Triple

T5425852
Position Surface form Disambiguated ID Type / Status
Subject Ernst Lindelöf E121359 entity
Predicate notableWork P4 FINISHED
Object Le calcul des résidus et ses applications à la théorie des fonctions
*Le calcul des résidus et ses applications à la théorie des fonctions* is a mathematical treatise on the theory of residues in complex analysis and its applications to the study of analytic functions.
E518482 NE FINISHED

How this triple was built (4 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: Le calcul des résidus et ses applications à la théorie des fonctions | Statement: [Ernst Lindelöf, notableWork, Le calcul des résidus et ses applications à la théorie des fonctions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Le calcul des résidus et ses applications à la théorie des fonctions
Context triple: [Ernst Lindelöf, notableWork, Le calcul des résidus et ses applications à la théorie des fonctions]
  • A. 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.
  • B. Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes
    Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes is a seminal mathematical paper by Niels Henrik Abel that develops fundamental results on transcendental functions and helped lay groundwork for modern analysis.
  • C. Recherches sur les fonctions elliptiques
    Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
  • D. Cours d’Analyse
    Cours d’Analyse is a foundational 19th-century mathematics textbook by Augustin-Louis Cauchy that rigorously developed the theory of functions, limits, and continuity, helping to formalize modern analysis.
  • E. Essai sur l’étude des fonctions données par leur développement de Taylor
    Essai sur l’étude des fonctions données par leur développement de Taylor is a foundational mathematical treatise by Jacques Hadamard that investigates the behavior and properties of functions defined through their Taylor series expansions.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Le calcul des résidus et ses applications à la théorie des fonctions
Triple: [Ernst Lindelöf, notableWork, Le calcul des résidus et ses applications à la théorie des fonctions]
Generated description
*Le calcul des résidus et ses applications à la théorie des fonctions* is a mathematical treatise on the theory of residues in complex analysis and its applications to the study of analytic functions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Le calcul des résidus et ses applications à la théorie des fonctions
Target entity description: *Le calcul des résidus et ses applications à la théorie des fonctions* is a mathematical treatise on the theory of residues in complex analysis and its applications to the study of analytic functions.
  • A. 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.
  • B. Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes
    Mémoire sur une propriété générale d’une classe très étendue de fonctions transcendantes is a seminal mathematical paper by Niels Henrik Abel that develops fundamental results on transcendental functions and helped lay groundwork for modern analysis.
  • C. Recherches sur les fonctions elliptiques
    Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
  • D. Cours d’Analyse
    Cours d’Analyse is a foundational 19th-century mathematics textbook by Augustin-Louis Cauchy that rigorously developed the theory of functions, limits, and continuity, helping to formalize modern analysis.
  • E. Essai sur l’étude des fonctions données par leur développement de Taylor
    Essai sur l’étude des fonctions données par leur développement de Taylor is a foundational mathematical treatise by Jacques Hadamard that investigates the behavior and properties of functions defined through their Taylor series expansions.
  • F. None of above. chosen

Provenance (5 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_69bd463b58d88190b258261573de9e91 completed March 20, 2026, 1:06 p.m.
NER Named-entity recognition batch_69bd881598448190a9bb456dee36004b completed March 20, 2026, 5:47 p.m.
NED1 Entity disambiguation (via context triple) batch_69bf3abfc7e88190b8f0a31b61c33973 completed March 22, 2026, 12:41 a.m.
NEDg Description generation batch_69bf3b592a08819090e2873bcf4e797f completed March 22, 2026, 12:44 a.m.
NED2 Entity disambiguation (via description) batch_69bf3c0b9e5481909101eccbd55f24b2 completed March 22, 2026, 12:47 a.m.
Created at: March 20, 2026, 2:06 p.m.