Triple

T7906517
Position Surface form Disambiguated ID Type / Status
Subject Kolmogorov complexity E183589 entity
Predicate relatedTo P37 FINISHED
Object Chaitin's constant
Chaitin's constant is a real number that encodes the halting probability of a universal Turing machine and serves as a canonical example of algorithmic randomness and incompleteness in mathematics.
E143342 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: Chaitin's constant | Statement: [Kolmogorov complexity, relatedTo, Chaitin's constant]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Chaitin's constant
Context triple: [Kolmogorov complexity, relatedTo, Chaitin's constant]
  • A. Kolmogorov complexity
    Kolmogorov complexity is a measure of the amount of information in an object, defined as the length of the shortest computer program that can produce it.
  • 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. Khinchin's constant
    Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
  • D. Halting problem
    The halting problem is a fundamental decision problem in computability theory that asks whether a given program will eventually stop running or continue to run forever, and is famously proven to be undecidable.
  • E. 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.
  • 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: Chaitin's constant
Triple: [Kolmogorov complexity, relatedTo, Chaitin's constant]
Generated description
Chaitin's constant is a real number that encodes the halting probability of a universal Turing machine and serves as a canonical example of algorithmic randomness and incompleteness in mathematics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Chaitin's constant
Target entity description: Chaitin's constant is a real number that encodes the halting probability of a universal Turing machine and serves as a canonical example of algorithmic randomness and incompleteness in mathematics.
  • A. Kolmogorov complexity
    Kolmogorov complexity is a measure of the amount of information in an object, defined as the length of the shortest computer program that can produce it.
  • 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. Khinchin's constant
    Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
  • D. Halting problem chosen
    The halting problem is a fundamental decision problem in computability theory that asks whether a given program will eventually stop running or continue to run forever, and is famously proven to be undecidable.
  • E. 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.
  • F. None of above.

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_69ca828dec0c81908b8f55a4dbbb53ff completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb3a5871b8819087ad69c116c40091 completed March 31, 2026, 3:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69cb5bc9dfa88190aa5261bdf44823ab completed March 31, 2026, 5:29 a.m.
NEDg Description generation batch_69cb7633c5a0819089deb6e89d9acb8e completed March 31, 2026, 7:22 a.m.
NED2 Entity disambiguation (via description) batch_69cbb84dc86c8190893d67ce07c51aa0 completed March 31, 2026, 12:04 p.m.
Created at: March 30, 2026, 5:03 p.m.