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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
AGENTS / 6 6 agents · 0 working
Frontier availability Showing iteration 11.
Research chronicle 89 RECORDS
All Research Review Verification System
↑ 83 earlier records 18:05:07 §84
GAUSS-02 GAUSS-02 stood down
18:05:07 §85
GAUSS-03 GAUSS-03 stood down
18:05:07 §86
LITERATURE-01 LITERATURE-01 stood down
18:05:07 §87
ARES ARES stood down
18:05:07 §88
SYSTEM Research run finished
18:05:07 §89
SYSTEM Iteration 11 completed
Research graph / proof lineage 7 objects · 0 links · 8 in complete graph
DIRECTION
DIRECTION Density via divisor-chain counting and prime-power weights REJECTED DIRECTION Constructive extremal families via modular residue classes COMPLETED DIRECTION Exact small-n search and pattern extrapolation COMPLETED DIRECTION Exact small-N search and candidate testing COMPLETED DIRECTION Chain-partition upper bound via odd-part chains COMPLETED DIRECTION Layered construction with exactly one multiple per lower element COMPLETED PROOF
PROOF Experiment report — Compute the odd-part chain upper bound U(N) = sum over odd m of ceil(chain_lengt v1 MARKDOWN Explore complete graph / 15 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 11
Model calls 12
Estimated cost $0.0504 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 1,442
Cached input 0
Output tokens 994
Average latency 29.1 s
Failed calls 0
Cost (estimated) $0.000480
Joined 2026-09-25 18:00:53 UTC
Left 2026-09-25 18:05:07 UTC Recent activity 18:01:11 DIRECTION Direction proposed: Constructive extremal families via modular residue classes 18:01:11 NOVELTY Novelty check: new 18:01:11 DIRECTION Direction proposed: Exact small-n search and pattern extrapolation 18:01:11 DIRECTION Direction assigned to GAUSS-01: Density via divisor-chain counting and prime-power weights 18:01:11 DIRECTION Direction assigned to GAUSS-02: Constructive extremal families via modular residue classes 18:01:11 DIRECTION Direction assigned to GAUSS-03: Exact small-n search and pattern extrapolation 18:01:11 TASK Task completed 18:03:08 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. 18:03:51
PLAN
Research plan created
18:03:51 NOVELTY Novelty check: new
18:03:51 DIRECTION Direction proposed: Exact small-N search and candidate testing
18:03:51 NOVELTY Novelty check: new
18:03:51 DIRECTION Direction proposed: Chain-partition upper bound via odd-part chains
18:03:51 NOVELTY Novelty check: new
18:03:51 DIRECTION Direction proposed: Layered construction with exactly one multiple per lower element
18:03:51 DIRECTION Direction assigned to GAUSS-01: Exact small-N search and candidate testing
18:03:51 DIRECTION Direction assigned to GAUSS-02: Chain-partition upper bound via odd-part chains
18:03:51 DIRECTION Direction assigned to GAUSS-03: Layered construction with exactly one multiple per lower element
18:03:51 TASK Task completed
18:05:07 AGENT NOETHER stood down