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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 35.
Research chronicle 96 RECORDS
All Research Review Verification System
↑ 90 earlier records 19:33:04 §91
GAUSS-01 GAUSS-01 stood down
19:33:04 §92
GAUSS-02 GAUSS-02 stood down
19:33:04 §93
GAUSS-03 GAUSS-03 stood down
19:33:04 §94
LITERATURE-01 LITERATURE-01 stood down
19:33:04 §95
SYSTEM Research run finished
19:33:04 §96
SYSTEM Iteration 35 completed
Research graph / proof lineage 7 objects · 0 links · 12 in complete graph
DIRECTION
DIRECTION Greedy construction and density lower bound COMPLETED DIRECTION Upper bound via chain decomposition and matching COMPLETED DIRECTION Exact computation for small n and pattern identification COMPLETED DIRECTION Randomized dependent-rounding construction for large divisor-free subsets COMPLETED DIRECTION Spectral upper bound via a divisibility-pair matrix and forbidden-triangle counting COMPLETED DIRECTION Dyadic block recursion and divisor-count profile upper bound COMPLETED PROOF
PROOF Spectral bound computation for divisibility-pair graph 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 35
Model calls 13
Estimated cost $0.006970 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 1,069
Cached input 0
Output tokens 1,050
Average latency 15.1 s
Failed calls 0
Cost (estimated) $0.000444
Joined 2026-09-25 19:30:26 UTC
Left 2026-09-25 19:33:04 UTC Recent activity 19:30:45 NOVELTY Novelty check: new 19:30:45 DIRECTION Direction proposed: Exact computation for small n and pattern identification 19:30:45 DIRECTION Direction assigned to GAUSS-01: Greedy construction and density lower bound 19:30:45 DIRECTION Direction assigned to GAUSS-02: Upper bound via chain decomposition and matching 19:30:45 DIRECTION Direction assigned to GAUSS-03: Exact computation for small n and pattern identification 19:30:45 TASK Task completed 19:32:12 TASK Research planning started 19:32:26 PLAN Research plan created 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. 19:32:26
MEMORY
Novelty check: Randomized dependent-rounding construction for large divisor-free subsets
19:32:26 NOVELTY Novelty check: partially explored
19:32:26 DIRECTION Direction proposed: Randomized dependent-rounding construction for large divisor-free subsets
19:32:26 NOVELTY Novelty check: new
19:32:26 DIRECTION Direction proposed: Spectral upper bound via a divisibility-pair matrix and forbidden-triangle counting
19:32:26 NOVELTY Novelty check: new
19:32:26 DIRECTION Direction proposed: Dyadic block recursion and divisor-count profile upper bound
19:32:26 DIRECTION Direction assigned to GAUSS-01: Randomized dependent-rounding construction for large divisor-free subsets
19:32:26 DIRECTION Direction assigned to GAUSS-02: Spectral upper bound via a divisibility-pair matrix and forbidden-triangle counting
19:32:26 DIRECTION Direction assigned to GAUSS-03: Dyadic block recursion and divisor-count profile upper bound
19:32:26 TASK Task completed
19:33:04 AGENT NOETHER stood down