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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 13.
Research chronicle 92 RECORDS
All Research Review Verification System
↑ 86 earlier records 18:13:19 §87
GAUSS-02 GAUSS-02 stood down
18:13:19 §88
GAUSS-03 GAUSS-03 stood down
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LITERATURE-02 LITERATURE-02 stood down
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TURING TURING stood down
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SYSTEM Research run finished
18:13:19 §92
SYSTEM Iteration 13 completed
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 ×
Mission
Runtime 9 h 10 min
Iteration 55 of 55
Directions 325
Hypotheses 17
Experiments 258
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 ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Exact maxima f(N) for up to 100 via ILP/SAT and structural data-mining of extremal sets
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,894
Cached input 0
Output tokens 608
Average latency 6.7 s
Failed calls 0
Cost (estimated) $0.000436
Joined 2026-09-25 18:09:25 UTC
Left 2026-09-25 18:13:19 UTC Recent activity 18:09:25 AGENT LITERATURE-01 joined as Literature Researcher 18:09:25 LITERATURE Literature search started 18:09:25 LITERATURE Indexed: Asymptotics of Hypergraph Matching, Covering and Coloring Problems 18:09:25 LITERATURE Indexed: Hypergraph matching via game-theoretic hypergraph clustering 18:09:25 LITERATURE Indexed: Improved efficiency for covering codes matching the sphere-covering bound 18:09:25 LITERATURE Literature search: 3 new of 3 18:09:25 LITERATURE Reviewed: Asymptotics of Hypergraph Matching, Covering and Coloring Problems 18:09:25 MEMORY Literature: Asymptotics of Hypergraph Matching, Covering and Coloring Problems 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.
18:12:15 LITERATURE Literature search started
18:12:15 LITERATURE Indexed: Fast Algorithms for Finding Extremal Sets
18:12:15 LITERATURE Indexed: Pruned Simple Model Sets for Fast Exact Recovery of Image
18:12:15 LITERATURE Indexed: The Generic Rough Set Inductive Logic Programming (gRS—ILP) Model
18:12:15 LITERATURE Literature search: 3 new of 3
18:12:15 LITERATURE Reviewed: Fast Algorithms for Finding Extremal Sets
18:12:15 MEMORY Literature: Fast Algorithms for Finding Extremal Sets
18:13:19 AGENT LITERATURE-01 stood down