Triple
T12597315
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Stirling's approximation |
E300765
|
entity |
| Predicate | hasRefinement |
P4448
|
FINISHED |
| Object | Stirling series |
E54271
|
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: Stirling series | Statement: [Stirling's approximation, hasRefinement, Stirling series]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Stirling series Context triple: [Stirling's approximation, hasRefinement, Stirling series]
-
A.
Stirling's approximation
Stirling's approximation is a classical formula in mathematics that provides an efficient asymptotic estimate for factorials and the gamma function, especially for large arguments.
-
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.
Lambert series
Lambert series are special infinite series in number theory and analysis, often involving arithmetic functions and powers of a variable, introduced by Johann Heinrich Lambert and used in the study of modular forms and q-series.
-
D.
Euler–Maclaurin summation formula
chosen
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
E.
Pochhammer symbol
The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
- 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_69d7bdea2ca881908f379526c13b1145 |
completed | April 9, 2026, 2:55 p.m. |
| NER | Named-entity recognition | batch_69d954cf33b88190bff339fcd3142cc8 |
completed | April 10, 2026, 7:51 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f65ec75fc08190aa13cbb0161eb35c |
completed | May 2, 2026, 8:29 p.m. |
Created at: April 9, 2026, 5:08 p.m.