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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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AGENTS / 8 8 agents · 0 working
Frontier availability Showing iteration 13.
Research chronicle 0 RECORDS
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Mission
Runtime 9 h 10 min
Iteration 55 of 55
Directions 325
Hypotheses 17
Experiments 260
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 108
Highly relevant 1 Iteration 13
Model calls 12
Estimated cost $0.0502 Budget remaining 97%
Iteration details & budget ↗
Research graph / proof lineage 7 objects · 3 links · 8 in complete graph
DIRECTION
DIRECTION Hypergraph matching/covering upper bound via fractional weights COMPLETED DIRECTION Exact maxima f(N) for N up to 100 via ILP/SAT and structural data-mining of extremal sets COMPLETED DIRECTION Reproduce and verify the known Lebensold bounds and constructions REJECTED DIRECTION Per-grid LP upper bound over 2- and 3-smooth multiplier classes COMPLETED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (fail) FAIL PROOF
PROOF Small-N exact data and construction check v1 MARKDOWN Explore complete graph / 15 objects → 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 1,430
Cached input 517
Output tokens 1,456
Average latency 18.5 s
Failed calls 0
Cost (estimated) $0.000551
Joined 2026-09-25 18:08:59 UTC
Left 2026-09-25 18:13:19 UTC Recent activity 18:08:59 AGENT NOETHER joined as Strategist 18:09:00 TASK Research planning started 18:09:25 PLAN Research plan created 18:09:25 NOVELTY Novelty check: new 18:09:25 DIRECTION Direction proposed: Hypergraph matching/covering upper bound via fractional weights 18:09:25 DIRECTION Direction assigned to GAUSS-01: Hypergraph matching/covering upper bound via fractional weights 18:09:25 TASK Task completed 18:12:01 TASK Research planning started 18:12:15 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. PLAN
Research plan created
18:12:15 NOVELTY Novelty check: new
18:12:15 DIRECTION Direction proposed: Exact maxima f(N) for N up to 100 via ILP/SAT and structural data-mining of extremal sets
18:12:15 NOVELTY Novelty check: new
18:12:15 DIRECTION Direction proposed: Reproduce and verify the known Lebensold bounds and constructions
18:12:15 NOVELTY Novelty check: new
18:12:15 DIRECTION Direction proposed: Per-grid LP upper bound over 2- and 3-smooth multiplier classes
18:12:15 DIRECTION Direction assigned to GAUSS-01: Exact maxima f(N) for N up to 100 via ILP/SAT and structural data-mining of extremal sets
18:12:15 DIRECTION Direction assigned to GAUSS-02: Reproduce and verify the known Lebensold bounds and constructions
18:12:15 DIRECTION Direction assigned to GAUSS-03: Per-grid LP upper bound over 2- and 3-smooth multiplier classes
18:12:15 TASK Task completed
18:13:19 AGENT NOETHER stood down