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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 46.
Research chronicle 92 RECORDS
All Research Review Verification System
19:59:28 §1
SYSTEM Iteration 46 opened
19:59:30 §2
SYSTEM Iteration 46 started
19:59:30 §3
SYSTEM Initializing research run
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NOETHER NOETHER joined as Strategist
19:59:30 §5
SYSTEM Research started
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NOETHER Research planning started
↑ 86 earlier records Research record
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LITERATURE-01 Literature researcher
Reading the landscape around: Weighted density upper bound via divisor-chain penalties
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,879
Cached input 0
Output tokens 599
Average latency 3.4 s
Failed calls 0
Cost (estimated) $0.000431
Joined 2026-09-25 19:59:39 UTC
Left 2026-09-25 20:01:33 UTC Recent activity 19:59:39 AGENT LITERATURE-01 joined as Literature Researcher 19:59:39 LITERATURE Literature search started 19:59:39 LITERATURE Literature search: 3 new of 3 19:59:39 LITERATURE Reviewed: An Upper Bound on the Divisor Counting Function 19:59:39 MEMORY Literature: An Upper Bound on the Divisor Counting Function 20:00:29 LITERATURE Literature search started 20:00:29 LITERATURE Indexed: Convex optimization formulation of density upper bound constraints in Markov chain synthesis 20:00:29 LITERATURE Literature search: 3 new of 3 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. 20:00:29
LITERATURE
Reviewed: Convex optimization formulation of density upper bound constraints in Markov chain synthesis
20:00:29 MEMORY Literature: Convex optimization formulation of density upper bound constraints in Markov chain synthesis
20:01:33 AGENT LITERATURE-01 stood down 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 46
Model calls 12
Estimated cost $0.006373 Budget remaining 99%
Iteration details & budget ↗
Research graph / proof lineage 7 objects · 0 links · 12 in complete graph
DIRECTION
DIRECTION Probabilistic upper bound via divisor-count weighting COMPLETED DIRECTION Constructive lower bound from prime-power layers COMPLETED DIRECTION Exact small-n computation and extremal pattern extraction COMPLETED DIRECTION Weighted density upper bound via divisor-chain penalties COMPLETED DIRECTION Block decomposition into divisor-closed intervals COMPLETED DIRECTION Greedy removal and potential-function lower bound COMPLETED PROOF
PROOF Weighted double-counting search results v1 MARKDOWN Explore complete graph / 19 objects →