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.