Triple

T4461421
Position Surface form Disambiguated ID Type / Status
Subject Wigner’s theorem on symmetry transformations E98262 entity
Predicate relatedConcept P37 FINISHED
Object Stone’s theorem on one-parameter unitary groups
Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
E443147 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: Stone’s theorem on one-parameter unitary groups | Statement: [Wigner’s theorem on symmetry transformations, relatedConcept, Stone’s theorem on one-parameter unitary groups]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Stone’s theorem on one-parameter unitary groups
Context triple: [Wigner’s theorem on symmetry transformations, relatedConcept, Stone’s theorem on one-parameter unitary groups]
  • A. 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.
  • B. 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).
  • C. 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.
  • D. Theory of Linear Operations
    Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
  • E. 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.
  • 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: Stone’s theorem on one-parameter unitary groups
Triple: [Wigner’s theorem on symmetry transformations, relatedConcept, Stone’s theorem on one-parameter unitary groups]
Generated description
Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Stone’s theorem on one-parameter unitary groups
Target entity description: Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
  • A. 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.
  • B. 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).
  • C. 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.
  • D. Theory of Linear Operations
    Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
  • E. 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.
  • 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_69b3454a7c608190944f5455c8031d73 completed March 12, 2026, 10:59 p.m.
NER Named-entity recognition batch_69b35674f718819089388c3924dd1414 completed March 13, 2026, 12:12 a.m.
NED1 Entity disambiguation (via context triple) batch_69b6284b90708190b557b66bd7533f4e completed March 15, 2026, 3:32 a.m.
NEDg Description generation batch_69b629532cac8190b959adc0ef13305a completed March 15, 2026, 3:36 a.m.
NED2 Entity disambiguation (via description) batch_69b62d9c287c8190a305f9d21517f913 completed March 15, 2026, 3:55 a.m.
Created at: March 12, 2026, 11:34 p.m.