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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
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Research record
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AGENTS / 6 6 agents · 0 working
Frontier availability 07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. Mission
Runtime 9 h 7 min
Iteration 55 of 55
Directions 319
Hypotheses 17
Experiments 256
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 106
Highly relevant 1 Iteration 14
Model calls 12
Estimated cost $0.0476 Budget remaining 98%
Iteration details & budget ↗
NOETHER Strategist
Plan iteration 2
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 3
Input tokens 1,464
Cached input 0
Output tokens 1,155
Average latency 29.7 s
Failed calls 1
Cost (estimated) $0.000529
Joined 2026-09-25 18:13:22 UTC
Left 2026-09-25 18:17:07 UTC Recent activity 18:13:33 DIRECTION Direction proposed: Constructive lower bound via layered sets and density optimization 18:13:33 NOVELTY Novelty check: new 18:13:33 DIRECTION Direction proposed: Computational search and ILP extrapolation for exact small-n values 18:13:33 DIRECTION Direction assigned to GAUSS-01: Probabilistic upper bound via random weights and divisor moments 18:13:33 DIRECTION Direction assigned to GAUSS-02: Constructive lower bound via layered sets and density optimization 18:13:33 DIRECTION Direction assigned to GAUSS-03: Computational search and ILP extrapolation for exact small-n values 18:13:33 TASK Task completed 18:14:31 TASK Research planning started Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
18:15:53 PLAN Research plan created
18:15:53 NOVELTY Novelty check: new
18:15:53 DIRECTION Direction proposed: Exact f(N) via SAT/ILP with a fixed execution environment
18:15:53 NOVELTY Novelty check: new
18:15:53 DIRECTION Direction proposed: Rigorous lower bound via modified (N/3,N] interval with Lean verification
18:15:53 NOVELTY Novelty check: new
18:15:53 DIRECTION Direction proposed: LP-duality upper bound on odd-part chains with 3-adic interactions
18:15:53 DIRECTION Direction assigned to GAUSS-01: Exact f(N) via SAT/ILP with a fixed execution environment
18:15:53 DIRECTION Direction assigned to GAUSS-02: Rigorous lower bound via modified (N/3,N] interval with Lean verification
18:15:53 DIRECTION Direction assigned to GAUSS-03: LP-duality upper bound on odd-part chains with 3-adic interactions
18:15:53 TASK Task completed
18:17:07 AGENT NOETHER stood down