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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 30.
Research chronicle 108 RECORDS
All Research Review Verification System
↑ 102 earlier records 19:18:54 §103
GAUSS-03 GAUSS-03 stood down
19:18:54 §104
LITERATURE-01 LITERATURE-01 stood down
19:18:54 §105
LITERATURE-02 LITERATURE-02 stood down
19:18:54 §106
TURING TURING stood down
19:18:54 §107
SYSTEM Research run finished
19:18:54 §108
SYSTEM Iteration 30 completed
Research graph / proof lineage 9 objects · 3 links · 11 in complete graph
DIRECTION
DIRECTION Weighted divisor-count upper bound and greedy construction COMPLETED DIRECTION Probabilistic method and random subset density COMPLETED DIRECTION Divisor-chain layer decomposition and exact DP for small n COMPLETED DIRECTION Large-prime-factor construction via prime gaps COMPLETED DIRECTION Hypergraph independent set with fractional relaxation REJECTED DIRECTION Compression and density increment on the divisor poset REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (fail) FAIL PROOF
PROOF Large-prime-factor construction size computation 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 30
Model calls 15
Estimated cost $0.009723 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 1,074
Cached input 517
Output tokens 1,022
Average latency 15.3 s
Failed calls 0
Cost (estimated) $0.000380
Joined 2026-09-25 19:15:24 UTC
Left 2026-09-25 19:18:54 UTC Recent activity 19:15:44 MEMORY Novelty check: Divisor-chain layer decomposition and exact DP for small n 19:15:44 NOVELTY Novelty check: partially explored 19:15:44 DIRECTION Direction proposed: Divisor-chain layer decomposition and exact DP for small n 19:15:44 DIRECTION Direction assigned to GAUSS-01: Weighted divisor-count upper bound and greedy construction 19:15:44 DIRECTION Direction assigned to GAUSS-02: Probabilistic method and random subset density 19:15:44 DIRECTION Direction assigned to GAUSS-03: Divisor-chain layer decomposition and exact DP for small n 19:15:44 TASK Task completed 19:16:46 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.
19:17:01 PLAN Research plan created
19:17:01 NOVELTY Novelty check: new
19:17:01 DIRECTION Direction proposed: Large-prime-factor construction via prime gaps
19:17:01 NOVELTY Novelty check: new
19:17:01 DIRECTION Direction proposed: Hypergraph independent set with fractional relaxation
19:17:01 NOVELTY Novelty check: new
19:17:01 DIRECTION Direction proposed: Compression and density increment on the divisor poset
19:17:01 DIRECTION Direction assigned to GAUSS-01: Large-prime-factor construction via prime gaps
19:17:01 DIRECTION Direction assigned to GAUSS-02: Hypergraph independent set with fractional relaxation
19:17:01 DIRECTION Direction assigned to GAUSS-03: Compression and density increment on the divisor poset
19:17:01 TASK Task completed
19:18:54 AGENT NOETHER stood down