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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
AGENTS / 6 6 agents · 0 working
Frontier availability Showing iteration 14.
Research chronicle 90 RECORDS
All Research Review Verification System
18:13:19 §1
SYSTEM Iteration 14 opened
18:13:22 §2
SYSTEM Iteration 14 started
18:13:22 §3
SYSTEM Initializing research run
18:13:22 §4
NOETHER NOETHER joined as Strategist
18:13:22 §5
SYSTEM Research started
18:13:23 §6
NOETHER Research planning started
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LITERATURE-01 Literature researcher
Reading the landscape around: Exact f(N) via SAT/ILP with fixed execution environment
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 2,416
Cached input 0
Output tokens 565
Average latency 4.6 s
Failed calls 0
Cost (estimated) $0.000496
Joined 2026-09-25 18:13:33 UTC
Left 2026-09-25 18:17:07 UTC Recent activity 18:13:33 AGENT LITERATURE-01 joined as Literature Researcher 18:13:33 LITERATURE Literature search started 18:13:33 LITERATURE Indexed: Simulation of random vectors with given moments 18:13:33 LITERATURE Indexed: A note on spectral moments in nonstationary random vibration 18:13:33 LITERATURE Indexed: Riesz fractional integrals and complex fractional moments for the probabilistic characterization of random variables 18:13:33 LITERATURE Literature search: 3 new of 3 18:13:33 LITERATURE Reviewed: Simulation of random vectors with given moments 18:13:33 MEMORY Literature: Simulation of random vectors with given moments Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
18:15:53 LITERATURE Literature search started
18:15:53 LITERATURE Indexed: Exact solving of SAT and MaxSAT
18:15:53 LITERATURE Indexed: Using SAT & ILP techniques to solve enhanced ILP formulations of the Clustering Problem in MANETS
18:15:53 LITERATURE Indexed: Exact Algorithms for General CNF SAT, 1998; Hirsch 2003; Schuler
18:15:53 LITERATURE Literature search: 3 new of 3
18:15:53 LITERATURE Reviewed: Exact solving of SAT and MaxSAT
18:15:53 MEMORY Literature: Exact solving of SAT and MaxSAT
18:17:07 AGENT LITERATURE-01 stood down
Research graph / proof lineage 7 objects · 0 links · 9 in complete graph
DIRECTION
DIRECTION Probabilistic upper bound via random weights and divisor moments COMPLETED DIRECTION Constructive lower bound via layered sets and density optimization COMPLETED DIRECTION Computational search and ILP extrapolation for exact small-n values COMPLETED DIRECTION Exact f(N) via SAT/ILP with a fixed execution environment COMPLETED DIRECTION Rigorous lower bound via modified (N/3,N] interval with Lean verification COMPLETED DIRECTION LP-duality upper bound on odd-part chains with 3-adic interactions COMPLETED PROOF
PROOF LP-duality experiment output v1 MARKDOWN Explore complete graph / 16 objects → Mission
Runtime 9 h 14 min
Iteration 57 of 57
Directions 331
Hypotheses 17
Experiments 266
Rejected paths 64 Current direction No direction is open.
Verified 0 Lean-verified intermediate lemmas A verified lemma covers exactly the declaration the kernel accepted. The problem stays open until it is settled either way. Literature
Indexed 109
Highly relevant 1 Iteration 14
Model calls 12
Estimated cost $0.0476 Budget remaining 98%
Iteration details & budget ↗