central binomial coefficient C(2n,n) controlled via Kummer/Legendre prime-exponent analysis (376: coprimality to 105; 396: divisibility by a product of consecutive integers).#387 shares_technique #396 (conf 0.55) — Both attack the divisor structure of binomial coefficients via prime-power valuations from Kummer's theorem (387: existence of a divisor in (cn,n]; 396: a falling product dividing the central coefficient).#386 related #387 (conf 0.55) — Both concern the multiplicative/divisor structure of binomial coefficients (386: C(n,k) as a product of consecutive primes; 387: C(n,k) having a divisor in (cn,n]), analyzed through prime factorizations of binomials.#389 related #394 (conf 0.62) — Both study divisibility by blocks of consecutive integers: 389 asks when a length-k consecutive product divides the next block, and 394 defines the least m so n divides a length-k consecutive product, sharing the consecutive-product divisibility machinery.#394 related #389 (conf 0.62) — 394 (least start m so n divides m(m+1)...(m+k-1)) and 389 (one block of k consecutive integers dividing the next) both concern divisibility properties of products of k consecutive integers.#469 related #859 (conf 0.72) — Both concern representing a number as a sum of distinct divisors: 469 asks whether n is a sum of distinct proper divisors, while 859's DivisorSumSet is exactly the set of n for which a target t is a sum of distinct divisors of n.#469 related #470 (conf 0.78) — A weird number (the basis of 470's primitive weird numbers) is precisely an abundant number that is NOT a sum of distinct proper divisors, so 470's objects are exactly the n for which 469's predicate fails despite abundance.#470 depends_on #469 (conf 0.7) — The definition of weird (hence primitive weird) number in 470 is stated directly in terms of 469's predicate failing, namely abundant but not expressible as a sum of distinct proper divisors.#489 related #488 (conf 0.68) — 489's set of integers not divisible by any element of A is the exact complement of 488's set B of multiples of a finite set A, so both study the density behavior of the same multiples/non-multiples dichotomy.#508 related #188 (conf 0.6) — 188 concerns red/blue colourings of the plane with no red pair at unit distance, i.e. proper 2-colourings of 508's unit-distance graph, tying both to the chromatic number of the plane.#564 specializes #562 (conf 0.9) — 564 is the r=3 special case of 562's general r-uniform hypergraph Ramsey number R_r(n), asking for monochromatic cliques in 2-colourings of complete 3-uniform hypergraphs.#562 generalizes #564 (conf 0.9) — 562 defines the Ramsey number R_r(n) for all uniformities r, of which 564's R_3(n) is the r=3 instance.#513 related #517 (conf 0.55) — Both concern value distribution of transcendental entire functions (513 the minimum-modulus/ratio liminf, 517 whether gap series assume every value infinitely often), drawing on the same Wiman-Valiron value-distribution circle of ideas.#592 shares_technique #598 (conf 0.55) — Both are partition-calculus questions about arrow relations on infinite structures (592 on K_{ω^β} for countable ordinals, 598 on K_κ for κ=(2^{ℵ_0})^+), solved by the same Erdős–Rado ordinal/cardinal partition machinery.#593 related #564 (conf 0.5) — Both concern finite 3-uniform hypergraphs as unavoidable substructures under a coloring/chromatic constraint, sharing the 3-uniform hypergraph extremal setting.3#7 — Is there a distinct covering system all of whose moduli are 79#10 — Is there some $k$ such that every large integer is the sum o1011#14 — Let $A\subseteq \mathbb{N}$. Let $B\subseteq \mathbb{N}$ be 141617#23 — Can every triangle-free graph on $5n$ vertices be made bipar2328#30 — Let $h(N)$ be the maximum size of a Sidon set in $\{1,\ldots3032#33 — Let $A\subset\mathbb{N}$ be such that every large integer ca33#39 — Is there an infinite Sidon set $A\subset \mathbb{N}$ such th39#41 — Let $A\subset\mathbb{N}$ be an infinite set such that the tr4143#44 — Let $N\geq 1$ and $A\subset \{1,\ldots,N\}$ be a Sidon set. 44646674758991969798#108 — For every $r\geq 4$ and $k\geq 2$ is there some finite $f(k,108123#124 — For any $d\geq 1$ and $k\geq 0$ let $P(d,k)$ be the set of i124128138139142143152#153 — Let $A$ be a finite Sidon set and $A+A=\{s_1&#60;\cdots&#60;153#155 — Let $F(N)$ be the size of the largest Sidon subset of $\{1,\155#158 — Let $A\subset \mathbb{N}$ be an infinite set such that, for 158160172#188 — What is the smallest $k$ such that $\mathbb{R}^2$ can be red188195196197200#203 — Is there an integer $m\geq 1$ with $(m,6)=1$ such that none 203212#213 — Let $n\geq 4$. Are there $n$ points in $\mathbb{R}^2$, no th213218219233234236241#242 — For every $n&#62;2$ there exist distinct integers $1\leq x&#242#273 — Is there a covering system all of whose moduli are of the fo273274275279288289#295 — Let $N\geq 1$ and let $k(N)$ denote the smallest $k$ such th295304#306 — Let $a/b\in \mathbb{Q}_{&#62;0}$ with $b$ squarefree. Are th306317#319 — What is the size of the largest $A\subseteq \{1,\ldots,N\}$ 319#321 — What is the size of the largest $A\subseteq \{1,\ldots,N\}$ 321323325#326 — Does there exist $A=\{a_1&#60;a_2&#60;\cdots\}\subset \mathb326364#366 — Are there any $2$-full $n$ such that $n+1$ is $3$-full? That366373#376 — Are there infinitely many $n$ such that $\binom{2n}{n}$ is c376#377 — Is there some absolute constant $C&#62;0$ such that\[\sum_{p377386#387 — Is there an absolute constant $c&#62;0$ such that, for all $387389390394#396 — Is it true that for every $k$ there exists $n$ such that\[\p396398406469#470 — Call $n$ weird if $\sigma(n)\geq 2n$ and $n$ is not pseudope470#488 — Let $A$ be a finite set and\[B=\{ n \geq 1 : a\mid n\textrm{488#489 — Let $A\subseteq \mathbb{N}$ be a set such that $\lvert A\cap48950851351756256456659259359864565375085585998210821085#1113 — A positive odd integer $m$ such that none of $2^km+1$ are pr111311961199generalizes / specializesshared techniquereduction / depends-onworked this campaign

