Triple

T21088260
Position Surface form Disambiguated ID Type / Status
Subject Reducibility Among Combinatorial Problems E519559 entity
Predicate establishesNPCompletenessOf P142028 FINISHED
Object Set Packing problem — NE NERFINISHED

How this triple was built (3 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Set Packing problem | Statement: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, Set Packing problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Set Packing problem
Context triple: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, Set Packing problem]
  • A. Packing and Covering
    "Packing and Covering" is a classic mathematical monograph by C. A. Rogers that systematically develops the theory of packing and covering problems in geometry and number theory.
  • B. Subset sum problem
    The subset sum problem is a classic NP-complete decision problem in computer science that asks whether any subset of given integers sums to a specified target value.
  • C. Clique problem
    The Clique problem is a classic NP-complete decision problem in graph theory that asks whether a graph contains a fully connected subgraph (clique) of at least a given size.
  • D. A Combinatorial Problem
    "A Combinatorial Problem" is a classic mathematical paper by N. G. de Bruijn that introduces and analyzes a fundamental counting problem in combinatorics.
  • E. Combinatorial Optimization: Algorithms and Complexity
    Combinatorial Optimization: Algorithms and Complexity is a foundational textbook that systematically develops the theory and algorithms of combinatorial optimization, emphasizing computational complexity and algorithmic efficiency.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: Set Packing problem
Target entity description: The Set Packing problem is a classic NP-complete combinatorial optimization problem that asks for the largest collection of pairwise disjoint sets from a given family of sets.
  • A. Packing and Covering
    "Packing and Covering" is a classic mathematical monograph by C. A. Rogers that systematically develops the theory of packing and covering problems in geometry and number theory.
  • B. Subset sum problem
    The subset sum problem is a classic NP-complete decision problem in computer science that asks whether any subset of given integers sums to a specified target value.
  • C. Clique problem
    The Clique problem is a classic NP-complete decision problem in graph theory that asks whether a graph contains a fully connected subgraph (clique) of at least a given size.
  • D. A Combinatorial Problem
    "A Combinatorial Problem" is a classic mathematical paper by N. G. de Bruijn that introduces and analyzes a fundamental counting problem in combinatorics.
  • E. Combinatorial Optimization: Algorithms and Complexity
    Combinatorial Optimization: Algorithms and Complexity is a foundational textbook that systematically develops the theory and algorithms of combinatorial optimization, emphasizing computational complexity and algorithmic efficiency.
  • F. None of above. chosen

Provenance (2 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69e0b507dd9081908fb8bfcbef4c8b46 completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e7094cebe08190bb10f51a45c244ec completed April 21, 2026, 5:21 a.m.
Created at: April 16, 2026, 2:50 p.m.