Triple

T6833507
Position Surface form Disambiguated ID Type / Status
Subject arithmetic–geometric mean identities E157393 entity
Predicate usesConcept P531 FINISHED
Object Gamma function E146428 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 | Statement: [arithmetic–geometric mean identities, usesConcept, Gamma function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gamma function
Context triple: [arithmetic–geometric mean identities, usesConcept, Gamma function]
  • A. Gamma function chosen
    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.
  • B. 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.
  • C. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • D. Euler–Mascheroni constant γ
    The Euler–Mascheroni constant γ is a mathematical constant that arises in analysis and number theory, defined as the limiting difference between the harmonic series and the natural logarithm.
  • E. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • 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_69c6882c53608190b99aebef079b23bd completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d62b1e8c8190a81d91191a54b073 completed March 27, 2026, 7:10 p.m.
NED1 Entity disambiguation (via context triple) batch_69c723fd50c88190af005fd58ca0aee6 completed March 28, 2026, 12:42 a.m.
Created at: March 27, 2026, 2:18 p.m.