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.