Triple

T10992316
Position Surface form Disambiguated ID Type / Status
Subject Hadamard fractional integral E259779 entity
Predicate connectedTo P37 FINISHED
Object Mellin convolution E637297 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: Mellin convolution | Statement: [Hadamard fractional integral, connectedTo, Mellin convolution]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Mellin convolution
Context triple: [Hadamard fractional integral, connectedTo, Mellin convolution]
  • A. Mellin transforms chosen
    Mellin transforms are integral transforms that convert functions into complex-variable representations, playing a central role in analytic number theory by linking arithmetic functions to Dirichlet series and zeta functions.
  • B. 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.
  • C. Dirichlet convolution
    Dirichlet convolution is a binary operation on arithmetic functions that combines them via summation over divisors and plays a central role in multiplicative number theory and Dirichlet series.
  • D. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • E. Poisson summation formula
    The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
  • 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d32f9081909def643571499521 completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
Created at: April 8, 2026, 9:24 p.m.