Triple

T2866510
Position Surface form Disambiguated ID Type / Status
Subject Princeton Mathematical Series E63452 entity
Predicate workIncluded P10663 FINISHED
Object "Partial Differential Equations"
"Partial Differential Equations" is a foundational mathematical text that systematically develops the theory and methods for analyzing equations involving multivariable functions and their partial derivatives.
E305926 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: "Partial Differential Equations" | Statement: [Princeton Mathematical Series, workIncluded, "Partial Differential Equations"]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: "Partial Differential Equations"
Context triple: [Princeton Mathematical Series, workIncluded, "Partial Differential Equations"]
  • A. Methods of Mathematical Physics
    Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
  • B. Asymptotic Methods in Analysis
    Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
  • C. Generalized Functions (multi-volume series)
    Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
  • D. "Invariante Variationsprobleme"
    "Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
  • E. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • 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: "Partial Differential Equations"
Triple: [Princeton Mathematical Series, workIncluded, "Partial Differential Equations"]
Generated description
"Partial Differential Equations" is a foundational mathematical text that systematically develops the theory and methods for analyzing equations involving multivariable functions and their partial derivatives.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: "Partial Differential Equations"
Target entity description: "Partial Differential Equations" is a foundational mathematical text that systematically develops the theory and methods for analyzing equations involving multivariable functions and their partial derivatives.
  • A. Methods of Mathematical Physics
    Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
  • B. Asymptotic Methods in Analysis
    Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
  • C. Generalized Functions (multi-volume series)
    Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
  • D. "Invariante Variationsprobleme"
    "Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
  • E. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • 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_69ab4c42fb8c8190b36e161d47c03b81 completed March 6, 2026, 9:50 p.m.
NER Named-entity recognition batch_69abe08ae5048190a0a3b573d9a5fdbc completed March 7, 2026, 8:23 a.m.
NED1 Entity disambiguation (via context triple) batch_69b01da85930819092d19a5e712cfa18 completed March 10, 2026, 1:33 p.m.
NEDg Description generation batch_69b01e34639c8190b1c6e8a14cd31d96 completed March 10, 2026, 1:35 p.m.
NED2 Entity disambiguation (via description) batch_69b01f5a6784819089499926fb115d9c completed March 10, 2026, 1:40 p.m.
Created at: March 6, 2026, 10:02 p.m.