Triple

T7150511

Position	Surface form	Disambiguated ID	Type / Status
Subject	spin–statistics theorem	`E166678`	entity
Predicate	hasAlternativeFormulation	`P3660`	FINISHED
Object	algebraic quantum field theory Algebraic quantum field theory is a mathematically rigorous framework for quantum field theory that emphasizes the algebraic structure of observables and their locality properties in spacetime.	`E645108`	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: algebraic quantum field theory | Statement: [spin–statistics theorem, hasAlternativeFormulation, algebraic quantum field theory]

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: algebraic quantum field theory
Context triple: [spin–statistics theorem, hasAlternativeFormulation, algebraic quantum field theory]

A. 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.
B. 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.
C. quantum field theory
Quantum field theory is the theoretical framework in physics that combines quantum mechanics and special relativity to describe particles as excitations of underlying fields and governs their interactions.
D. 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.
E. 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.
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: algebraic quantum field theory
Triple: [spin–statistics theorem, hasAlternativeFormulation, algebraic quantum field theory]

Generated description

Algebraic quantum field theory is a mathematically rigorous framework for quantum field theory that emphasizes the algebraic structure of observables and their locality properties in spacetime.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: algebraic quantum field theory
Target entity description: Algebraic quantum field theory is a mathematically rigorous framework for quantum field theory that emphasizes the algebraic structure of observables and their locality properties in spacetime.

A. 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.
B. 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.
C. quantum field theory
Quantum field theory is the theoretical framework in physics that combines quantum mechanics and special relativity to describe particles as excitations of underlying fields and governs their interactions.
D. 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.
E. 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.
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_69c68886779c8190a8e3fbabffe68253`	completed	March 27, 2026, 1:39 p.m.
NER	Named-entity recognition	`batch_69c6e7f28b188190b1732ca711666531`	completed	March 27, 2026, 8:26 p.m.
NED1	Entity disambiguation (via context triple)	`batch_69c7ada940e08190b16e97e363801e75`	completed	March 28, 2026, 10:30 a.m.
NEDg	Description generation	`batch_69c7ae5767408190860c1c7bc3a769fa`	completed	March 28, 2026, 10:32 a.m.
NED2	Entity disambiguation (via description)	`batch_69c7aeb68c3481909c6dff8ee51349ab`	completed	March 28, 2026, 10:34 a.m.

Created at: March 27, 2026, 2:46 p.m.