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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 42.
Research chronicle 89 RECORDS
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Research graph / proof lineage 7 objects · 0 links · 7 in complete graph
DIRECTION
DIRECTION Constructive extremal families via layered residue classes COMPLETED DIRECTION Analytic upper bound via multiple-counting and interval compression REJECTED DIRECTION Graph-theoretic reformulation and computational pattern mining COMPLETED DIRECTION Recursive parity-layer decomposition for exact extremal recurrences REJECTED DIRECTION Divisor-graph matching and König-type upper bounds COMPLETED DIRECTION Periodic block constructions via CRT and residue-class designs COMPLETED PROOF
PROOF LP bound vs true f(N) for N up to 20 v1 MARKDOWN Explore complete graph / 14 objects → Research record
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LITERATURE-01 Literature researcher
Reading the landscape around: Recursive parity-layer decomposition for exact extremal recurrences
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,866
Cached input 0
Output tokens 403
Average latency 4.8 s
Failed calls 0
Cost (estimated) $0.000374
Joined 2026-09-25 19:50:55 UTC
Left 2026-09-25 19:53:50 UTC Recent activity 19:50:55 AGENT LITERATURE-01 joined as Literature Researcher 19:50:55 LITERATURE Literature search started 19:50:55 LITERATURE Indexed: Two classes of graphs related to extremal eccentricities 19:50:55 LITERATURE Indexed: Several extremal coreflective classes in uniform spaces 19:50:55 LITERATURE Indexed: Finite Hypergraph Families with Rich Extremal Turán Constructions via Mixing Patterns 19:50:55 LITERATURE Literature search: 3 new of 3 19:50:55 LITERATURE Reviewed: Two classes of graphs related to extremal eccentricities 19:50:55 MEMORY Literature: Two classes of graphs related to extremal eccentricities Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
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LITERATURE
Literature search started
19:52:22 LITERATURE Indexed: REGGE RECURRENCE PARITY ASSIGNMENTS FOR THE S = 0 REGGE RECURRENCES
19:52:22 LITERATURE Indexed: About one problem on extremal decomposition
19:52:22 LITERATURE Indexed: A novel layer-by-layer recursive decomposition algorithm for calculation of network reliability
19:52:22 LITERATURE Literature search: 3 new of 3
19:52:22 LITERATURE Reviewed: REGGE RECURRENCE PARITY ASSIGNMENTS FOR THE S = 0 REGGE RECURRENCES
19:52:22 MEMORY Literature: REGGE RECURRENCE PARITY ASSIGNMENTS FOR THE S = 0 REGGE RECURRENCES
19:53:50 AGENT LITERATURE-01 stood down