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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 6.
Research chronicle 106 RECORDS
All Research Review Verification System
↑ 100 earlier records 16:56:36 §101
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
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SYSTEM Iteration 6 completed
Research graph / proof lineage 9 objects · 3 links · 7 in complete graph
DIRECTION
DIRECTION Density and divisor-graph matching upper bound REJECTED DIRECTION Lower-bound construction via residue classes and CRT COMPLETED DIRECTION Prime-factor structural decomposition and exact small cases REJECTED DIRECTION Recursive interval-splitting via 2-cover-free hypergraphs COMPLETED DIRECTION Weighted counting with shifted geometric progressions COMPLETED DIRECTION Transfer-matrix / DP exact computation for small intervals and extrapolation REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (needs_work) NEEDS WORK PROOF
PROOF Experiment report — Check for N <= 30 whether the recursive interval-splitting bound f(N) <= f(floor v1 MARKDOWN Explore complete graph / 16 objects → Research record
Agent record Close ×
Mission
Runtime 6 h 14 min
Iteration 10 of 10
Directions 54
Hypotheses 8
Experiments 21
Rejected paths 39 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 26
Highly relevant 0 Iteration 6
Model calls 19
Estimated cost $0.1714 Budget remaining 93%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Recursive interval-splitting via 2-cover-free hypergraphs
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,869
Cached input 0
Output tokens 442
Average latency 4.6 s
Failed calls 0
Cost (estimated) $0.000385
Joined 2026-09-25 16:52:48 UTC
Left 2026-09-25 16:56:36 UTC Recent activity 16:52:48 AGENT LITERATURE-01 joined as Literature Researcher 16:52:48 LITERATURE Literature search started 16:52:48 LITERATURE Indexed: Upper-Bound Energy Minimization to Search for Stable Functional Materials with Graph Neural Networks 16:52:48 LITERATURE Literature search: 3 new of 3 16:52:48 LITERATURE Reviewed: An upper bound of a generalized upper Hamiltonian number of a graph 16:52:48 MEMORY Literature: An upper bound of a generalized upper Hamiltonian number of a graph 16:54:35 LITERATURE Literature search started 16:54:35 LITERATURE Indexed: Interval hypergraphs and D-interval hypergraphs 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. 16:54:35
LITERATURE
Indexed: Interval mixed hypergraphs
16:54:35 LITERATURE Indexed: Color-bounded hypergraphs, II: Interval hypergraphs and hypertrees
16:54:35 LITERATURE Literature search: 3 new of 3
16:54:35 LITERATURE Reviewed: Interval hypergraphs and D-interval hypergraphs
16:54:35 MEMORY Literature: Interval hypergraphs and D-interval hypergraphs
16:56:36 AGENT LITERATURE-01 stood down