Triple

T4597255
Position Surface form Disambiguated ID Type / Status
Subject Kronecker’s lemma E100233 entity
Predicate relatedTo P37 FINISHED
Object Abel’s theorem E451517 NE FINISHED

How this triple was built (2 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: [Kronecker’s lemma, relatedTo, Abel’s theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Abel’s theorem
Context triple: [Kronecker’s lemma, 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. 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.
  • D. 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.
  • E. Tauberian theorems chosen
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69bd43cbc014819098b45f435908f88a completed March 20, 2026, 12:55 p.m.
NER Named-entity recognition batch_69bd59420c108190b5c2c5039e964da5 completed March 20, 2026, 2:27 p.m.
NED1 Entity disambiguation (via context triple) batch_69bdfa4a99c88190b7332fd2e1799b3a completed March 21, 2026, 1:54 a.m.
Created at: March 20, 2026, 1:11 p.m.