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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 19.
Research chronicle 90 RECORDS
All Research Review Verification System
18:35:41 §1
SYSTEM Iteration 19 opened
18:35:44 §2
SYSTEM Iteration 19 started
18:35:44 §3
SYSTEM Initializing research run
18:35:44 §4
NOETHER NOETHER joined as Strategist
18:35:44 §5
SYSTEM Research started
18:35:45 §6
NOETHER Research planning started
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GAUSS-02 Explorer
Explore direction: Per-chain upper bound via 2^a 3^b m decomposition
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 7,667
Cached input 0
Output tokens 1,678
Average latency 29.9 s
Failed calls 0
Cost (estimated) $0.001543
Joined 2026-09-25 18:36:14 UTC
Left 2026-09-25 18:39:36 UTC Recent activity 18:36:14 AGENT GAUSS-02 joined as Explorer 18:36:41 TASK Exploration started 18:37:08 EXPERIMENT Experiment refused before it ran 18:37:08 DIRECTION Direction exhausted 18:37:08 MEMORY Density/entropy approach via random subsets and multiplicative structure 18:37:08 TASK Task completed 18:38:38 TASK Exploration started 18:39:15 EXPERIMENT Experiment refused before it ran 18:39:15 DIRECTION 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. Direction exhausted
18:39:15 MEMORY Per-chain upper bound via 2^a 3^b m decomposition
18:39:15 TASK Task completed
18:39:36 AGENT GAUSS-02 stood down 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 19
Model calls 11
Estimated cost $0.0475 Budget remaining 98%
Iteration details & budget ↗
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Extremal construction and divisor-chain counting upper bound COMPLETED DIRECTION Density/entropy approach via random subsets and multiplicative structure COMPLETED DIRECTION Computational search and induction for small intervals to guess exact extremal function COMPLETED DIRECTION Exact f(N) for N up to 30 and canonical problem statement COMPLETED DIRECTION Per-chain upper bound via 2^a 3^b m decomposition COMPLETED DIRECTION Literature check and comparison against ceil(2N/3) baseline COMPLETED PROOF
PROOF Experiment report — Compute exact f(N) for N=1..30 by bitmask DP over divisor constraints, and verif v1 MARKDOWN Explore complete graph / 17 objects →