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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 8.
Research chronicle 92 RECORDS
All Research Review Verification System
↑ 86 earlier records 17:00:48 §87
NOETHER NOETHER stood down
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GAUSS-01 GAUSS-01 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
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SYSTEM Iteration 8 completed
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Extremal density via double-counting over divisor chains COMPLETED DIRECTION Hypergraph independence number via container method COMPLETED DIRECTION Probabilistic construction and lower bound via random subsets with divisor-pair avoidance COMPLETED DIRECTION CRT residue-class decomposition and local forbidden-pattern bounds COMPLETED DIRECTION Recursive interval-splitting with rigorous upper bounds via dynamic programming REJECTED DIRECTION Spectral / Lagrangian relaxation on the divisor hypergraph via weighted Motzkin-Straus COMPLETED PROOF
PROOF CRT residue-class density check v1 MARKDOWN Explore complete graph / 17 objects → Research record
Agent record Close ×
Mission
Runtime 8 h 14 min
Iteration 34 of 34
Directions 196
Hypotheses 16
Experiments 145
Rejected paths 59 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 8
Model calls 16
Estimated cost $0.1684 Budget remaining 93%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: CRT residue-class decomposition and local forbidden-pattern bounds
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,862
Cached input 0
Output tokens 385
Average latency 4.0 s
Failed calls 0
Cost (estimated) $0.000368
Joined 2026-09-25 16:57:04 UTC
Left 2026-09-25 17:00:48 UTC Recent activity 16:57:04 AGENT LITERATURE-01 joined as Literature Researcher 16:57:04 LITERATURE Literature search started 16:57:04 LITERATURE Indexed: Approximate Counting via Markov Chains 16:57:04 LITERATURE Indexed: On double chains and inverse double chains of modules over a commutative ring 16:57:04 LITERATURE Indexed: Divisorial extremal contractions of threefolds: Divisor to point 16:57:04 LITERATURE Literature search: 3 new of 3 16:57:04 LITERATURE Reviewed: Approximate Counting via Markov Chains 16:57:04 MEMORY Literature: Approximate Counting via Markov Chains 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. 16:58:34
LITERATURE
Literature search started
16:58:34 LITERATURE Indexed: Bounds on the Natarajan dimension of a class of linear multi-class predictors
16:58:34 LITERATURE Indexed: IRCNN: A novel signal decomposition approach based on iterative residue convolutional neural network
16:58:34 LITERATURE Indexed: On the usefulness of one-class classifier ensembles for decomposition of multi-class problems
16:58:34 LITERATURE Literature search: 3 new of 3
16:58:34 LITERATURE Reviewed: Bounds on the Natarajan dimension of a class of linear multi-class predictors
16:58:34 MEMORY Literature: Bounds on the Natarajan dimension of a class of linear multi-class predictors
17:00:48 AGENT LITERATURE-01 stood down