Triple

T6594144
Position Surface form Disambiguated ID Type / Status
Subject Stephen Kleene E148433 entity
Predicate notableConcept P201 FINISHED
Object Kleene’s recursion theorem
Kleene’s recursion theorem is a fundamental result in computability theory that guarantees the existence of self-referential programs, allowing a program to effectively obtain and use its own description.
E607898 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’s recursion theorem | Statement: [Stephen Kleene, notableConcept, Kleene’s recursion theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kleene’s recursion theorem
Context triple: [Stephen Kleene, notableConcept, Kleene’s recursion theorem]
  • A. Kleene’s normal form theorem
    Kleene’s normal form theorem is a fundamental result in computability theory that characterizes all partial recursive (effectively computable) functions using a universal primitive recursive function and the μ-operator.
  • B. Rice's theorem
    Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
  • C. Löb's theorem
    Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
  • D. 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.
  • E. 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.
  • 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’s recursion theorem
Triple: [Stephen Kleene, notableConcept, Kleene’s recursion theorem]
Generated description
Kleene’s recursion theorem is a fundamental result in computability theory that guarantees the existence of self-referential programs, allowing a program to effectively obtain and use its own description.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kleene’s recursion theorem
Target entity description: Kleene’s recursion theorem is a fundamental result in computability theory that guarantees the existence of self-referential programs, allowing a program to effectively obtain and use its own description.
  • A. Kleene’s normal form theorem
    Kleene’s normal form theorem is a fundamental result in computability theory that characterizes all partial recursive (effectively computable) functions using a universal primitive recursive function and the μ-operator.
  • B. Rice's theorem
    Rice's theorem is a fundamental result in computability theory stating that any non-trivial semantic property of the language recognized by a Turing machine is undecidable.
  • C. Löb's theorem
    Löb's theorem is a fundamental result in mathematical logic that characterizes when a sufficiently strong formal system can prove statements about its own provability, closely refining the insights of Gödel’s incompleteness theorems.
  • D. 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.
  • E. 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.
  • 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_69c687e7b8688190811ffee72e096468 completed March 27, 2026, 1:36 p.m.
NER Named-entity recognition batch_69c6aed0b364819081cb02af7a38ef11 completed March 27, 2026, 4:22 p.m.
NED1 Entity disambiguation (via context triple) batch_69c6e42d6ba08190beccfad588594780 completed March 27, 2026, 8:10 p.m.
NEDg Description generation batch_69c6e7c75140819082a32e4662e0b07c completed March 27, 2026, 8:25 p.m.
NED2 Entity disambiguation (via description) batch_69c6e8881b848190bd6184aeaf311d24 completed March 27, 2026, 8:28 p.m.
Created at: March 27, 2026, 1:55 p.m.