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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 40.
Research chronicle 96 RECORDS
All Research Review Verification System
↑ 90 earlier records 19:48:16 §91
GAUSS-01 GAUSS-01 stood down
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GAUSS-02 GAUSS-02 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 40 completed
Research graph / proof lineage 7 objects · 0 links · 12 in complete graph
DIRECTION
DIRECTION Random multiplicative construction with density above 1/3 COMPLETED DIRECTION Hypergraph container and flag-algebra bound on the divisor poset COMPLETED DIRECTION Chain decomposition and weighted LYM inequality COMPLETED DIRECTION Parity-coloring and cross-divisibility matching bound COMPLETED DIRECTION Density increment via iterative removal of small divisors COMPLETED DIRECTION Extremal construction via (n/3, n] plus small elements and LP bound COMPLETED PROOF
PROOF Experiment report — Check, for N up to 200, that forbidden triples a|b, a|c (b!=c) occur with all fo 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 40
Model calls 12
Estimated cost $0.006645 Budget remaining 99%
Iteration details & budget ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Parity-coloring and cross-divisibility matching bound
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,859
Cached input 0
Output tokens 557
Average latency 6.6 s
Failed calls 0
Cost (estimated) $0.000417
Joined 2026-09-25 19:45:56 UTC
Left 2026-09-25 19:48:16 UTC Recent activity 19:45:56 AGENT LITERATURE-01 joined as Literature Researcher 19:45:56 LITERATURE Literature search started 19:45:56 LITERATURE Indexed: Spectral density of random signals corrupted by multiplicative noise 19:45:56 LITERATURE Indexed: The construction of fast portable multiplicative congruential random number generators 19:45:56 LITERATURE Indexed: On mean values of random multiplicative functions 19:45:56 LITERATURE Literature search: 3 new of 3 19:45:56 LITERATURE Reviewed: Spectral density of random signals corrupted by multiplicative noise 19:45:56 MEMORY Literature: Spectral density of random signals corrupted by multiplicative noise 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.
19:47:27 LITERATURE Literature search started
19:47:27 LITERATURE Indexed: Improved bound on facial parity edge coloring
19:47:27 LITERATURE Indexed: Perfect divisibility and coloring in fork-free graphs
19:47:27 LITERATURE Literature search: 3 new of 3
19:47:27 LITERATURE Reviewed: Coloring Graph Classes with no Induced Hammer via 2-Divisibility and Perfect Divisibility
19:47:27 MEMORY Literature: Coloring Graph Classes with no Induced Hammer via 2-Divisibility and Perfect Divisibility
19:48:16 AGENT LITERATURE-01 stood down