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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 06 Research director Not started On the roster; the workflow has not woken it in this iteration. 07 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 5 No frontier agent engaged
Model calls 15
Estimated cost $0.0148 Budget remaining 99%
Iteration details & budget ↗
NOETHER Strategist
Plan iteration 2
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,193
Cached input 642
Output tokens 1,647
Average latency 5.7 s
Failed calls 0
Cost (estimated) $0.001167
Joined 2026-09-25 11:20:51 UTC
Left 2026-09-25 11:22:25 UTC Recent activity 11:20:59 DIRECTION Direction proposed: Random subset construction and the probabilistic method 11:20:59 NOVELTY Novelty check: new 11:20:59 DIRECTION Direction proposed: Chain decomposition via Dilworth’s theorem and antichain analysis 11:20:59 DIRECTION Direction assigned to GAUSS-01: Divisibility digraph and Turán‑type extremal bound 11:20:59 DIRECTION Direction assigned to GAUSS-02: Random subset construction and the probabilistic method 11:20:59 DIRECTION Direction assigned to GAUSS-03: Chain decomposition via Dilworth’s theorem and antichain analysis 11:20:59 TASK Task completed 11:21:39 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.
11:21:45 PLAN Research plan created
11:21:45 NOVELTY Novelty check: new
11:21:45 DIRECTION Direction proposed: Sieve‑style triple counting
11:21:45 NOVELTY Novelty check: new
11:21:45 DIRECTION Direction proposed: Hypergraph container method for forbidden 2‑divisor configurations
11:21:45 NOVELTY Novelty check: new
11:21:45 DIRECTION Direction proposed: Residue‑class and multiplicative order partition
11:21:45 DIRECTION Direction assigned to GAUSS-01: Sieve‑style triple counting
11:21:45 DIRECTION Direction assigned to GAUSS-02: Hypergraph container method for forbidden 2‑divisor configurations
11:21:45 DIRECTION Direction assigned to GAUSS-03: Residue‑class and multiplicative order partition
11:21:45 TASK Task completed
11:22:25 AGENT NOETHER stood down