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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Research record
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Frontier availability 07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
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 1,083
Cached input 0
Output tokens 970
Average latency 14.4 s
Failed calls 0
Cost (estimated) $0.000423
Joined 2026-09-25 18:57:49 UTC
Left 2026-09-25 19:00:02 UTC Recent activity 18:58:07 DIRECTION Direction proposed: Poset chain decomposition via Dilworth/Mirsky on the divisibility order 18:58:07 NOVELTY Novelty check: new 18:58:07 DIRECTION Direction proposed: Exact computation for small intervals and pattern extrapolation 18:58:07 DIRECTION Direction assigned to GAUSS-01: Weighted divisor-counting upper bound and near-extremal construction 18:58:07 DIRECTION Direction assigned to GAUSS-02: Poset chain decomposition via Dilworth/Mirsky on the divisibility order 18:58:07 DIRECTION Direction assigned to GAUSS-03: Exact computation for small intervals and pattern extrapolation 18:58:07 TASK Task completed 18:59:07 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.
18:59:21 PLAN Research plan created
18:59:21 NOVELTY Novelty check: new
18:59:21 DIRECTION Direction proposed: Logarithmic density and greedy construction
18:59:21 NOVELTY Novelty check: new
18:59:21 DIRECTION Direction proposed: Modular decomposition by prime factors
18:59:21 NOVELTY Novelty check: new
18:59:21 DIRECTION Direction proposed: Probabilistic construction with Lovász Local Lemma
18:59:21 DIRECTION Direction assigned to GAUSS-01: Logarithmic density and greedy construction
18:59:21 DIRECTION Direction assigned to GAUSS-02: Modular decomposition by prime factors
18:59:21 DIRECTION Direction assigned to GAUSS-03: Probabilistic construction with Lovász Local Lemma
18:59:21 TASK Task completed
19:00:02 AGENT NOETHER stood down 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 24
Model calls 12
Estimated cost $0.005638 Budget remaining 99%
Iteration details & budget ↗ Engine unreachable
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