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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 5.
Research chronicle 70 RECORDS
All Research Review Verification System
↑ 64 earlier records 11:22:25 §65
SYSTEM GATE No hypothesis passed the workflow gate No hypothesis passed the workflow gate: 0 of 0 signals cleared logical completeness 0.6. This is a workflow prioritization signal, not a proof of correctness.
11:22:25 §66
NOETHER NOETHER stood down
11:22:25 §67
GAUSS-02 GAUSS-02 stood down
11:22:25 §68
LITERATURE-01 LITERATURE-01 stood down
11:22:25 §69
SYSTEM Research run finished
11:22:25 §70
SYSTEM Iteration 5 completed
Research graph / proof lineage 7 objects · 0 links · 2 in complete graph
DIRECTION
DIRECTION Divisibility digraph and Turán‑type extremal bound REJECTED DIRECTION Random subset construction and the probabilistic method REJECTED DIRECTION Chain decomposition via Dilworth’s theorem and antichain analysis REJECTED DIRECTION Sieve‑style triple counting REJECTED DIRECTION Hypergraph container method for forbidden 2‑divisor configurations COMPLETED DIRECTION Residue‑class and multiplicative order partition REJECTED PROOF
PROOF Research plan v2 MARKDOWN Explore complete graph / 9 objects → Research record
Agent record Close ×
Mission
Runtime 5 h 32 min
Iteration 7 of 7
Directions 33
Hypotheses 7
Experiments 3
Rejected paths 34 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 18
Highly relevant 0 Iteration 5 No frontier agent engaged
Model calls 15
Estimated cost $0.0148 Budget remaining 99%
Iteration details & budget ↗
NOETHER Strategist
Plan iteration 2
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 2
Input tokens 1,193
Cached input 642
Output tokens 1,647
Average latency 5.7 s
Failed calls 0
Cost (estimated) $0.001167
Joined 2026-09-25 11:20:51 UTC
Left 2026-09-25 11:22:25 UTC Recent activity 11:20:59 DIRECTION Direction proposed: Random subset construction and the probabilistic method 11:20:59 NOVELTY Novelty check: new 11:20:59 DIRECTION Direction proposed: Chain decomposition via Dilworth’s theorem and antichain analysis 11:20:59 DIRECTION Direction assigned to GAUSS-01: Divisibility digraph and Turán‑type extremal bound 11:20:59 DIRECTION Direction assigned to GAUSS-02: Random subset construction and the probabilistic method 11:20:59 DIRECTION Direction assigned to GAUSS-03: Chain decomposition via Dilworth’s theorem and antichain analysis 11:20:59 TASK Task completed 11:21:39 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.
06 Research director Not started On the roster; the workflow has not woken it in this iteration. 07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration.
11:21:45 PLAN Research plan created
11:21:45 NOVELTY Novelty check: new
11:21:45 DIRECTION Direction proposed: Sieve‑style triple counting
11:21:45 NOVELTY Novelty check: new
11:21:45 DIRECTION Direction proposed: Hypergraph container method for forbidden 2‑divisor configurations
11:21:45 NOVELTY Novelty check: new
11:21:45 DIRECTION Direction proposed: Residue‑class and multiplicative order partition
11:21:45 DIRECTION Direction assigned to GAUSS-01: Sieve‑style triple counting
11:21:45 DIRECTION Direction assigned to GAUSS-02: Hypergraph container method for forbidden 2‑divisor configurations
11:21:45 DIRECTION Direction assigned to GAUSS-03: Residue‑class and multiplicative order partition
11:21:45 TASK Task completed
11:22:25 AGENT NOETHER stood down