Triple

T18479319
Position Surface form Disambiguated ID Type / Status
Subject Abel summation E451515 entity
Predicate relatedTo P37 FINISHED
Object Abel’s theorem
Abel’s theorem is a result in mathematical analysis that relates the behavior of power series at the boundary of their interval of convergence to the limit of their coefficients, providing conditions under which the sum of the series converges to a given value.
E1325981 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: Abel’s theorem | Statement: [Abel summation, relatedTo, Abel’s theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Abel’s theorem
Context triple: [Abel summation, relatedTo, Abel’s theorem]
  • A. Cauchy–Hadamard theorem
    The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
  • B. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • C. Limb’s Theorem
    Limb’s Theorem is a contemporary dance work by choreographer William Forsythe that exemplifies his deconstructive, concept-driven approach to ballet and movement.
  • D. Abel–Ruffini theorem
    The Abel–Ruffini theorem is a fundamental result in algebra proving that there is no general solution in radicals for polynomial equations of degree five or higher.
  • E. Weierstrass preparation theorem
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • 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: Abel’s theorem
Triple: [Abel summation, relatedTo, Abel’s theorem]
Generated description
Abel’s theorem is a result in mathematical analysis that relates the behavior of power series at the boundary of their interval of convergence to the limit of their coefficients, providing conditions under which the sum of the series converges to a given value.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Abel’s theorem
Target entity description: Abel’s theorem is a result in mathematical analysis that relates the behavior of power series at the boundary of their interval of convergence to the limit of their coefficients, providing conditions under which the sum of the series converges to a given value.
  • A. Cauchy–Hadamard theorem
    The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
  • B. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • C. Limb’s Theorem
    Limb’s Theorem is a contemporary dance work by choreographer William Forsythe that exemplifies his deconstructive, concept-driven approach to ballet and movement.
  • D. Abel–Ruffini theorem
    The Abel–Ruffini theorem is a fundamental result in algebra proving that there is no general solution in radicals for polynomial equations of degree five or higher.
  • E. Weierstrass preparation theorem
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53065e8388190bb216dae89f8cf75 completed April 19, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_6a043f2f64848190808075254008e6e1 completed May 13, 2026, 9:06 a.m.
NEDg Description generation batch_6a043fb7db388190bb50cfade4f025f9 completed May 13, 2026, 9:09 a.m.
NED2 Entity disambiguation (via description) batch_6a044063c6048190b65620af8ceed897 completed May 13, 2026, 9:12 a.m.
Created at: April 10, 2026, 11:35 a.m.