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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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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 32
Model calls 13
Estimated cost $0.006439 Budget remaining 99%
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 1,073
Cached input 0
Output tokens 954
Average latency 19.6 s
Failed calls 0
Cost (estimated) $0.000417
Joined 2026-09-25 19:21:35 UTC
Left 2026-09-25 19:24:18 UTC Recent activity 19:21:51 NOVELTY Novelty check: new 19:21:51 DIRECTION Direction proposed: ILP-guided pattern discovery and induction proof 19:21:51 DIRECTION Direction assigned to GAUSS-01: Extremal construction and divisor-chain counting upper bound 19:21:51 DIRECTION Direction assigned to GAUSS-02: Probabilistic and density method for unavoidable triples 19:21:51 DIRECTION Direction assigned to GAUSS-03: ILP-guided pattern discovery and induction proof 19:21:51 TASK Task completed 19:22:58 TASK Research planning started 19:23:24 PLAN Research plan created Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
19:23:24
MEMORY
Novelty check: Prime-power layer decomposition and layer-wise extremal bounds
19:23:24 NOVELTY Novelty check: partially explored
19:23:24 DIRECTION Direction proposed: Prime-power layer decomposition and layer-wise extremal bounds
19:23:24 NOVELTY Novelty check: new
19:23:24 DIRECTION Direction proposed: Recursive divide-and-conquer via multiplicative doubling
19:23:24 NOVELTY Novelty check: new
19:23:24 DIRECTION Direction proposed: Small-interval exact pattern search and closed-form conjecture
19:23:24 DIRECTION Direction assigned to GAUSS-01: Prime-power layer decomposition and layer-wise extremal bounds
19:23:24 DIRECTION Direction assigned to GAUSS-02: Recursive divide-and-conquer via multiplicative doubling
19:23:24 DIRECTION Direction assigned to GAUSS-03: Small-interval exact pattern search and closed-form conjecture
19:23:24 TASK Task completed
19:24:18 AGENT NOETHER stood down