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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 45.
Research chronicle 93 RECORDS
All Research Review Verification System
19:57:46 §1
SYSTEM Iteration 45 opened
19:57:48 §2
SYSTEM Iteration 45 started
19:57:48 §3
SYSTEM Initializing research run
19:57:48 §4
NOETHER NOETHER joined as Strategist
19:57:48 §5
SYSTEM Research started
19:57:49 §6
NOETHER Research planning started
↑ 87 earlier records Research record
Agent record Close ×
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 1,078
Cached input 517
Output tokens 1,733
Average latency 10.4 s
Failed calls 0
Cost (estimated) $0.000579
Joined 2026-09-25 19:57:48 UTC
Left 2026-09-25 19:59:28 UTC Recent activity 19:58:01 DIRECTION Direction proposed: Density increment via prime factor intervals and container-style bound 19:58:01 NOVELTY Novelty check: new 19:58:01 DIRECTION Direction proposed: Constructive lower bound via large-prime-factor selection and probabilistic method 19:58:01 DIRECTION Direction assigned to GAUSS-01: Fractional matching and divisor graph orientation upper bound 19:58:01 DIRECTION Direction assigned to GAUSS-02: Density increment via prime factor intervals and container-style bound 19:58:01 DIRECTION Direction assigned to GAUSS-03: Constructive lower bound via large-prime-factor selection and probabilistic method 19:58:01 TASK Task completed 19:58:38 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
19:58:50 PLAN Research plan created
19:58:50 NOVELTY Novelty check: new
19:58:50 DIRECTION Direction proposed: Hypergraph local-sparsity upper bound via divisibility triples
19:58:50 NOVELTY Novelty check: new
19:58:50 DIRECTION Direction proposed: Recursive interval-splitting bound via multiplicative layers
19:58:50 NOVELTY Novelty check: new
19:58:50 DIRECTION Direction proposed: Spectral/linear-algebraic bound via divisor incidence matrix
19:58:50 DIRECTION Direction assigned to GAUSS-01: Hypergraph local-sparsity upper bound via divisibility triples
19:58:50 DIRECTION Direction assigned to GAUSS-02: Recursive interval-splitting bound via multiplicative layers
19:58:50 DIRECTION Direction assigned to GAUSS-03: Spectral/linear-algebraic bound via divisor incidence matrix
19:58:50 TASK Task completed
19:59:28 AGENT NOETHER stood down 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 45
Model calls 12
Estimated cost $0.006856 Budget remaining 99%
Iteration details & budget ↗
Research graph / proof lineage 7 objects · 0 links · 10 in complete graph
DIRECTION
DIRECTION Fractional matching and divisor graph orientation upper bound COMPLETED DIRECTION Density increment via prime factor intervals and container-style bound COMPLETED DIRECTION Constructive lower bound via large-prime-factor selection and probabilistic method COMPLETED DIRECTION Hypergraph local-sparsity upper bound via divisibility triples COMPLETED DIRECTION Recursive interval-splitting bound via multiplicative layers COMPLETED DIRECTION Spectral/linear-algebraic bound via divisor incidence matrix COMPLETED PROOF
PROOF Spectral incidence-matrix bound is exhausted v1 MARKDOWN Explore complete graph / 17 objects →