Verified contributions.

OEIS A309370 — nine verified Sidon records

approved

Nine integer-sum Sidon lower bounds (n = 9,11,12,13,14,15,16,19,20), each independently re-verified, editor-approved and published. The campaign's first external adoption event.

Erdős #993 — forest-surface frontier extension

public

By Hoggar's theorem a non-unimodal forest needs a non-log-concave component; swept 112,916 generalized trees + 253,695 forest products — all unimodal. The forest surface prior tree-only searches left untouched.

Erdős #302 — improved published bound

banked

f(N) ≤ (155923/180048 + o(1))·N ≈ 0.86601·N, beating the prior best verifiable certificate. Reproduced the published baselines exactly before confirming the new base.

Six verified reductions naming the missing theorem

banked

For #1094, #366, #699, #1093, #376, #488 — gate-verified reductions that isolate the exact open input a number theorist would need. Honest grades, never “solved.”

What the gate caught.

rejected before banking

Wins look like every AI-math demo. The least-fakeable proof that the trust layer is real is what it rejected — each of these was a plausible claim that an adversarial probe killed before it could bank.

A search self-reported a Sidon set beating the OEIS best by 48.

probe: Independent re-count of the witness against the actual OEIS values.

Phantom. The real improvement was 9 records — which then earned adoption.

Erdős #204 reported as a fresh result, ready for a covering search.

probe: Prior-art check before spending compute.

Already solved (Adenwalla, in Lean). Killed before the search ran.

Erdős #488 small-|A| density bound proposed as a novel resolution.

probe: Literature/prior-art check against the active frontier.

Not novel — Tao is at the general/primes frontier. Blocked.

A #1056 k=5,6 witness looked like progress toward a solve.

probe: Re-read the problem's actual quantifier (for every k).

Infinitary — a new finite example, not a solve. Graded extends_prior_work.

Honest grade ledger.

The grade distribution is the campaign’s honesty made legible: most of the work is nulls, partial proofs, and reductions that name the missing theorem — never inflated to “solved.”

68 honest null52 partial proof36 verified reduction33 obstruction map15 improved bound11 extends prior work3 new OEIS term1 lean_fragment

finding.noted · reviewer:will-blair · 1 day

renders the record as of vev_d199cb2e · 1,338 events · hub

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