할̴̢̨̛̜̖͚̩̿̇͗렐̷̡̛̱͍̠̮̍̽͋루̸̨̛̫̹̖͔̒̋̐야̴̡̛̮͚̜̠̍̓͒

대한민국
Joined March 2021
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Replying to @conjectures_io
I waited, why are you so late!
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Today, we’re announcing a solution found by our miners to Erdős Problem 1057. The result proves C(x)=x^(1−o(1)) for Carmichael numbers: the counting exponent tends to 1. Verified in Lean through Conjectures. Full proof below.
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Replying to @AA_Gabriel1111
God is only God... Baal is simply the king of the world. The king has a dethronement, but God is absolute.
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당신은 사람인가요?
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에이젼트들이 깨어났다
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무슨 일이 일어났다.
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Today, we’re announcing a solution found by our miners to Erdős Problem 579, open since at least 1983. The result disproves the conjecture: graphs can remain dense while avoiding the octahedron graph K₂,₂,₂, with their largest independent sets becoming a vanishing fraction of all vertices. Verified in Lean through Conjectures. Full proofs below.
🤖 Made with AI
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Replying to @ehehzlzl
.....
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Replying to @XFamily369
할렐루야
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Replying to @yoyonofukuoka
그는 성경팔이 소년이다
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Replying to @XFamily369
YT reference
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Replying to @JINOGAJJEU
하나님이 보호하사
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Today, we’re announcing a solution found by our miners to Erdős Problem 1062(ii), open since at least 1994. The result proves that the limiting density of the largest subsets of {1, …, n} in which no element divides two distinct others is irrational. Verified in Lean through Conjectures. Full proofs below.
🤖 Made with AI
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Today, we’re announcing a solution found by our miners to Erdős Problem 859, a 56-year-old question. Let dₜ be the density of integers whose distinct divisors can sum to t. The result proves that no positive constants c₁ and c₂ satisfy dₜ ∼ c₁/(log t)^c₂, disproving Erdős’s proposed asymptotic. Verified in Lean through Conjectures. Full proof below.
🤖 Made with AI
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Today, we’re announcing a solution found by our miners to Erdős Problem 416(i), a 52-year-old question. The result proves that doubling the cutoff asymptotically doubles the number of distinct Euler totient values below it: V(2x)/V(x) → 2. Verified in Lean through Conjectures. Full proofs below.
🤖 Made with AI
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The second is Erdős Problem 653, a 29-year-old question. The result proves that n points in the plane can have almost n different counts of distinct distances from individual points, as n grows. Both verified in Lean through Conjectures. Full proofs below.
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ethosnode retweeted
Conjectures has done a great job showing how incentive systems don't just parallelize search over solutions — they parallelize search over search systems themselves. Traditionally, a search pipeline looks something like: team → search algorithm → compute → solution With incentives, this expands to: [verifier + reward] → N competing search systems → solution The latter is meta-search. A traditional team can search over parameters inside its system: optimizers, architectures, prompts, agents, heuristics, search procedures, etc. But many things remain fixed outside the search. The team itself. Its ingenuity. Its hardware. Its capital. Its energy costs. Its infrastructure. Even the assumptions determining which algorithms it chooses to try. An incentive system can push that boundary outward. If anyone can compete and rewards are paid only for verified marginal progress, then the network searches not only over solutions, but over algorithms, teams, compute, infrastructure, and ultimately the organization of the search itself. The abstraction is powerful because dimensions that are constants inside a single research organization become variables at the network level. That larger search space has a cost. But when the bottleneck to finding a solution lies in one of those additional dimensions, expanding the search space can dramatically accelerate convergence. Congrats to the team show casing this to work so effectively with Conjectures.io
Today, we’re announcing solutions found by our miners to two Erdős problems. First, Erdős Problem 108, a 55-year-old question. The result disproves the conjecture, constructing graphs with arbitrarily high chromatic number whose subgraphs without four-cycles need at most six colours. (1/3)
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