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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 3
Input tokens 1,589
Cached input 517
Output tokens 1,672
Average latency 20.2 s
Failed calls 1
Cost (estimated) $0.000635
Joined 2026-09-25 19:12:21 UTC
Left 2026-09-25 19:15:22 UTC Recent activity 19:13:01 DIRECTION Direction proposed: Greedy and matching-based lower bounds 19:13:01 NOVELTY Novelty check: new 19:13:01 DIRECTION Direction proposed: Probabilistic and random subset analysis 19:13:01 DIRECTION Direction assigned to GAUSS-01: Extremal density via double-counting over divisor chains 19:13:01 DIRECTION Direction assigned to GAUSS-02: Greedy and matching-based lower bounds 19:13:01 DIRECTION Direction assigned to GAUSS-03: Probabilistic and random subset analysis 19:13:01 TASK Task completed 19:14:01 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.
19:14:25
PLAN
Research plan created
19:14:25 NOVELTY Novelty check: new
19:14:25 DIRECTION Direction proposed: Structural decomposition by divisor intervals and rank layers
19:14:25 NOVELTY Novelty check: new
19:14:25 DIRECTION Direction proposed: Recursive interval-splitting bound via largest element and its multiples
19:14:25 NOVELTY Novelty check: new
19:14:25 DIRECTION Direction proposed: Linear-algebraic and poset chain-decomposition bound
19:14:25 DIRECTION Direction assigned to GAUSS-01: Structural decomposition by divisor intervals and rank layers
19:14:25 DIRECTION Direction assigned to GAUSS-02: Recursive interval-splitting bound via largest element and its multiples
19:14:25 DIRECTION Direction assigned to GAUSS-03: Linear-algebraic and poset chain-decomposition bound
19:14:25 TASK Task completed
19:15:22 AGENT NOETHER stood down Engine unreachable
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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 29
Model calls 13
Estimated cost $0.006519 Budget remaining 99%
Iteration details & budget ↗