Triple

T4492992
Position Surface form Disambiguated ID Type / Status
Subject Gödel numbering E100622 entity
Predicate relatedConcept P37 FINISHED
Object Kleene numbering
Kleene numbering is a method in computability theory for effectively assigning natural numbers to partial recursive functions, refining Gödel numbering to study algorithmic properties of functions.
E446862 NE FINISHED

How this triple was built (4 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: Kleene numbering | Statement: [Gödel numbering, relatedConcept, Kleene numbering]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kleene numbering
Context triple: [Gödel numbering, relatedConcept, Kleene numbering]
  • A. Gödel numbering
    Gödel numbering is a method in mathematical logic that encodes symbols, formulas, and proofs as unique natural numbers, enabling arithmetic to represent and reason about syntactic statements.
  • B. On Computable Numbers with an Application to the Entscheidungsproblem
    "On Computable Numbers, with an Application to the Entscheidungsproblem" is Alan Turing’s landmark 1936 paper that introduced the Turing machine model and founded the formal study of computability and the limits of algorithmic decision procedures.
  • C. Computability and Unsolvability
    Computability and Unsolvability is a classic 1958 textbook by Martin Davis that systematically develops the theory of computable functions and undecidable problems, helping to shape modern computability theory.
  • D. Peano arithmetic
    Peano arithmetic is a formal first-order axiomatic system that captures the basic properties of the natural numbers and underpins much of modern mathematical logic and number theory.
  • E. Church–Turing thesis
    The Church–Turing thesis is a foundational principle in computability theory stating that any function that can be effectively computed by an algorithm can be computed by a Turing machine (or equivalently by other formal models of computation).
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Kleene numbering
Triple: [Gödel numbering, relatedConcept, Kleene numbering]
Generated description
Kleene numbering is a method in computability theory for effectively assigning natural numbers to partial recursive functions, refining Gödel numbering to study algorithmic properties of functions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kleene numbering
Target entity description: Kleene numbering is a method in computability theory for effectively assigning natural numbers to partial recursive functions, refining Gödel numbering to study algorithmic properties of functions.
  • A. Gödel numbering
    Gödel numbering is a method in mathematical logic that encodes symbols, formulas, and proofs as unique natural numbers, enabling arithmetic to represent and reason about syntactic statements.
  • B. On Computable Numbers with an Application to the Entscheidungsproblem
    "On Computable Numbers, with an Application to the Entscheidungsproblem" is Alan Turing’s landmark 1936 paper that introduced the Turing machine model and founded the formal study of computability and the limits of algorithmic decision procedures.
  • C. Computability and Unsolvability
    Computability and Unsolvability is a classic 1958 textbook by Martin Davis that systematically develops the theory of computable functions and undecidable problems, helping to shape modern computability theory.
  • D. Peano arithmetic
    Peano arithmetic is a formal first-order axiomatic system that captures the basic properties of the natural numbers and underpins much of modern mathematical logic and number theory.
  • E. Church–Turing thesis
    The Church–Turing thesis is a foundational principle in computability theory stating that any function that can be effectively computed by an algorithm can be computed by a Turing machine (or equivalently by other formal models of computation).
  • F. None of above. chosen

Provenance (5 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_69bd43cdf15081909a4fa2585ff63b3e completed March 20, 2026, 12:55 p.m.
NER Named-entity recognition batch_69bd5570ba0881908f5fb4f8d0730e64 completed March 20, 2026, 2:10 p.m.
NED1 Entity disambiguation (via context triple) batch_69bd67b40fd4819098636b6f29304312 completed March 20, 2026, 3:28 p.m.
NEDg Description generation batch_69bd688e84fc8190a8900be40e3cf694 completed March 20, 2026, 3:32 p.m.
NED2 Entity disambiguation (via description) batch_69bd69bcf10c8190bd6ceb6bc604b3f5 completed March 20, 2026, 3:37 p.m.
Created at: March 20, 2026, 12:59 p.m.