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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 29.
Research chronicle 93 RECORDS
All Research Review Verification System
↑ 87 earlier records 19:15:22 §88
GAUSS-01 GAUSS-01 stood down
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GAUSS-02 GAUSS-02 stood down
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GAUSS-03 GAUSS-03 stood down
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LITERATURE-01 LITERATURE-01 stood down
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SYSTEM Research run finished
19:15:22 §93
SYSTEM Iteration 29 completed
Research graph / proof lineage 7 objects · 0 links · 11 in complete graph
DIRECTION
DIRECTION Extremal density via double-counting over divisor chains COMPLETED DIRECTION Greedy and matching-based lower bounds COMPLETED DIRECTION Probabilistic and random subset analysis COMPLETED DIRECTION Structural decomposition by divisor intervals and rank layers COMPLETED DIRECTION Recursive interval-splitting bound via largest element and its multiples COMPLETED DIRECTION Linear-algebraic and poset chain-decomposition bound COMPLETED PROOF
PROOF Rank-layer bound check v1 MARKDOWN Explore complete graph / 18 objects → Research record
Agent record Close ×
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 The corpus is not published by the engine.
Iteration 29
Model calls 13
Estimated cost $0.006519 Budget remaining 99%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Structural decomposition by divisor intervals and rank layers
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,861
Cached input 0
Output tokens 455
Average latency 6.8 s
Failed calls 0
Cost (estimated) $0.000388
Joined 2026-09-25 19:13:01 UTC
Left 2026-09-25 19:15:22 UTC Recent activity 19:13:01 AGENT LITERATURE-01 joined as Literature Researcher 19:13:01 LITERATURE Literature search started 19:13:01 LITERATURE Literature search: 3 new of 3 19:13:01 LITERATURE Reviewed: Approximate Counting via Markov Chains 19:13:01 MEMORY Literature: Approximate Counting via Markov Chains 19:14:25 LITERATURE Literature search started 19:14:25 LITERATURE Indexed: Structural Evolution of Iron(III) Trifluoroacetate upon Thermal Decomposition: Chains, Layers, and Rings 19:14:25 LITERATURE Indexed: Structural Evolution of Iron(III) Trifluoroacetate upon Thermal Decomposition: Chains, Layers, and Rings Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. 19:14:25
LITERATURE
Indexed: Structural Evolution of Iron(III) Trifluoroacetate upon Thermal Decomposition: Chains, Layers, and Rings
19:14:25 LITERATURE Literature search: 3 new of 3
19:14:25 LITERATURE Reviewed: Structural Evolution of Iron(III) Trifluoroacetate upon Thermal Decomposition: Chains, Layers, and Rings
19:14:25 MEMORY Literature: Structural Evolution of Iron(III) Trifluoroacetate upon Thermal Decomposition: Chains, Layers, and Rings
19:15:22 AGENT LITERATURE-01 stood down