Triple

T839947
Position Surface form Disambiguated ID Type / Status
Subject Kurt Gödel E18153 entity
Predicate notableWork P4 FINISHED
Object 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.
E100622 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: Gödel numbering | Statement: [Kurt Gödel, notableWork, Gödel numbering]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gödel numbering
Context triple: [Kurt Gödel, notableWork, Gödel numbering]
  • A. Gödel's incompleteness theorems
    Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
  • B. Tarski's undefinability theorem
    Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
  • C. Hilbert’s program
    Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
  • D. 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).
  • E. 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.
  • 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: Gödel numbering
Triple: [Kurt Gödel, notableWork, Gödel numbering]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gödel numbering
Target entity description: 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.
  • A. Gödel's incompleteness theorems
    Gödel's incompleteness theorems are two fundamental results in mathematical logic showing that any sufficiently powerful, consistent formal system cannot prove all true statements about arithmetic, and cannot prove its own consistency.
  • B. Tarski's undefinability theorem
    Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.
  • C. Hilbert’s program
    Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
  • D. 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).
  • E. 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.
  • 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_69a49389f44881909a608fb27d89f247 completed March 1, 2026, 7:29 p.m.
NER Named-entity recognition batch_69a4abe4ab1081909207ae2eec1898d9 completed March 1, 2026, 9:13 p.m.
NED1 Entity disambiguation (via context triple) batch_69a7929860f081909c86f84d7cfe6acb completed March 4, 2026, 2:02 a.m.
NEDg Description generation batch_69a796370f388190b23cd19cc3fa5a3b completed March 4, 2026, 2:17 a.m.
NED2 Entity disambiguation (via description) batch_69a796bee5388190ab0abf0bfa08ad97 completed March 4, 2026, 2:19 a.m.
Created at: March 1, 2026, 7:38 p.m.