Triple

T12597332
Position Surface form Disambiguated ID Type / Status
Subject Stirling's approximation E300765 entity
Predicate relatedTo P37 FINISHED
Object Gamma function reflection formula E596522 NE FINISHED

How this triple was built (2 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: Gamma function reflection formula | Statement: [Stirling's approximation, relatedTo, Gamma function reflection formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Gamma function reflection formula
Context triple: [Stirling's approximation, relatedTo, Gamma function reflection formula]
  • A. Euler’s reflection formula chosen
    Euler’s reflection formula is a fundamental identity in complex analysis that relates the values of the Gamma function at z and 1−z through the sine function, revealing a deep symmetry of the Gamma function.
  • B. 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.
  • C. 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.
  • D. Gauss hypergeometric function
    The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
  • E. Barnes G-function
    The Barnes G-function is a special function that generalizes the superfactorial and is closely related to the gamma and multiple gamma functions in complex analysis and number theory.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d7bdea2ca881908f379526c13b1145 completed April 9, 2026, 2:55 p.m.
NER Named-entity recognition batch_69d954cf33b88190bff339fcd3142cc8 completed April 10, 2026, 7:51 p.m.
NED1 Entity disambiguation (via context triple) batch_69f65ec75fc08190aa13cbb0161eb35c completed May 2, 2026, 8:29 p.m.
Created at: April 9, 2026, 5:08 p.m.