Triple

T145464
Position Surface form Disambiguated ID Type / Status
Subject Freeman Dyson E2943 entity
Predicate notableWork P4 FINISHED
Object Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
E17018 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: Dyson’s transform in number theory | Statement: [Freeman Dyson, notableWork, Dyson’s transform in number theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Dyson’s transform in number theory
Context triple: [Freeman Dyson, notableWork, Dyson’s transform in number theory]
  • A. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • B. Dyson series
    The Dyson series is a perturbative expansion in quantum field theory that expresses time-ordered exponentials and scattering amplitudes as an infinite series of integrals, each term corresponding to a Feynman diagram.
  • C. Levine-Fricke Field
    Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
  • D. Born–Huang expansion
    The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
  • E. The Mathematical Theory of Black Holes
    The Mathematical Theory of Black Holes is a landmark monograph that presents a rigorous, comprehensive treatment of the physics and mathematics underlying black hole solutions in general relativity.
  • 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: Dyson’s transform in number theory
Triple: [Freeman Dyson, notableWork, Dyson’s transform in number theory]
Generated description
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Dyson’s transform in number theory
Target entity description: Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • A. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • B. Dyson series
    The Dyson series is a perturbative expansion in quantum field theory that expresses time-ordered exponentials and scattering amplitudes as an infinite series of integrals, each term corresponding to a Feynman diagram.
  • C. Levine-Fricke Field
    Levine-Fricke Field is the home softball stadium of the University of California, Berkeley Golden Bears, located on the university’s campus in Berkeley, California.
  • D. Born–Huang expansion
    The Born–Huang expansion is a quantum mechanical method that systematically improves upon the Born–Oppenheimer approximation by including couplings between electronic and nuclear motions in molecular systems.
  • E. The Mathematical Theory of Black Holes
    The Mathematical Theory of Black Holes is a landmark monograph that presents a rigorous, comprehensive treatment of the physics and mathematics underlying black hole solutions in general relativity.
  • 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_69a2521e35c08190b28e5c9f1e3c9b59 completed Feb. 28, 2026, 2:25 a.m.
NER Named-entity recognition batch_69a257ea7eac8190884a53453a9e0dd6 completed Feb. 28, 2026, 2:50 a.m.
NED1 Entity disambiguation (via context triple) batch_69a2bf69fd2081908df35ea5ade4307c completed Feb. 28, 2026, 10:11 a.m.
NEDg Description generation batch_69a2bfb9ad848190ae1412d0e180f48f completed Feb. 28, 2026, 10:13 a.m.
NED2 Entity disambiguation (via description) batch_69a2c09721a88190a6268360c34a0b01 completed Feb. 28, 2026, 10:16 a.m.
Created at: Feb. 28, 2026, 2:31 a.m.