Skip to content
How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
AGENTS / 8 8 agents · 0 working
Frontier availability Showing iteration 15.
Research chronicle 104 RECORDS
All Research Review Verification System
↑ 98 earlier records 18:20:14 §99
LITERATURE-01 LITERATURE-01 stood down
18:20:14 §100
LITERATURE-02 LITERATURE-02 stood down
18:20:14 §101
TURING TURING stood down
18:20:14 §102
ARES ARES stood down
18:20:14 §103
SYSTEM Research run finished
18:20:14 §104
SYSTEM Iteration 15 completed
Research graph / proof lineage 9 objects · 3 links · 9 in complete graph
DIRECTION
DIRECTION Probabilistic upper bound via divisor-count weighting REJECTED DIRECTION Construction from multiples of a large prime COMPLETED DIRECTION Exact computation for small n and pattern detection COMPLETED DIRECTION Exact computation via ILP/SAT and extremal set census COMPLETED DIRECTION Lower-bound constructions from dyadic/triadic layers with paired multiples COMPLETED DIRECTION Upper bounds via chain decompositions and forbidden 3-chains COMPLETED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (fail) FAIL PROOF
PROOF Experiment report — Check whether the odd-part chain-decomposition upper bound is non-vacuous (stric v1 MARKDOWN Explore complete graph / 18 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 15
Model calls 13
Estimated cost $0.0579 Budget remaining 97%
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 1,894
Cached input 517
Output tokens 999
Average latency 13.9 s
Failed calls 0
Cost (estimated) $0.000488
Joined 2026-09-25 18:17:10 UTC
Left 2026-09-25 18:20:14 UTC Recent activity 18:17:20 DIRECTION Direction proposed: Construction from multiples of a large prime 18:17:20 NOVELTY Novelty check: new 18:17:20 DIRECTION Direction proposed: Exact computation for small n and pattern detection 18:17:20 DIRECTION Direction assigned to GAUSS-01: Probabilistic upper bound via divisor-count weighting 18:17:20 DIRECTION Direction assigned to GAUSS-02: Construction from multiples of a large prime 18:17:20 DIRECTION Direction assigned to GAUSS-03: Exact computation for small n and pattern detection 18:17:20 TASK Task completed 18:18:47 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.
09 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. 18:19:09
PLAN
Research plan created
18:19:09 NOVELTY Novelty check: new
18:19:09 DIRECTION Direction proposed: Exact computation via ILP/SAT and extremal set census
18:19:09 NOVELTY Novelty check: new
18:19:09 DIRECTION Direction proposed: Lower-bound constructions from dyadic/triadic layers with paired multiples
18:19:09 NOVELTY Novelty check: new
18:19:09 DIRECTION Direction proposed: Upper bounds via chain decompositions and forbidden 3-chains
18:19:09 DIRECTION Direction assigned to GAUSS-01: Exact computation via ILP/SAT and extremal set census
18:19:09 DIRECTION Direction assigned to GAUSS-02: Lower-bound constructions from dyadic/triadic layers with paired multiples
18:19:09 DIRECTION Direction assigned to GAUSS-03: Upper bounds via chain decompositions and forbidden 3-chains
18:19:09 TASK Task completed
18:20:14 AGENT NOETHER stood down