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.