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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 39.
Research chronicle 95 RECORDS
All Research Review Verification System
↑ 89 earlier records 19:45:31 §90
GAUSS-01 GAUSS-01 stood down
19:45:31 §91
GAUSS-02 GAUSS-02 stood down
19:45:31 §92
GAUSS-03 GAUSS-03 stood down
19:45:31 §93
LITERATURE-01 LITERATURE-01 stood down
19:45:31 §94
SYSTEM Research run finished
19:45:31 §95
SYSTEM Iteration 39 completed
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Probabilistic lower bound via random subsets with divisibility constraints COMPLETED DIRECTION Upper bound via chain decomposition and matching in the divisibility poset COMPLETED DIRECTION Computational exploration and pattern detection for small intervals COMPLETED DIRECTION Constructive lower bound via threshold plus sparse small-number layer COMPLETED DIRECTION Upper bound via product/AM-GM inequality over the subset COMPLETED DIRECTION Recursive interval-splitting upper bound via block automata COMPLETED PROOF
PROOF LP optimum over all block partitions equals N for N <= 60 v1 MARKDOWN Explore complete graph / 17 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 39
Model calls 14
Estimated cost $0.006789 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 1,079
Cached input 0
Output tokens 1,168
Average latency 17.3 s
Failed calls 0
Cost (estimated) $0.000478
Joined 2026-09-25 19:41:29 UTC
Left 2026-09-25 19:45:31 UTC Recent activity 19:41:45 DIRECTION Direction proposed: Upper bound via chain decomposition and matching in the divisibility poset 19:41:45 NOVELTY Novelty check: new 19:41:45 DIRECTION Direction proposed: Computational exploration and pattern detection for small intervals 19:41:45 DIRECTION Direction assigned to GAUSS-01: Probabilistic lower bound via random subsets with divisibility constraints 19:41:45 DIRECTION Direction assigned to GAUSS-02: Upper bound via chain decomposition and matching in the divisibility poset 19:41:45 DIRECTION Direction assigned to GAUSS-03: Computational exploration and pattern detection for small intervals 19:41:45 TASK Task completed 19:42:56 TASK 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. Research planning started
19:43:18 PLAN Research plan created
19:43:18 NOVELTY Novelty check: new
19:43:18 DIRECTION Direction proposed: Constructive lower bound via threshold plus sparse small-number layer
19:43:18 NOVELTY Novelty check: new
19:43:18 DIRECTION Direction proposed: Upper bound via product/AM-GM inequality over the subset
19:43:18 NOVELTY Novelty check: new
19:43:18 DIRECTION Direction proposed: Recursive interval-splitting upper bound via block automata
19:43:18 DIRECTION Direction assigned to GAUSS-01: Constructive lower bound via threshold plus sparse small-number layer
19:43:18 DIRECTION Direction assigned to GAUSS-02: Upper bound via product/AM-GM inequality over the subset
19:43:18 DIRECTION Direction assigned to GAUSS-03: Recursive interval-splitting upper bound via block automata
19:43:18 TASK Task completed
19:45:31 AGENT NOETHER stood down