Skip to content
How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Engine unreachable
The research engine answered a mission's knowledge in a shape this page cannot read.
Nothing is shown rather than something invented. Start the orchestrator API and reload.
Research record
Agent record Close ×
Frontier availability 07 Senior reviewer Not started On the roster; the workflow has not woken it in this iteration. 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 36
Model calls 14
Estimated cost $0.007647 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 1,074
Cached input 517
Output tokens 979
Average latency 11.8 s
Failed calls 0
Cost (estimated) $0.000367
Joined 2026-09-25 19:33:06 UTC
Left 2026-09-25 19:35:33 UTC Recent activity 19:33:21 DIRECTION Direction proposed: Weighted chain LP and divisor-poset upper bounds 19:33:21 NOVELTY Novelty check: new 19:33:21 DIRECTION Direction proposed: Exact small-n search and inductive pattern extrapolation 19:33:21 DIRECTION Direction assigned to GAUSS-01: Random weighted subsets and divisibility-free constructions 19:33:21 DIRECTION Direction assigned to GAUSS-02: Weighted chain LP and divisor-poset upper bounds 19:33:21 DIRECTION Direction assigned to GAUSS-03: Exact small-n search and inductive pattern extrapolation 19:33:21 TASK Task completed 19:33:55 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.
19:34:06
PLAN
Research plan created
19:34:06 NOVELTY Novelty check: new
19:34:06 DIRECTION Direction proposed: Density increment via divisor-neighborhood containers
19:34:06 NOVELTY Novelty check: new
19:34:06 DIRECTION Direction proposed: Prime-power layer decomposition and CRT packing
19:34:06 NOVELTY Novelty check: new
19:34:06 DIRECTION Direction proposed: Transfer-matrix bound on the divisor poset via interval automata
19:34:06 DIRECTION Direction assigned to GAUSS-01: Density increment via divisor-neighborhood containers
19:34:06 DIRECTION Direction assigned to GAUSS-02: Prime-power layer decomposition and CRT packing
19:34:06 DIRECTION Direction assigned to GAUSS-03: Transfer-matrix bound on the divisor poset via interval automata
19:34:06 TASK Task completed
19:35:33 AGENT NOETHER stood down