Triple

T17229073
Position Surface form Disambiguated ID Type / Status
Subject John Stuart Mill as logician E418195 entity
Predicate method P859 FINISHED
Object Method of Residues
The Method of Residues is a logical technique, associated with John Stuart Mill, in which known causes are subtracted from a complex set of effects so that the remaining unexplained portion can be attributed to a previously unidentified cause.
E1257393 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: Method of Residues | Statement: [John Stuart Mill as logician, method, Method of Residues]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Method of Residues
Context triple: [John Stuart Mill as logician, method, Method of Residues]
  • A. 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.
  • B. Cauchy residue theorem
    The Cauchy residue theorem is a fundamental result in complex analysis that relates contour integrals of analytic functions around singularities to the sum of their residues, greatly simplifying the evaluation of many complex and real integrals.
  • C. Harmonic Integrals in the Theory of Analytic Functions
    "Harmonic Integrals in the Theory of Analytic Functions" is a foundational mathematical work by Kunihiko Kodaira that develops the theory of harmonic integrals and lays groundwork for modern complex analysis and complex geometry.
  • D. Lagrange’s variation of parameters method
    Lagrange’s variation of parameters method is a classical analytical technique in celestial mechanics and differential equations that determines how orbital or system parameters evolve over time under perturbing forces.
  • E. Wiener–Hopf equations
    Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
  • 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: Method of Residues
Triple: [John Stuart Mill as logician, method, Method of Residues]
Generated description
The Method of Residues is a logical technique, associated with John Stuart Mill, in which known causes are subtracted from a complex set of effects so that the remaining unexplained portion can be attributed to a previously unidentified cause.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Method of Residues
Target entity description: The Method of Residues is a logical technique, associated with John Stuart Mill, in which known causes are subtracted from a complex set of effects so that the remaining unexplained portion can be attributed to a previously unidentified cause.
  • A. 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.
  • B. Cauchy residue theorem
    The Cauchy residue theorem is a fundamental result in complex analysis that relates contour integrals of analytic functions around singularities to the sum of their residues, greatly simplifying the evaluation of many complex and real integrals.
  • C. Harmonic Integrals in the Theory of Analytic Functions
    "Harmonic Integrals in the Theory of Analytic Functions" is a foundational mathematical work by Kunihiko Kodaira that develops the theory of harmonic integrals and lays groundwork for modern complex analysis and complex geometry.
  • D. Lagrange’s variation of parameters method
    Lagrange’s variation of parameters method is a classical analytical technique in celestial mechanics and differential equations that determines how orbital or system parameters evolve over time under perturbing forces.
  • E. Wiener–Hopf equations
    Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.
  • 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_69d886d8e96081909870bff6c3d0bf09 completed April 10, 2026, 5:12 a.m.
NER Named-entity recognition batch_69e42df55e788190b442ffd4fac768c9 completed April 19, 2026, 1:20 a.m.
NED1 Entity disambiguation (via context triple) batch_6a01675eae08819093427b4dc1ffee5f completed May 11, 2026, 5:21 a.m.
NEDg Description generation batch_6a016a1f6eac8190951ae30f37144d2a completed May 11, 2026, 5:33 a.m.
NED2 Entity disambiguation (via description) batch_6a016a92af248190aaed36040486bf40 completed May 11, 2026, 5:35 a.m.
Created at: April 10, 2026, 5:39 a.m.