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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 31.
Research chronicle 111 RECORDS
All Research Review Verification System
↑ 105 earlier records 19:21:33 §106
GAUSS-03 GAUSS-03 stood down
19:21:33 §107
LITERATURE-01 LITERATURE-01 stood down
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LITERATURE-02 LITERATURE-02 stood down
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TURING TURING stood down
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SYSTEM Research run finished
19:21:33 §111
SYSTEM Iteration 31 completed
Research graph / proof lineage 9 objects · 3 links · 11 in complete graph
DIRECTION
DIRECTION Weighted counting and random greedy construction COMPLETED DIRECTION Hypergraph matching and container method COMPLETED DIRECTION Odd-part chain decomposition and local bounds COMPLETED DIRECTION Density increment via divisor graph and pivot induction REJECTED DIRECTION Residue-class block decomposition and local extremal inequality COMPLETED DIRECTION LP duality and weighted upper bounds COMPLETED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (needs_work) NEEDS WORK PROOF
PROOF Experiment report — Compute exactly, for N=1..60, the maximum size f(N) of a subset of {1,...,N} wit v1 MARKDOWN Explore complete graph / 20 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 31
Model calls 14
Estimated cost $0.008718 Budget remaining 99%
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 1,066
Cached input 517
Output tokens 1,286
Average latency 13.3 s
Failed calls 0
Cost (estimated) $0.000453
Joined 2026-09-25 19:18:57 UTC
Left 2026-09-25 19:21:33 UTC Recent activity 19:19:09 MEMORY Novelty check: Odd-part chain decomposition and local bounds 19:19:09 NOVELTY Novelty check: partially explored 19:19:09 DIRECTION Direction proposed: Odd-part chain decomposition and local bounds 19:19:09 DIRECTION Direction assigned to GAUSS-01: Weighted counting and random greedy construction 19:19:09 DIRECTION Direction assigned to GAUSS-02: Hypergraph matching and container method 19:19:09 DIRECTION Direction assigned to GAUSS-03: Odd-part chain decomposition and local bounds 19:19:09 TASK Task completed 19:19:55 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. 19:20:12
PLAN
Research plan created
19:20:12 NOVELTY Novelty check: new
19:20:12 DIRECTION Direction proposed: Density increment via divisor graph and pivot induction
19:20:12 NOVELTY Novelty check: new
19:20:12 DIRECTION Direction proposed: Residue-class block decomposition and local extremal inequality
19:20:12 NOVELTY Novelty check: new
19:20:12 DIRECTION Direction proposed: LP duality and weighted upper bounds
19:20:12 DIRECTION Direction assigned to GAUSS-01: Density increment via divisor graph and pivot induction
19:20:12 DIRECTION Direction assigned to GAUSS-02: Residue-class block decomposition and local extremal inequality
19:20:12 DIRECTION Direction assigned to GAUSS-03: LP duality and weighted upper bounds
19:20:12 TASK Task completed
19:21:33 AGENT NOETHER stood down