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.