Triple

T6594126
Position Surface form Disambiguated ID Type / Status
Subject Stephen Kleene E148433 entity
Predicate knownFor P22 FINISHED
Object 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.
E601580 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 normal form theorem | Statement: [Stephen Kleene, knownFor, Kleene’s normal form theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kleene’s normal form theorem
Context triple: [Stephen Kleene, knownFor, Kleene’s normal form theorem]
  • A. 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.
  • B. arithmetization of syntax
    Arithmetization of syntax is a method in mathematical logic that encodes formal language expressions and proofs as natural numbers so that syntactic properties can be studied using arithmetic.
  • 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. Tarski–Mostowski–Robinson theorem
    The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
  • E. 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.
  • 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 normal form theorem
Triple: [Stephen Kleene, knownFor, Kleene’s normal form theorem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kleene’s normal form theorem
Target entity description: 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.
  • A. 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.
  • B. arithmetization of syntax
    Arithmetization of syntax is a method in mathematical logic that encodes formal language expressions and proofs as natural numbers so that syntactic properties can be studied using arithmetic.
  • 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. Tarski–Mostowski–Robinson theorem
    The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
  • E. 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.
  • 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_69c6cbba656c81909c3876a8f2f7300e completed March 27, 2026, 6:26 p.m.
NEDg Description generation batch_69c6cd09753c81909df166156ffbf82a completed March 27, 2026, 6:31 p.m.
NED2 Entity disambiguation (via description) batch_69c6ce9ba47c819091496c87117e7a03 completed March 27, 2026, 6:38 p.m.
Created at: March 27, 2026, 1:55 p.m.