Triple

T18479385
Position Surface form Disambiguated ID Type / Status
Subject Borel summation E451516 entity
Predicate relatedTo P37 FINISHED
Object Laplace–Borel transform NE NERFINISHED

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: Laplace–Borel transform | Statement: [Borel summation, relatedTo, Laplace–Borel transform]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Laplace–Borel transform
Context triple: [Borel summation, relatedTo, Laplace–Borel transform]
  • A. Laplace transform chosen
    The Laplace transform is an integral transform widely used in mathematics, physics, and engineering to convert functions of time into functions of a complex variable, simplifying the analysis and solution of differential equations and linear systems.
  • B. Laplace–Stieltjes transforms
    Laplace–Stieltjes transforms are a generalization of the Laplace transform that integrate with respect to a nondecreasing function, widely used in probability theory, stochastic processes, and the analysis of distributions and random variables.
  • C. Mellin transforms
    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.
  • D. Bailey transform
    The Bailey transform is a technique in the theory of basic hypergeometric series that relates pairs of sequences (Bailey pairs) and underlies many identities and transformations in q-series and partition theory.
  • E. Stieltjes transform
    The Stieltjes transform is an integral transform that encodes a measure or distribution via a complex-analytic function, widely used in random matrix theory to study limiting spectral distributions and resolvents.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53065e8388190bb216dae89f8cf75 completed April 19, 2026, 7:43 p.m.
Created at: April 10, 2026, 11:35 a.m.