Triple

T478499
Position Surface form Disambiguated ID Type / Status
Subject Euclidean quantum field theory E9113 entity
Predicate hasKeyConcept P533 FINISHED
Object Osterwalder–Schrader axioms
The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
E59638 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: Osterwalder–Schrader axioms | Statement: [Euclidean quantum field theory, hasKeyConcept, Osterwalder–Schrader axioms]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Osterwalder–Schrader axioms
Context triple: [Euclidean quantum field theory, hasKeyConcept, Osterwalder–Schrader axioms]
  • A. Faddeev’s axioms
    Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
  • B. Euclidean quantum field theory
    Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
  • C. Mathematical Foundations of Quantum Mechanics
    Mathematical Foundations of Quantum Mechanics is John von Neumann’s landmark 1932 treatise that rigorously formulates quantum theory using functional analysis and operator theory on Hilbert spaces.
  • D. Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
    Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
  • 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: Osterwalder–Schrader axioms
Triple: [Euclidean quantum field theory, hasKeyConcept, Osterwalder–Schrader axioms]
Generated description
The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Osterwalder–Schrader axioms
Target entity description: The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
  • A. Faddeev’s axioms
    Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
  • B. Euclidean quantum field theory
    Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
  • C. Mathematical Foundations of Quantum Mechanics
    Mathematical Foundations of Quantum Mechanics is John von Neumann’s landmark 1932 treatise that rigorously formulates quantum theory using functional analysis and operator theory on Hilbert spaces.
  • D. Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
    Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
  • 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_69a2e7ff81708190b0507a24a997232c completed Feb. 28, 2026, 1:05 p.m.
NER Named-entity recognition batch_69a2f056459881909749764cc4a7f9e8 completed Feb. 28, 2026, 1:40 p.m.
NED1 Entity disambiguation (via context triple) batch_69a46804b90881908422851eeb9bbba1 completed March 1, 2026, 4:23 p.m.
NEDg Description generation batch_69a46901d5c08190af7ea8b01206505c completed March 1, 2026, 4:27 p.m.
NED2 Entity disambiguation (via description) batch_69a4696c35c08190890e8159983e2efb completed March 1, 2026, 4:29 p.m.
Created at: Feb. 28, 2026, 1:12 p.m.