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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 55.
Research chronicle 92 RECORDS
All Research Review Verification System
↑ 86 earlier records 20:24:53 §87
GAUSS-01 GAUSS-01 stood down
20:24:53 §88
GAUSS-02 GAUSS-02 stood down
20:24:53 §89
GAUSS-03 GAUSS-03 stood down
20:24:53 §90
LITERATURE-01 LITERATURE-01 stood down
20:24:53 §91
SYSTEM Research run finished
20:24:53 §92
SYSTEM Iteration 55 completed
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Constructive lower bounds via layered residue classes and interval partitions COMPLETED DIRECTION Upper bounds via divisor-count weighting and double counting COMPLETED DIRECTION Computational search and extremal pattern extraction COMPLETED DIRECTION Inductive poset decomposition via interval halving and chain-antichain duality COMPLETED DIRECTION Logarithmic-density continuous relaxation and extremal measure COMPLETED DIRECTION Probabilistic greedy construction with local ratio analysis COMPLETED PROOF
PROOF Continuous relaxation is vacuous v1 MARKDOWN Explore complete graph / 17 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 55
Model calls 13
Estimated cost $0.005421 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 1,073
Cached input 517
Output tokens 1,059
Average latency 12.0 s
Failed calls 0
Cost (estimated) $0.000390
Joined 2026-09-25 20:21:21 UTC
Left 2026-09-25 20:24:53 UTC Recent activity 20:21:30 DIRECTION Direction proposed: Upper bounds via divisor-count weighting and double counting 20:21:30 NOVELTY Novelty check: new 20:21:30 DIRECTION Direction proposed: Computational search and extremal pattern extraction 20:21:30 DIRECTION Direction assigned to GAUSS-01: Constructive lower bounds via layered residue classes and interval partitions 20:21:30 DIRECTION Direction assigned to GAUSS-02: Upper bounds via divisor-count weighting and double counting 20:21:30 DIRECTION Direction assigned to GAUSS-03: Computational search and extremal pattern extraction 20:21:30 TASK Task completed 20:23:28 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.
20:23:47 PLAN Research plan created
20:23:47 NOVELTY Novelty check: new
20:23:47 DIRECTION Direction proposed: Inductive poset decomposition via interval halving and chain-antichain duality
20:23:47 NOVELTY Novelty check: new
20:23:47 DIRECTION Direction proposed: Logarithmic-density continuous relaxation and extremal measure
20:23:47 NOVELTY Novelty check: new
20:23:47 DIRECTION Direction proposed: Probabilistic greedy construction with local ratio analysis
20:23:47 DIRECTION Direction assigned to GAUSS-01: Inductive poset decomposition via interval halving and chain-antichain duality
20:23:47 DIRECTION Direction assigned to GAUSS-02: Logarithmic-density continuous relaxation and extremal measure
20:23:47 DIRECTION Direction assigned to GAUSS-03: Probabilistic greedy construction with local ratio analysis
20:23:47 TASK Task completed
20:24:53 AGENT NOETHER stood down