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.