Triple
T2631450
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Osterwalder–Schrader axioms |
E59638
|
entity |
| Predicate | implies |
P1661
|
FINISHED |
| Object |
Wightman axioms for the reconstructed Minkowski theory
The Wightman axioms for the reconstructed Minkowski theory are a set of rigorous mathematical conditions that define a relativistic quantum field theory on Minkowski spacetime, ensuring properties like locality, covariance, and the existence of a stable vacuum state.
|
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: Wightman axioms for the reconstructed Minkowski theory | Statement: [Osterwalder–Schrader axioms, implies, Wightman axioms for the reconstructed Minkowski theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Wightman axioms for the reconstructed Minkowski theory Context triple: [Osterwalder–Schrader axioms, implies, Wightman axioms for the reconstructed Minkowski theory]
-
A.
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.
-
B.
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.
-
C.
Wigner’s theorem on symmetry transformations
Wigner’s theorem on symmetry transformations is a fundamental result in quantum mechanics stating that any symmetry of transition probabilities is represented by either a unitary or antiunitary operator on the system’s Hilbert space.
-
D.
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.
-
E.
Infeld–van der Waerden formalism
The Infeld–van der Waerden formalism is a mathematical framework in general relativity that reformulates the theory using spinor calculus to describe gravitational and electromagnetic fields.
- 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: Wightman axioms for the reconstructed Minkowski theory Triple: [Osterwalder–Schrader axioms, implies, Wightman axioms for the reconstructed Minkowski theory]
Generated description
The Wightman axioms for the reconstructed Minkowski theory are a set of rigorous mathematical conditions that define a relativistic quantum field theory on Minkowski spacetime, ensuring properties like locality, covariance, and the existence of a stable vacuum state.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Wightman axioms for the reconstructed Minkowski theory Target entity description: The Wightman axioms for the reconstructed Minkowski theory are a set of rigorous mathematical conditions that define a relativistic quantum field theory on Minkowski spacetime, ensuring properties like locality, covariance, and the existence of a stable vacuum state.
-
A.
Osterwalder–Schrader axioms
chosen
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.
-
B.
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.
-
C.
Wigner’s theorem on symmetry transformations
Wigner’s theorem on symmetry transformations is a fundamental result in quantum mechanics stating that any symmetry of transition probabilities is represented by either a unitary or antiunitary operator on the system’s Hilbert space.
-
D.
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.
-
E.
Infeld–van der Waerden formalism
The Infeld–van der Waerden formalism is a mathematical framework in general relativity that reformulates the theory using spinor calculus to describe gravitational and electromagnetic fields.
- F. None of above.
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_69ab4ac8596c8190b34997e73d9e991c |
completed | March 6, 2026, 9:44 p.m. |
| NER | Named-entity recognition | batch_69abd8c6e540819087c7f92432b27b0f |
completed | March 7, 2026, 7:50 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69af90a7021081909f81c4ddb48fa00c |
completed | March 10, 2026, 3:31 a.m. |
| NEDg | Description generation | batch_69af9172ba248190bbc68a00b43d9b44 |
completed | March 10, 2026, 3:35 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69af92500920819082c651f75a06dd72 |
completed | March 10, 2026, 3:38 a.m. |
Created at: March 6, 2026, 9:50 p.m.