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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 34.
Research chronicle 109 RECORDS
All Research Review Verification System
19:27:00 §1
SYSTEM Iteration 34 opened
19:27:02 §2
SYSTEM Iteration 34 started
19:27:02 §3
SYSTEM Initializing research run
19:27:02 §4
NOETHER NOETHER joined as Strategist
19:27:02 §5
SYSTEM Research started
19:27:03 §6
NOETHER Research planning started
↑ 103 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 1,074
Cached input 0
Output tokens 966
Average latency 7.6 s
Failed calls 0
Cost (estimated) $0.000421
Joined 2026-09-25 19:27:02 UTC
Left 2026-09-25 19:30:24 UTC Recent activity 19:27:14 DIRECTION Direction proposed: Hypergraph matching and computational extremal search 19:27:14 NOVELTY Novelty check: new 19:27:14 DIRECTION Direction proposed: Divisor-sum analytic bound via entropy or density 19:27:14 DIRECTION Direction assigned to GAUSS-01: Probabilistic construction and weighted double-counting upper bound 19:27:14 DIRECTION Direction assigned to GAUSS-02: Hypergraph matching and computational extremal search 19:27:14 DIRECTION Direction assigned to GAUSS-03: Divisor-sum analytic bound via entropy or density 19:27:14 TASK Task completed 19:28:53 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. 19:29:00
PLAN
Research plan created
19:29:00 NOVELTY Novelty check: new
19:29:00 DIRECTION Direction proposed: Constructive CRT/block packing for large 3-divisor-free interval subsets
19:29:00 NOVELTY Novelty check: new
19:29:00 DIRECTION Direction proposed: Poset width and chain-decomposition upper bound via interval divisibility
19:29:00 NOVELTY Novelty check: new
19:29:00 DIRECTION Direction proposed: Forbidden pattern via prime-exponent vectors and extremal set theory
19:29:00 DIRECTION Direction assigned to GAUSS-01: Constructive CRT/block packing for large 3-divisor-free interval subsets
19:29:00 DIRECTION Direction assigned to GAUSS-02: Poset width and chain-decomposition upper bound via interval divisibility
19:29:00 DIRECTION Direction assigned to GAUSS-03: Forbidden pattern via prime-exponent vectors and extremal set theory
19:29:00 TASK Task completed
19:30:24 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 34
Model calls 16
Estimated cost $0.009553 Budget remaining 99%
Iteration details & budget ↗
Research graph / proof lineage 9 objects · 3 links · 11 in complete graph
DIRECTION
DIRECTION Probabilistic construction and weighted double-counting upper bound COMPLETED DIRECTION Hypergraph matching and computational extremal search REJECTED DIRECTION Divisor-sum analytic bound via entropy or density COMPLETED DIRECTION Constructive CRT/block packing for large 3-divisor-free interval subsets COMPLETED DIRECTION Poset width and chain-decomposition upper bound via interval divisibility COMPLETED DIRECTION Forbidden pattern via prime-exponent vectors and extremal set theory REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (fail) FAIL PROOF
PROOF Odd-part chain-decomposition bound is vacuous v1 MARKDOWN Explore complete graph / 20 objects →