Triple

T21088254
Position Surface form Disambiguated ID Type / Status
Subject Reducibility Among Combinatorial Problems E519559 entity
Predicate establishesNPCompletenessOf P142028 FINISHED
Object Exact Cover 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: Exact Cover problem | Statement: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, Exact Cover problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Exact Cover problem
Context triple: [Reducibility Among Combinatorial Problems, establishesNPCompletenessOf, Exact Cover problem]
  • A. Boolean satisfiability problem
    The Boolean satisfiability problem (SAT) is the canonical NP-complete decision problem of determining whether there exists an assignment of truth values to variables that makes a given Boolean formula evaluate to true.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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: Exact Cover problem
Target entity description: The Exact Cover problem is a classic NP-complete decision problem in combinatorics and computer science that asks whether a collection of subsets contains a subcollection that covers each element of a universe exactly once.
  • A. Boolean satisfiability problem
    The Boolean satisfiability problem (SAT) is the canonical NP-complete decision problem of determining whether there exists an assignment of truth values to variables that makes a given Boolean formula evaluate to true.
  • B. 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.
  • C. 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.
  • D. 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.
  • E. 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.
  • 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.