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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
AGENTS / 8 8 agents · 0 working
Frontier availability Showing iteration 21.
Research chronicle 105 RECORDS
All Research Review Verification System
18:46:44 §1
SYSTEM Iteration 21 opened
18:46:47 §2
SYSTEM Iteration 21 started
18:46:47 §3
SYSTEM Initializing research run
18:46:47 §4
NOETHER NOETHER joined as Strategist
18:46:47 §5
SYSTEM Research started
18:46:48 §6
NOETHER Research planning started
↑ 99 earlier records Research record
Agent record Close ×
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 1,475
Cached input 0
Output tokens 1,244
Average latency 22.2 s
Failed calls 0
Cost (estimated) $0.000555
Joined 2026-09-25 18:46:47 UTC
Left 2026-09-25 18:50:23 UTC Recent activity 18:47:16 DIRECTION Direction proposed: Constructive lower bound via layered odd-part families 18:47:16 NOVELTY Novelty check: new 18:47:16 DIRECTION Direction proposed: Exact values for small n via ILP and pattern extraction 18:47:16 DIRECTION Direction assigned to GAUSS-01: Probabilistic upper bound via random weights and divisor-count concentration 18:47:16 DIRECTION Direction assigned to GAUSS-02: Constructive lower bound via layered odd-part families 18:47:16 DIRECTION Direction assigned to GAUSS-03: Exact values for small n via ILP and pattern extraction 18:47:16 TASK Task completed 18:48:51 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.
09 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
18:49:09 PLAN Research plan created
18:49:09 NOVELTY Novelty check: new
18:49:09 DIRECTION Direction proposed: Minimal exact search: ILP/SAT for f(N), N<=40, with extremal sets
18:49:09 NOVELTY Novelty check: new
18:49:09 DIRECTION Direction proposed: Baseline verification and structural decomposition of the interval construction
18:49:09 NOVELTY Novelty check: new
18:49:09 DIRECTION Direction proposed: Targeted literature lookup and Lean formalization of a small-N lemma
18:49:09 DIRECTION Direction assigned to GAUSS-01: Minimal exact search: ILP/SAT for f(N), N<=40, with extremal sets
18:49:09 DIRECTION Direction assigned to GAUSS-02: Baseline verification and structural decomposition of the interval construction
18:49:09 DIRECTION Direction assigned to GAUSS-03: Targeted literature lookup and Lean formalization of a small-N lemma
18:49:09 TASK Task completed
18:50:23 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 21
Model calls 13
Estimated cost $0.0533 Budget remaining 97%
Iteration details & budget ↗
Research graph / proof lineage 9 objects · 3 links · 10 in complete graph
DIRECTION
DIRECTION Probabilistic upper bound via random weights and divisor-count concentration COMPLETED DIRECTION Constructive lower bound via layered odd-part families COMPLETED DIRECTION Exact values for small n via ILP and pattern extraction COMPLETED DIRECTION Minimal exact search: ILP/SAT for f(N), N<=40, with extremal sets COMPLETED DIRECTION Baseline verification and structural decomposition of the interval construction COMPLETED DIRECTION Targeted literature lookup and Lean formalization of a small-N lemma REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (fail) FAIL PROOF
PROOF Interval verification and odd-part decomposition v1 MARKDOWN Explore complete graph / 19 objects →