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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
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GAUSS-02 GAUSS-02 stood down
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GAUSS-03 GAUSS-03 stood down
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LITERATURE-01 LITERATURE-01 stood down
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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 ↗
LITERATURE-01 Literature researcher
Reading the landscape around: Random subset with dependent rounding and divisor-count weighting
Model
Model used together / deepseek-ai/DeepSeek-V4-Flash-0731
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 2,209
Cached input 0
Output tokens 584
Average latency 2.3 s
Failed calls 0
Cost (estimated) $0.000472
Joined 2026-09-25 19:55:42 UTC
Left 2026-09-25 19:57:46 UTC Recent activity 19:55:42 AGENT LITERATURE-01 joined as Literature Researcher 19:55:42 LITERATURE Literature search started 19:55:42 LITERATURE Indexed: HERMITE–HADAMARD’S TYPE INEQUALITIES FOR SUPERQUADRATIC INTERVAL-VALUED FUNCTIONS VIA MULTIPLICATIVE FRACTIONAL INTERVAL CALCULUS 19:55:42 LITERATURE Indexed: Nonparametric multiplicative bias correction for kernel-type density estimation on the unit interval 19:55:42 LITERATURE Indexed: Interval Type-2 Multiplicative Fuzzy Partition C-Means Clustering 19:55:42 LITERATURE Literature search: 3 new of 3 19:55:42 LITERATURE Reviewed: HERMITE–HADAMARD’S TYPE INEQUALITIES FOR SUPERQUADRATIC INTERVAL-VALUED FUNCTIONS VIA MULTIPLICATIVE FRACTIONAL INTERVAL CALCULUS 19:55:42 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. MEMORY
Literature: HERMITE–HADAMARD’S TYPE INEQUALITIES FOR SUPERQUADRATIC INTERVAL-VALUED FUNCTIONS VIA MULTIPLICATIVE FRACTIONAL INTERVAL CALCULUS
19:56:57 LITERATURE Literature search started
19:56:57 LITERATURE Indexed: SmallCountRounding: Small Count Rounding of Tabular Data
19:56:57 LITERATURE Indexed: Divisor and Conquer
19:56:57 LITERATURE Indexed: Subset simulation for non-Gaussian dependent random variables given incomplete probability information
19:56:57 LITERATURE Literature search: 3 new of 3
19:56:57 LITERATURE Reviewed: SmallCountRounding: Small Count Rounding of Tabular Data
19:56:57 MEMORY Literature: SmallCountRounding: Small Count Rounding of Tabular Data
19:57:46 AGENT LITERATURE-01 stood down