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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
AGENTS / 6 6 agents · 0 working
Frontier availability Showing iteration 19.
Research chronicle 90 RECORDS
All Research Review Verification System
18:35:41 §1
SYSTEM Iteration 19 opened
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SYSTEM Iteration 19 started
18:35:44 §3
SYSTEM Initializing research run
18:35:44 §4
NOETHER NOETHER joined as Strategist
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SYSTEM Research started
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NOETHER Research planning started
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LITERATURE-01 Literature researcher
Reading the landscape around: Exact f(N) for up to 30 and canonical problem statement
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,843
Cached input 0
Output tokens 722
Average latency 11.8 s
Failed calls 0
Cost (estimated) $0.000460
Joined 2026-09-25 18:36:14 UTC
Left 2026-09-25 18:39:36 UTC Recent activity 18:36:14 AGENT LITERATURE-01 joined as Literature Researcher 18:36:14 LITERATURE Literature search started 18:36:14 LITERATURE Indexed: A New Upper Bound on Extremal Number of Even Cycles 18:36:14 LITERATURE Literature search: 3 new of 3 18:36:14 LITERATURE Reviewed: An Upper Bound on the Divisor Counting Function 18:36:14 MEMORY Literature: An Upper Bound on the Divisor Counting Function 18:38:16 LITERATURE Literature search started 18:38:16 LITERATURE Indexed: Statement of the problem. 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. 18:38:16
LITERATURE
Indexed: Fast exact and quasi-minimal minimization of highly testable fixed-polarity AND/XOR canonical networks
18:38:16 LITERATURE Indexed: Problem Statement Language/Problem Statement Analyzer
18:38:16 LITERATURE Literature search: 3 new of 3
18:38:16 LITERATURE Reviewed: Statement of the problem.
18:38:16 MEMORY Literature: Statement of the problem.
18:39:36 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 19
Model calls 11
Estimated cost $0.0475 Budget remaining 98%
Iteration details & budget ↗
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Extremal construction and divisor-chain counting upper bound COMPLETED DIRECTION Density/entropy approach via random subsets and multiplicative structure COMPLETED DIRECTION Computational search and induction for small intervals to guess exact extremal function COMPLETED DIRECTION Exact f(N) for N up to 30 and canonical problem statement COMPLETED DIRECTION Per-chain upper bound via 2^a 3^b m decomposition COMPLETED DIRECTION Literature check and comparison against ceil(2N/3) baseline COMPLETED PROOF
PROOF Experiment report — Compute exact f(N) for N=1..30 by bitmask DP over divisor constraints, and verif v1 MARKDOWN Explore complete graph / 17 objects →