Triple

T1390514
Position Surface form Disambiguated ID Type / Status
Subject Surreal numbers E29943 entity
Predicate relatedConcept P37 FINISHED
Object Hahn series
Hahn series are formal power series with exponents in an ordered abelian group and well-ordered supports, providing a general framework for constructing large ordered fields that include structures like the surreal numbers.
E159923 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: Hahn series | Statement: [Surreal numbers, relatedConcept, Hahn series]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hahn series
Context triple: [Surreal numbers, relatedConcept, Hahn series]
  • A. 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.
  • B. Taylor series
    A Taylor series is an infinite sum of terms calculated from the derivatives of a function at a single point, used to represent and approximate functions as power series.
  • C. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • D. TrizecHahn
    TrizecHahn was a major North American real estate investment and development company known for large-scale commercial and mixed-use projects.
  • E. 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.
  • 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: Hahn series
Triple: [Surreal numbers, relatedConcept, Hahn series]
Generated description
Hahn series are formal power series with exponents in an ordered abelian group and well-ordered supports, providing a general framework for constructing large ordered fields that include structures like the surreal numbers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hahn series
Target entity description: Hahn series are formal power series with exponents in an ordered abelian group and well-ordered supports, providing a general framework for constructing large ordered fields that include structures like the surreal numbers.
  • A. 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.
  • B. Taylor series
    A Taylor series is an infinite sum of terms calculated from the derivatives of a function at a single point, used to represent and approximate functions as power series.
  • C. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • D. TrizecHahn
    TrizecHahn was a major North American real estate investment and development company known for large-scale commercial and mixed-use projects.
  • E. 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.
  • 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_69a498dc92f8819094a1108f8ac90f43 completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c35e023c8190b45688796d90534b completed March 1, 2026, 10:53 p.m.
NED1 Entity disambiguation (via context triple) batch_69acde24d1d88190bd6d602923270cd1 completed March 8, 2026, 2:25 a.m.
NEDg Description generation batch_69acded052a88190945cf7a2af019c68 completed March 8, 2026, 2:28 a.m.
NED2 Entity disambiguation (via description) batch_69acdf41eb5c819088f2203f33995ccb completed March 8, 2026, 2:30 a.m.
Created at: March 1, 2026, 7:59 p.m.