Triple
T209669
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | binomial theorem |
E4686
|
entity |
| Predicate | forRealExponent |
P4746
|
FINISHED |
| Object | (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1 |
—
|
LITERAL 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: (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1 | Statement: [binomial theorem, forRealExponent, (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: forRealExponent
Context triple: [binomial theorem, forRealExponent, (1 + x)^α = Σ_{k=0}^∞ \binom{α}{k} x^k for |x| < 1]
-
A.
logarithmBaseDetermines
Indicates that the chosen base of a logarithm determines how a quantity is expressed or scaled in logarithmic terms.
-
B.
floatType
Indicates that an entity has a specific floating-point data type or is categorized as a floating-point numeric value.
-
C.
mathematicallyUses
chosen
Indicates that one entity employs or applies another entity within a mathematical context, such as in a formula, proof, computation, or theoretical framework.
-
D.
approximates
Indicates that one entity is close to, but not exactly equal to, the value, form, or behavior of another entity.
-
E.
approximationType
Indicates the specific method or scheme used to approximate a value, function, or relationship in a given context.
- F. None of above.
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_69a25737567c81908f9c505300239181 |
completed | Feb. 28, 2026, 2:47 a.m. |
| NER | Named-entity recognition | batch_69a25e8b9b908190b69a3f0594b95f7e |
completed | Feb. 28, 2026, 3:18 a.m. |
| PD | Predicate disambiguation | batch_69a25b4e3c2881908d83e8218aa9f2d9 |
completed | Feb. 28, 2026, 3:04 a.m. |
Created at: Feb. 28, 2026, 2:51 a.m.