Triple

T1286006
Position Surface form Disambiguated ID Type / Status
Subject generalized binomial theorem E27434 entity
Predicate relatedConcept P37 FINISHED
Object Pochhammer symbol
The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
E146427 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: Pochhammer symbol | Statement: [generalized binomial theorem, relatedConcept, Pochhammer symbol]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Pochhammer symbol
Context triple: [generalized binomial theorem, relatedConcept, Pochhammer symbol]
  • A. binomial theorem
    The binomial theorem is a fundamental algebraic formula that provides a systematic way to expand powers of binomial expressions, playing a key role in combinatorics and mathematical analysis.
  • B. Pascal's triangle
    Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
  • C. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • D. generalized binomial theorem
    The generalized binomial theorem extends the classical binomial theorem by allowing real or complex exponents, expressing powers of a binomial as an infinite series using generalized binomial coefficients.
  • E. multinomial theorem
    The multinomial theorem is a fundamental algebraic formula that generalizes the binomial theorem to express powers of sums with any number of terms using multinomial coefficients.
  • 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: Pochhammer symbol
Triple: [generalized binomial theorem, relatedConcept, Pochhammer symbol]
Generated description
The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Pochhammer symbol
Target entity description: The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
  • A. binomial theorem
    The binomial theorem is a fundamental algebraic formula that provides a systematic way to expand powers of binomial expressions, playing a key role in combinatorics and mathematical analysis.
  • B. Pascal's triangle
    Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
  • C. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • D. generalized binomial theorem
    The generalized binomial theorem extends the classical binomial theorem by allowing real or complex exponents, expressing powers of a binomial as an infinite series using generalized binomial coefficients.
  • E. multinomial theorem
    The multinomial theorem is a fundamental algebraic formula that generalizes the binomial theorem to express powers of sums with any number of terms using multinomial coefficients.
  • 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_69a496d4ec448190ad653b2590c46711 completed March 1, 2026, 7:43 p.m.
NER Named-entity recognition batch_69a4c0b85eb48190a8b61dc397fa6390 completed March 1, 2026, 10:42 p.m.
NED1 Entity disambiguation (via context triple) batch_69aca3004b648190a4148b0421699bf9 completed March 7, 2026, 10:13 p.m.
NEDg Description generation batch_69aca3a539848190a17e8bd578bc237a completed March 7, 2026, 10:16 p.m.
NED2 Entity disambiguation (via description) batch_69aca4158bbc8190bd1f5799715e3e4c completed March 7, 2026, 10:17 p.m.
Created at: March 1, 2026, 7:51 p.m.