Triple

T6482559
Position Surface form Disambiguated ID Type / Status
Subject Gamma function E146428 entity
Predicate hasMultiplicationFormula P71174 FINISHED
Object Gauss multiplication formula
The Gauss multiplication formula is a classical identity in complex analysis that expresses the gamma function of a multiple of a variable as a product of gamma functions evaluated at shifted fractions of that variable.
E596521 NE FINISHED

How this triple was built (5 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: Gauss multiplication formula | Statement: [Gamma function, hasMultiplicationFormula, Gauss multiplication formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gauss multiplication formula
Context triple: [Gamma function, hasMultiplicationFormula, Gauss multiplication formula]
  • A. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • B. Pochhammer symbol
    The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
  • C. Euler–Maclaurin summation formula
    The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
  • D. Gamma function
    The Gamma function is a fundamental extension of the factorial function to complex and real non-integer arguments, widely used in analysis, probability, and mathematical physics.
  • E. Jacobi triple product
    The Jacobi triple product is a fundamental identity in number theory and complex analysis that expresses an infinite product as an infinite sum, playing a key role in the theory of theta functions and q-series.
  • 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: Gauss multiplication formula
Triple: [Gamma function, hasMultiplicationFormula, Gauss multiplication formula]
Generated description
The Gauss multiplication formula is a classical identity in complex analysis that expresses the gamma function of a multiple of a variable as a product of gamma functions evaluated at shifted fractions of that variable.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gauss multiplication formula
Target entity description: The Gauss multiplication formula is a classical identity in complex analysis that expresses the gamma function of a multiple of a variable as a product of gamma functions evaluated at shifted fractions of that variable.
  • A. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • B. Pochhammer symbol
    The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
  • C. Euler–Maclaurin summation formula
    The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
  • D. Gamma function
    The Gamma function is a fundamental extension of the factorial function to complex and real non-integer arguments, widely used in analysis, probability, and mathematical physics.
  • E. Jacobi triple product
    The Jacobi triple product is a fundamental identity in number theory and complex analysis that expresses an infinite product as an infinite sum, playing a key role in the theory of theta functions and q-series.
  • F. None of above. chosen
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: hasMultiplicationFormula
Context triple: [Gamma function, hasMultiplicationFormula, Gauss multiplication formula]
  • A. hasSymbolicForm
    Indicates that one entity serves as the symbolic representation or abstract form of another entity.
  • B. hasMultiple
    Indicates that an entity is associated with more than one instance or occurrence of another related entity.
  • C. formulaUsed
    Indicates that a particular formula is employed or applied in performing a calculation, derivation, or reasoning step.
  • D. isProportionalityFactorIn
    Indicates that one quantity serves as the proportionality factor (constant of proportionality) in a specified proportional relationship or equation.
  • E. hasFormulation
    Indicates that one entity is expressed, prepared, or configured in a particular form or composition defined by another entity.
  • F. None of above. chosen

Provenance (7 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_69c0090158c08190af0df9a2348d2d52 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c06a6cd0c4819085a921e6a361d91c completed March 22, 2026, 10:17 p.m.
NED1 Entity disambiguation (via context triple) batch_69c653afb1148190a8683f24a553f64d completed March 27, 2026, 9:53 a.m.
NEDg Description generation batch_69c6559d06c8819082cad37d62fcb3a3 completed March 27, 2026, 10:02 a.m.
NED2 Entity disambiguation (via description) batch_69c6564e01748190a3a12abcc0dfd30f completed March 27, 2026, 10:05 a.m.
PD Predicate disambiguation batch_69c0673f6d48819080e10c85155c7195 completed March 22, 2026, 10:03 p.m.
PDg Predicate description generation batch_69c06822f73081908e6bb9edecbe77a6 completed March 22, 2026, 10:07 p.m.
Created at: March 22, 2026, 4:51 p.m.