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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 6.
Research chronicle 106 RECORDS
All Research Review Verification System
↑ 100 earlier records 16:56:36 §101
GAUSS-03 GAUSS-03 stood down
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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
16:56:36 §106
SYSTEM Iteration 6 completed
Research graph / proof lineage 9 objects · 3 links · 7 in complete graph
DIRECTION
DIRECTION Density and divisor-graph matching upper bound REJECTED DIRECTION Lower-bound construction via residue classes and CRT COMPLETED DIRECTION Prime-factor structural decomposition and exact small cases REJECTED DIRECTION Recursive interval-splitting via 2-cover-free hypergraphs COMPLETED DIRECTION Weighted counting with shifted geometric progressions COMPLETED DIRECTION Transfer-matrix / DP exact computation for small intervals and extrapolation REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (needs_work) NEEDS WORK PROOF
PROOF Experiment report — Check for N <= 30 whether the recursive interval-splitting bound f(N) <= f(floor v1 MARKDOWN Explore complete graph / 16 objects → Research record
Agent record Close ×
Mission
Runtime 7 h 15 min
Iteration 18 of 18
Directions 100
Hypotheses 12
Experiments 59
Rejected paths 48 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 45
Highly relevant 1 Iteration 6
Model calls 19
Estimated cost $0.1714 Budget remaining 93%
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 1,070
Cached input 0
Output tokens 1,102
Average latency 9.8 s
Failed calls 0
Cost (estimated) $0.000458
Joined 2026-09-25 16:52:38 UTC
Left 2026-09-25 16:56:36 UTC Recent activity 16:52:48 DIRECTION Direction proposed: Lower-bound construction via residue classes and CRT 16:52:48 NOVELTY Novelty check: new 16:52:48 DIRECTION Direction proposed: Prime-factor structural decomposition and exact small cases 16:52:48 DIRECTION Direction assigned to GAUSS-01: Density and divisor-graph matching upper bound 16:52:48 DIRECTION Direction assigned to GAUSS-02: Lower-bound construction via residue classes and CRT 16:52:48 DIRECTION Direction assigned to GAUSS-03: Prime-factor structural decomposition and exact small cases 16:52:48 TASK Task completed 16:54:20 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. 16:54:35
PLAN
Research plan created
16:54:35 NOVELTY Novelty check: new
16:54:35 DIRECTION Direction proposed: Recursive interval-splitting via 2-cover-free hypergraphs
16:54:35 NOVELTY Novelty check: new
16:54:35 DIRECTION Direction proposed: Weighted counting with shifted geometric progressions
16:54:35 NOVELTY Novelty check: new
16:54:35 DIRECTION Direction proposed: Transfer-matrix / DP exact computation for small intervals and extrapolation
16:54:35 DIRECTION Direction assigned to GAUSS-01: Recursive interval-splitting via 2-cover-free hypergraphs
16:54:35 DIRECTION Direction assigned to GAUSS-02: Weighted counting with shifted geometric progressions
16:54:35 DIRECTION Direction assigned to GAUSS-03: Transfer-matrix / DP exact computation for small intervals and extrapolation
16:54:35 TASK Task completed
16:56:36 AGENT NOETHER stood down