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.