Triple

T18865152
Position Surface form Disambiguated ID Type / Status
Subject Bogoliubov–Parasyuk theorem E461418 entity
Predicate relatedTo P37 FINISHED
Object BPHZ renormalization
BPHZ renormalization is a rigorous, diagrammatic procedure in quantum field theory that systematically removes ultraviolet divergences from Feynman integrals using the Bogoliubov–Parasyuk–Hepp–Zimmermann subtraction scheme.
E461418 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: BPHZ renormalization | Statement: [Bogoliubov–Parasyuk theorem, relatedTo, BPHZ renormalization]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: BPHZ renormalization
Context triple: [Bogoliubov–Parasyuk theorem, relatedTo, BPHZ renormalization]
  • A. 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.
  • B. Bogoliubov–Parasyuk theorem
    The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
  • C. Pauli–Villars regularization
    Pauli–Villars regularization is a technique in quantum field theory that controls ultraviolet divergences by introducing auxiliary heavy fields to render integrals finite.
  • D. 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.
  • E. Wilsonian renormalization group
    The Wilsonian renormalization group is a framework in theoretical physics that explains how a system’s behavior changes with scale by systematically integrating out short-distance degrees of freedom, providing deep insight into critical phenomena and quantum field theories.
  • 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: BPHZ renormalization
Triple: [Bogoliubov–Parasyuk theorem, relatedTo, BPHZ renormalization]
Generated description
BPHZ renormalization is a rigorous, diagrammatic procedure in quantum field theory that systematically removes ultraviolet divergences from Feynman integrals using the Bogoliubov–Parasyuk–Hepp–Zimmermann subtraction scheme.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: BPHZ renormalization
Target entity description: BPHZ renormalization is a rigorous, diagrammatic procedure in quantum field theory that systematically removes ultraviolet divergences from Feynman integrals using the Bogoliubov–Parasyuk–Hepp–Zimmermann subtraction scheme.
  • A. 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.
  • B. Bogoliubov–Parasyuk theorem chosen
    The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
  • C. Pauli–Villars regularization
    Pauli–Villars regularization is a technique in quantum field theory that controls ultraviolet divergences by introducing auxiliary heavy fields to render integrals finite.
  • D. 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.
  • E. Wilsonian renormalization group
    The Wilsonian renormalization group is a framework in theoretical physics that explains how a system’s behavior changes with scale by systematically integrating out short-distance degrees of freedom, providing deep insight into critical phenomena and quantum field theories.
  • 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_69d8dcfb7b9c8190854e7b171b98ea2e completed April 10, 2026, 11:20 a.m.
NER Named-entity recognition batch_69e5c2a5074481908941fcbb3b3eefa2 completed April 20, 2026, 6:07 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0575b902ec8190bcda2ab33b87bea4 completed May 14, 2026, 7:11 a.m.
NEDg Description generation batch_6a057927ddd881908809c9c27e1ae5a2 completed May 14, 2026, 7:26 a.m.
NED2 Entity disambiguation (via description) batch_6a0579982b4c8190a7cff4d2946bc15d completed May 14, 2026, 7:28 a.m.
Created at: April 10, 2026, 11:57 a.m.