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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 32.
Research chronicle 94 RECORDS
All Research Review Verification System
19:21:33 §1
SYSTEM Iteration 32 opened
19:21:35 §2
SYSTEM Iteration 32 started
19:21:35 §3
SYSTEM Initializing research run
19:21:35 §4
NOETHER NOETHER joined as Strategist
19:21:35 §5
SYSTEM Research started
19:21:36 §6
NOETHER Research planning started
↑ 88 earlier records Research record
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GAUSS-02 Explorer
Explore direction: Recursive divide-and-conquer via multiplicative doubling
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 7,001
Cached input 0
Output tokens 2,357
Average latency 23.3 s
Failed calls 0
Cost (estimated) $0.001640
Joined 2026-09-25 19:21:51 UTC
Left 2026-09-25 19:24:18 UTC Recent activity 19:21:51 AGENT GAUSS-02 joined as Explorer 19:22:14 TASK Exploration started 19:22:53 EXPERIMENT Experiment refused before it ran 19:22:53 DIRECTION Direction exhausted 19:22:53 MEMORY Probabilistic and density method for unavoidable triples 19:22:53 TASK Task completed 19:23:43 TASK Exploration started 19:23:54 EXPERIMENT Experiment refused before it ran 19:23:54 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
19:23:54 MEMORY Recursive divide-and-conquer via multiplicative doubling
19:23:54 TASK Task completed
19:24:18 AGENT GAUSS-02 stood down
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Extremal construction and divisor-chain counting upper bound COMPLETED DIRECTION Probabilistic and density method for unavoidable triples COMPLETED DIRECTION ILP-guided pattern discovery and induction proof COMPLETED DIRECTION Prime-power layer decomposition and layer-wise extremal bounds COMPLETED DIRECTION Recursive divide-and-conquer via multiplicative doubling COMPLETED DIRECTION Small-interval exact pattern search and closed-form conjecture COMPLETED PROOF
PROOF Layer-decomposition bound vs exact f(N) for N<=30 v1 MARKDOWN Explore complete graph / 17 objects → 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 32
Model calls 13
Estimated cost $0.006439 Budget remaining 99%
Iteration details & budget ↗