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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 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 22
Model calls 11
Estimated cost $0.0561 Budget remaining 97%
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 2
Input tokens 1,489
Cached input 0
Output tokens 1,248
Average latency 23.9 s
Failed calls 0
Cost (estimated) $0.000558
Joined 2026-09-25 18:50:26 UTC
Left 2026-09-25 18:53:53 UTC Recent activity 18:50:41 DIRECTION Direction proposed: Hypergraph container and extremal upper bound 18:50:41 NOVELTY Novelty check: new 18:50:41 DIRECTION Direction proposed: Computational search and inductive pattern discovery 18:50:41 DIRECTION Direction assigned to GAUSS-01: Probabilistic construction via random sparse sets 18:50:41 DIRECTION Direction assigned to GAUSS-02: Hypergraph container and extremal upper bound 18:50:41 DIRECTION Direction assigned to GAUSS-03: Computational search and inductive pattern discovery 18:50:41 TASK Task completed 18:52:04 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.
18:52:39
PLAN
Research plan created
18:52:39 NOVELTY Novelty check: new
18:52:39 DIRECTION Direction proposed: Exact computation of f(N) for N up to 200 and comparison with 2N/3
18:52:39 NOVELTY Novelty check: new
18:52:39 DIRECTION Direction proposed: Chain-decomposition upper bound and Lean formalisation
18:52:39 NOVELTY Novelty check: new
18:52:39 DIRECTION Direction proposed: 2D grid upper bound and pattern-based lower bound improvement
18:52:39 DIRECTION Direction assigned to GAUSS-01: Exact computation of f(N) for N up to 200 and comparison with 2N/3
18:52:39 DIRECTION Direction assigned to GAUSS-02: Chain-decomposition upper bound and Lean formalisation
18:52:39 DIRECTION Direction assigned to GAUSS-03: 2D grid upper bound and pattern-based lower bound improvement
18:52:39 TASK Task completed
18:53:53 AGENT NOETHER stood down