Triple

T3167253
Position Surface form Disambiguated ID Type / Status
Subject Jacques Hadamard E66240 entity
Predicate knownFor P22 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: [Jacques Hadamard, knownFor, Hadamard factorization theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hadamard factorization theorem
Context triple: [Jacques Hadamard, knownFor, 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. 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.
  • D. Weierstrass preparation theorem
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • E. Théorie des fonctions analytiques
    Théorie des fonctions analytiques is a foundational mathematical treatise by Joseph-Louis Lagrange that systematically develops calculus using power series and analytic functions instead of geometric or infinitesimal arguments.
  • 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_69ad8585d7988190af37365331093ccd completed March 8, 2026, 2:19 p.m.
NER Named-entity recognition batch_69ada6457acc8190b2b9acbd1cfcdb91 completed March 8, 2026, 4:39 p.m.
NED1 Entity disambiguation (via context triple) batch_69b235e108cc81909d5733bd00cb0bee completed March 12, 2026, 3:41 a.m.
Created at: March 8, 2026, 3:06 p.m.