Triple

T22594821
Position Surface form Disambiguated ID Type / Status
Subject Curtis Callan E574645 entity
Predicate notableWork P4 FINISHED
Object Callan–Symanzik equation NE NERFINISHED

How this triple was built (3 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: Callan–Symanzik equation | Statement: [Curtis Callan, notableWork, Callan–Symanzik equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Callan–Symanzik equation
Context triple: [Curtis Callan, notableWork, Callan–Symanzik equation]
  • A. Schwinger–Dyson equations
    The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
  • B. Slavnov–Taylor identities
    Slavnov–Taylor identities are relations in non-Abelian gauge theories that generalize Ward identities, ensuring the consistency and renormalizability of gauge-invariant quantum field theories.
  • C. Gell-Mann–Low theorem
    The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
  • D. Ward–Takahashi identities
    The Ward–Takahashi identities are fundamental relations in quantum field theory that express the consequences of gauge or global symmetries for Green’s functions and ensure the consistency of renormalization with these symmetries.
  • E. Renormalization and Galois Theories
    Renormalization and Galois Theories is a mathematical physics work that connects the renormalization process in quantum field theory with Galois theory and motives, revealing deep arithmetic and geometric structures underlying quantum phenomena.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Callan–Symanzik equation
Target entity description: The Callan–Symanzik equation is a fundamental renormalization group equation in quantum field theory that describes how physical quantities change with energy scale, encapsulating the running of coupling constants and anomalous dimensions.
  • A. Schwinger–Dyson equations
    The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
  • B. Slavnov–Taylor identities
    Slavnov–Taylor identities are relations in non-Abelian gauge theories that generalize Ward identities, ensuring the consistency and renormalizability of gauge-invariant quantum field theories.
  • C. Gell-Mann–Low theorem
    The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
  • D. Ward–Takahashi identities
    The Ward–Takahashi identities are fundamental relations in quantum field theory that express the consequences of gauge or global symmetries for Green’s functions and ensure the consistency of renormalization with these symmetries.
  • E. Renormalization and Galois Theories
    Renormalization and Galois Theories is a mathematical physics work that connects the renormalization process in quantum field theory with Galois theory and motives, revealing deep arithmetic and geometric structures underlying quantum phenomena.
  • F. None of above. chosen

Provenance (2 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_69e245bc11308190b69d794d5d1e0bb6 completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f16164d690819096f7c4efb6cedad9 completed April 29, 2026, 1:39 a.m.
Created at: April 17, 2026, 2:49 p.m.