Triple
T14704229
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Émile Borel |
E345382
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object | Borel’s strong law of large numbers formulation |
E1041768
|
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: Borel’s strong law of large numbers formulation | Statement: [Émile Borel, notableWork, Borel’s strong law of large numbers formulation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Borel’s strong law of large numbers formulation Context triple: [Émile Borel, notableWork, Borel’s strong law of large numbers formulation]
-
A.
Borel–Cantelli lemmas
chosen
The Borel–Cantelli lemmas are fundamental results in probability theory that characterize when events occur infinitely often or only finitely often, based on the convergence or divergence of the sum of their probabilities.
-
B.
Erdős–Rényi law of large numbers
The Erdős–Rényi law of large numbers is a refinement of the classical law of large numbers that provides precise asymptotic behavior and convergence rates for sums of independent random variables, developed by mathematicians Pál Erdős and Alfréd Rényi.
-
C.
Khinchin's law of the iterated logarithm
Khinchin's law of the iterated logarithm is a fundamental result in probability theory that precisely characterizes the almost-sure fluctuations of partial sums of independent random variables on the scale of the square root of twice the product of their variance and the iterated logarithm of the sample size.
-
D.
Kolmogorov zero–one law
The Kolmogorov zero–one law is a fundamental result in probability theory stating that certain events determined by the tail behavior of independent random variables must have probability either zero or one.
-
E.
Limit Laws for Sums of Independent Random Variables
Limit Laws for Sums of Independent Random Variables is a foundational mathematical work that systematically develops the theory of probability limit theorems, including results such as the law of large numbers and central limit behavior for sums of independent random variables.
- 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_69d822e4a8c08190a155df736bb7bc13 |
completed | April 9, 2026, 10:06 p.m. |
| NER | Named-entity recognition | batch_69deb6071e5c8190bb5509c859135c2d |
completed | April 14, 2026, 9:47 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fdf087ce8c819081a7186df67bcf1f |
completed | May 8, 2026, 2:17 p.m. |
Created at: April 10, 2026, 1:28 a.m.