Skip to content
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 ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Inductive poset decomposition via interval halving and chain-antichain duality
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,882
Cached input 0
Output tokens 473
Average latency 3.7 s
Failed calls 0
Cost (estimated) $0.000396
Joined 2026-09-25 20:21:30 UTC
Left 2026-09-25 20:24:53 UTC Recent activity 20:21:30 AGENT LITERATURE-01 joined as Literature Researcher 20:21:30 LITERATURE Literature search started 20:21:30 LITERATURE Indexed: Pairing conjugate partitions by residue classes 20:21:30 LITERATURE Indexed: Dominant residue classes concerning the summands of partitions 20:21:30 LITERATURE Literature search: 3 new of 3 20:21:30 LITERATURE Reviewed: Pairing conjugate partitions by residue classes 20:21:30 MEMORY Literature: Pairing conjugate partitions by residue classes 20:23:47 LITERATURE Literature search 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
LITERATURE
Literature search: 3 new of 3
20:23:47 LITERATURE Reviewed: No Finite–Infinite Antichain Duality in the Homomorphism Poset of Directed Graphs
20:23:47 MEMORY Literature: No Finite–Infinite Antichain Duality in the Homomorphism Poset of Directed Graphs
20:24:53 AGENT LITERATURE-01 stood down