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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 08 Research director Not started On the roster; the workflow has not woken it in this iteration. 09 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. Mission
Runtime 6 h 14 min
Iteration 10 of 10
Directions 54
Hypotheses 8
Experiments 21
Rejected paths 39 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 26
Highly relevant 0 Iteration 7 No frontier agent engaged
Model calls 44
Estimated cost $0.0449 Budget remaining 98%
Iteration details & budget ↗
NOETHER Strategist
Plan iteration 6
Blocked: The model returned an unusable response
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 8
Input tokens 6,147
Cached input 2,041
Output tokens 10,147
Average latency 10.7 s
Failed calls 3
Cost (estimated) $0.007011
Joined 2026-09-25 11:36:06 UTC
Left 2026-09-25 11:41:48 UTC Recent activity 11:39:45 NOVELTY Novelty check: new 11:39:45 DIRECTION Direction proposed: Exact Extremal Computation via SAT/SMT with Symmetry Breaking 11:39:45 DIRECTION Direction assigned to GAUSS-01: Entropy‑Based Upper Bound via Shearer’s Inequality 11:39:45 DIRECTION Direction assigned to GAUSS-02: Largest‑Prime‑Factor Partition and Smooth‑Number Estimates 11:39:45 DIRECTION Direction assigned to GAUSS-03: Exact Extremal Computation via SAT/SMT with Symmetry Breaking 11:39:45 TASK Task completed 11:40:29 TASK Research planning started 11:40:42 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.
11:40:42
NOVELTY
Novelty check: new
11:40:42 DIRECTION Direction proposed: Exponent‑vector antichain via Sperner theory
11:40:42 NOVELTY Novelty check: new
11:40:42 DIRECTION Direction proposed: Adaptation of multiplicative Sidon set results
11:40:42 NOVELTY Novelty check: new
11:40:42 DIRECTION Direction proposed: Recursive block decomposition and symmetry‑reduced integer programming
11:40:42 DIRECTION Direction assigned to GAUSS-01: Exponent‑vector antichain via Sperner theory
11:40:42 DIRECTION Direction assigned to GAUSS-02: Adaptation of multiplicative Sidon set results
11:40:42 DIRECTION Direction assigned to GAUSS-03: Recursive block decomposition and symmetry‑reduced integer programming
11:40:42 TASK Task completed
11:41:21 TASK Research planning started
11:41:48 TASK Task completed