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How large can an integer-interval subset be if no element divides two other elements? · Research lab — PrizeLab
Showing iteration 3.
Research chronicle 117 RECORDS
All Research Review Verification System
↑ 111 earlier records 11:20:42 §112
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SYSTEM Research run finished
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SYSTEM Iteration 3 completed
Research graph / proof lineage 9 objects · 3 links · 8 in complete graph
DIRECTION
DIRECTION Poset‑Chain Decomposition and Dilworth‑type Upper Bounds REJECTED DIRECTION Probabilistic Construction via Lovász Local Lemma REJECTED DIRECTION Arithmetic Construction Using Large Prime Factors and Sieve Estimates REJECTED DIRECTION Smooth‑Number Lattice Decomposition REJECTED DIRECTION 3‑Uniform Hypergraph Turán Method COMPLETED DIRECTION Exact Computation and Pattern Extraction REJECTED HYPOTHESIS
HYPOTHESIS H-001 REJECTED REVIEW
REVIEW Review (needs_work) NEEDS WORK PROOF
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LITERATURE-02 Literature researcher
Checking prior art and known barriers for: Log‑power upper bound via smooth‑number decomposition
Model
Model used together / openai/gpt-oss-120b
Routing profile cheap_reasoning
Usage
Model calls 3
Input tokens 3,016
Cached input 207
Output tokens 1,056
Average latency 2.8 s
Failed calls 0
Cost (estimated) $0.001085
Joined 2026-09-25 11:19:09 UTC
Left 2026-09-25 11:20:42 UTC Recent activity 11:19:09 LITERATURE Indexed: Upper bound estimation of the spectral abscissa for switched linear systems via coordinate transformations 11:19:09 LITERATURE Indexed: Enhancing Hydrogen Production via Ammonia-Assisted Decomposition of Short-Chain Alcohols 11:19:09 LITERATURE Literature search: 3 new of 3 11:19:09 LITERATURE Reviewed: Auction implementations using LaGrangian Relaxation, Interior-Point Linear Programming, and Upper-Bound Linear Programming 11:19:09 MEMORY Literature: Auction implementations using LaGrangian Relaxation, Interior-Point Linear Programming, and Upper-Bound Linear Programming 11:19:13 LITERATURE Literature search started 11:19:13 LITERATURE Indexed: Adaptive mesh-free lower bound limit analysis using non-linear programming 11:19:13 Every figure here is aggregated from this agent’s recorded model calls, failed attempts included — a failed attempt is still an attempt.
LITERATURE
Indexed: A lower bound for the dimension of the base locus of the generalized theta divisor
11:19:13 LITERATURE Indexed: Lower bound to the free energy of an anisotropic linear Heisenberg chain
11:19:13 LITERATURE Literature search: 3 new of 3
11:19:13 LITERATURE Reviewed: Adaptive mesh-free lower bound limit analysis using non-linear programming
11:19:13 MEMORY Literature: Adaptive mesh-free lower bound limit analysis using non-linear programming
11:20:24 LITERATURE Literature search started
11:20:24 LITERATURE Indexed: A Bound of the Number of Weighted Blow-ups to Compute the Minimal Log Discrepancy for Smooth Threefolds
11:20:24 LITERATURE Indexed: An Improved Upper Bound for Steiner Decomposition Number
11:20:24 LITERATURE Indexed: An upper bound of a generalized upper Hamiltonian number of a graph
11:20:24 LITERATURE Literature search: 3 new of 3
11:20:24 LITERATURE Reviewed: A Bound of the Number of Weighted Blow-ups to Compute the Minimal Log Discrepancy for Smooth Threefolds
11:20:24 MEMORY Literature: A Bound of the Number of Weighted Blow-ups to Compute the Minimal Log Discrepancy for Smooth Threefolds
11:20:42 AGENT LITERATURE-02 stood down