Triple

T2631451
Position Surface form Disambiguated ID Type / Status
Subject Osterwalder–Schrader axioms E59638 entity
Predicate relatedTo P37 FINISHED
Object Wightman axioms
The Wightman axioms are a set of rigorous mathematical conditions that formalize relativistic quantum field theory in terms of operator-valued distributions on Hilbert space.
E284685 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 | Statement: [Osterwalder–Schrader axioms, relatedTo, Wightman axioms]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Wightman axioms
Context triple: [Osterwalder–Schrader axioms, relatedTo, Wightman axioms]
  • 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. Wick’s theorem
    Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
  • E. Gelfand–Naimark theorem
    The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
  • 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
Triple: [Osterwalder–Schrader axioms, relatedTo, Wightman axioms]
Generated description
The Wightman axioms are a set of rigorous mathematical conditions that formalize relativistic quantum field theory in terms of operator-valued distributions on Hilbert space.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Wightman axioms
Target entity description: The Wightman axioms are a set of rigorous mathematical conditions that formalize relativistic quantum field theory in terms of operator-valued distributions on Hilbert space.
  • 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. Wick’s theorem
    Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
  • E. Gelfand–Naimark theorem
    The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
  • 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_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.