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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 44.
Research chronicle 97 RECORDS
All Research Review Verification System
↑ 91 earlier records 19:57:46 §92
GAUSS-01 GAUSS-01 stood down
19:57:46 §93
GAUSS-02 GAUSS-02 stood down
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GAUSS-03 GAUSS-03 stood down
19:57:46 §95
LITERATURE-01 LITERATURE-01 stood down
19:57:46 §96
SYSTEM Research run finished
19:57:46 §97
SYSTEM Iteration 44 completed
Research graph / proof lineage 7 objects · 0 links · 12 in complete graph
DIRECTION
DIRECTION Density via multiplicative chains and interval blocking COMPLETED DIRECTION Extremal poset and divisor DAG matching bound COMPLETED DIRECTION Computational search and pattern extrapolation for small intervals COMPLETED DIRECTION Random subset with dependent rounding and divisor-count weighting COMPLETED DIRECTION Spectral bound via the divisor incidence matrix COMPLETED DIRECTION Recursive interval splitting with weighted AM-GM on divisor counts COMPLETED PROOF
PROOF Experiment report — Verify that for N up to 200 the spectral radius of the divisor-hypergraph adjace v1 MARKDOWN Explore complete graph / 19 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 44
Model calls 13
Estimated cost $0.007170 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 1,072
Cached input 0
Output tokens 1,188
Average latency 25.2 s
Failed calls 0
Cost (estimated) $0.000482
Joined 2026-09-25 19:55:29 UTC
Left 2026-09-25 19:57:46 UTC Recent activity 19:55:42 MEMORY Novelty check: Computational search and pattern extrapolation for small intervals 19:55:42 NOVELTY Novelty check: partially explored 19:55:42 DIRECTION Direction proposed: Computational search and pattern extrapolation for small intervals 19:55:42 DIRECTION Direction assigned to GAUSS-01: Density via multiplicative chains and interval blocking 19:55:42 DIRECTION Direction assigned to GAUSS-02: Extremal poset and divisor DAG matching bound 19:55:42 DIRECTION Direction assigned to GAUSS-03: Computational search and pattern extrapolation for small intervals 19:55:42 TASK Task completed 19:56:18 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.
07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
19:56:57 PLAN Research plan created
19:56:57 NOVELTY Novelty check: new
19:56:57 DIRECTION Direction proposed: Random subset with dependent rounding and divisor-count weighting
19:56:57 NOVELTY Novelty check: new
19:56:57 DIRECTION Direction proposed: Spectral bound via the divisor incidence matrix
19:56:57 NOVELTY Novelty check: new
19:56:57 DIRECTION Direction proposed: Recursive interval splitting with weighted AM-GM on divisor counts
19:56:57 DIRECTION Direction assigned to GAUSS-01: Random subset with dependent rounding and divisor-count weighting
19:56:57 DIRECTION Direction assigned to GAUSS-02: Spectral bound via the divisor incidence matrix
19:56:57 DIRECTION Direction assigned to GAUSS-03: Recursive interval splitting with weighted AM-GM on divisor counts
19:56:57 TASK Task completed
19:57:46 AGENT NOETHER stood down