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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 26.
Research chronicle 111 RECORDS
All Research Review Verification System
↑ 105 earlier records 19:05:50 §106
GAUSS-03 GAUSS-03 stood down
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LITERATURE-01 LITERATURE-01 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
19:05:50 §111
SYSTEM Iteration 26 completed
Research graph / proof lineage 9 objects · 3 links · 10 in complete graph
DIRECTION
DIRECTION Probabilistic lower bound via random subsets and divisor hypergraph independence COMPLETED DIRECTION Upper bound via hypergraph Turán and container methods COMPLETED DIRECTION Computational exploration and structural conjecture for small n COMPLETED DIRECTION Constructive lower bounds via modular residue classes and interval packing COMPLETED DIRECTION Upper bounds via divisor-weight double counting and local sparsity COMPLETED DIRECTION Structural characterization via maximal chains in the divisibility poset REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (fail) FAIL PROOF
PROOF Experiment report — Compute exact f(N) for N<=22 by exhaustive subset search and for N<=30 by branch v1 MARKDOWN Explore complete graph / 19 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
Indexed 109
Highly relevant 1 Iteration 26
Model calls 14
Estimated cost $0.007592 Budget remaining 99%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Constructive lower bounds via modular residue classes and interval packing
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,870
Cached input 0
Output tokens 577
Average latency 10.0 s
Failed calls 0
Cost (estimated) $0.000423
Joined 2026-09-25 19:02:51 UTC
Left 2026-09-25 19:05:50 UTC Recent activity 19:02:51 AGENT LITERATURE-01 joined as Literature Researcher 19:02:51 LITERATURE Literature search started 19:02:51 LITERATURE Indexed: A Probabilistic lower bound on the independence number of graphs 19:02:51 LITERATURE Indexed: Probabilistic Methods and Random Graphs 19:02:51 LITERATURE Indexed: An upper bound on k-connectivity for a random geometric r-uniform hypergraph 19:02:51 LITERATURE Literature search: 3 new of 3 19:02:51 LITERATURE Reviewed: A Probabilistic lower bound on the independence number of graphs 19:02:51 MEMORY Literature: A Probabilistic lower bound on the independence number of graphs 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. 19:04:06
LITERATURE
Literature search started
19:04:06 LITERATURE Indexed: New classes of fast lower bounds for bin packing problems
19:04:06 LITERATURE Indexed: New lower bounds for certain classes of bin packing algorithms
19:04:06 LITERATURE Indexed: Dual linear programming bounds for sphere packing via modular forms
19:04:06 LITERATURE Literature search: 3 new of 3
19:04:06 LITERATURE Reviewed: New classes of fast lower bounds for bin packing problems
19:04:06 MEMORY Literature: New classes of fast lower bounds for bin packing problems
19:05:50 AGENT LITERATURE-01 stood down