Triple

T13965473
Position Surface form Disambiguated ID Type / Status
Subject Essai sur l’étude des fonctions données par leur développement de Taylor E335909 entity
Predicate relatedConcept P37 FINISHED
Object Hadamard factorization theorem E110607 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: Hadamard factorization theorem | Statement: [Essai sur l’étude des fonctions données par leur développement de Taylor, relatedConcept, Hadamard factorization theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hadamard factorization theorem
Context triple: [Essai sur l’étude des fonctions données par leur développement de Taylor, relatedConcept, Hadamard factorization theorem]
  • A. Weierstrass factorization theorem chosen
    The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
  • B. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • C. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • D. Hermite–Biehler theorem
    The Hermite–Biehler theorem is a result in complex analysis and control theory that characterizes when a complex polynomial has all its zeros in the open upper half-plane in terms of the interlacing of zeros of two associated real polynomials.
  • E. Cauchy–Hadamard theorem
    The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
  • 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_69d81c61f3508190aaf2ca0dc0002c59 completed April 9, 2026, 9:38 p.m.
NER Named-entity recognition batch_69de2e7e24f08190ba939a8044860033 completed April 14, 2026, 12:09 p.m.
NED1 Entity disambiguation (via context triple) batch_69fba1d890d48190affd194b2439c271 completed May 6, 2026, 8:17 p.m.
Created at: April 9, 2026, 10:18 p.m.