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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
19:48:16 §92
GAUSS-02 GAUSS-02 stood down
19:48:16 §93
GAUSS-03 GAUSS-03 stood down
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LITERATURE-01 LITERATURE-01 stood down
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SYSTEM Research run finished
19:48:16 §96
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 ↗
NOETHER Strategist
Plan iteration 2
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,076
Cached input 0
Output tokens 1,233
Average latency 23.7 s
Failed calls 0
Cost (estimated) $0.000496
Joined 2026-09-25 19:45:33 UTC
Left 2026-09-25 19:48:16 UTC Recent activity 19:45:56 MEMORY Novelty check: Chain decomposition and weighted LYM inequality 19:45:56 NOVELTY Novelty check: partially explored 19:45:56 DIRECTION Direction proposed: Chain decomposition and weighted LYM inequality 19:45:56 DIRECTION Direction assigned to GAUSS-01: Random multiplicative construction with density above 1/3 19:45:56 DIRECTION Direction assigned to GAUSS-02: Hypergraph container and flag-algebra bound on the divisor poset 19:45:56 DIRECTION Direction assigned to GAUSS-03: Chain decomposition and weighted LYM inequality 19:45:56 TASK Task completed 19:46:58 TASK Research planning started 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
PLAN
Research plan created
19:47:27 NOVELTY Novelty check: new
19:47:27 DIRECTION Direction proposed: Parity-coloring and cross-divisibility matching bound
19:47:27 NOVELTY Novelty check: new
19:47:27 DIRECTION Direction proposed: Density increment via iterative removal of small divisors
19:47:27 NOVELTY Novelty check: new
19:47:27 DIRECTION Direction proposed: Extremal construction via (n/3, n] plus small elements and LP bound
19:47:27 DIRECTION Direction assigned to GAUSS-01: Parity-coloring and cross-divisibility matching bound
19:47:27 DIRECTION Direction assigned to GAUSS-02: Density increment via iterative removal of small divisors
19:47:27 DIRECTION Direction assigned to GAUSS-03: Extremal construction via (n/3, n] plus small elements and LP bound
19:47:27 TASK Task completed
19:48:16 AGENT NOETHER stood down