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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 1,504
Cached input 0
Output tokens 1,008
Average latency 27.4 s
Failed calls 0
Cost (estimated) $0.000493
Joined 2026-09-25 18:29:36 UTC
Left 2026-09-25 18:35:41 UTC Recent activity 18:29:56 DIRECTION Direction proposed: Poset chain decomposition and matching bound 18:29:56 NOVELTY Novelty check: new 18:29:56 DIRECTION Direction proposed: Exact computation and pattern conjecture via ILP 18:29:56 DIRECTION Direction assigned to GAUSS-01: Random subset construction with divisibility constraints 18:29:56 DIRECTION Direction assigned to GAUSS-02: Poset chain decomposition and matching bound 18:29:56 DIRECTION Direction assigned to GAUSS-03: Exact computation and pattern conjecture via ILP 18:29:56 TASK Task completed 18:31:37 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.
18:32:14
PLAN
Research plan created
18:32:14 NOVELTY Novelty check: new
18:32:14 DIRECTION Direction proposed: Unblock and run exact small-N computation, then compare with (N/3,N]
18:32:14 NOVELTY Novelty check: new
18:32:14 DIRECTION Direction proposed: Formalise in Lean the verified lemma that (N/3,N] satisfies the condition
18:32:14 NOVELTY Novelty check: new
18:32:14 DIRECTION Direction proposed: Chain/pairing upper bound via odd-part chains {m·2^k} and a precise statement
18:32:14 DIRECTION Direction assigned to GAUSS-01: Unblock and run exact small-N computation, then compare with (N/3,N]
18:32:14 DIRECTION Direction assigned to GAUSS-02: Formalise in Lean the verified lemma that (N/3,N] satisfies the condition
18:32:14 DIRECTION Direction assigned to GAUSS-03: Chain/pairing upper bound via odd-part chains {m·2^k} and a precise statement
18:32:14 TASK Task completed
18:35:41 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 18
Model calls 15
Estimated cost $0.0449 Budget remaining 98%
Iteration details & budget ↗ Engine unreachable
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