Triple
T15502491
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Khinchin's constant |
E378994
|
entity |
| Predicate | hasInfiniteProductRepresentation |
P71179
|
FINISHED |
| Object | K_0 = ∏_{m=1}^{∞} (1 + 1/(m(m+2)))^{ rac{1}{ ext{log}_2(m+1) - ext{log}_2 m}} (up to equivalent standard forms) |
—
|
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: K_0 = ∏_{m=1}^{∞} (1 + 1/(m(m+2)))^{ rac{1}{ ext{log}_2(m+1) - ext{log}_2 m}} (up to equivalent standard forms) | Statement: [Khinchin's constant, hasInfiniteProductRepresentation, K_0 = ∏_{m=1}^{∞} (1 + 1/(m(m+2)))^{ rac{1}{ ext{log}_2(m+1) - ext{log}_2 m}} (up to equivalent standard forms)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasInfiniteProductRepresentation
Context triple: [Khinchin's constant, hasInfiniteProductRepresentation, K_0 = ∏_{m=1}^{∞} (1 + 1/(m(m+2)))^{ rac{1}{ ext{log}_2(m+1) - ext{log}_2 m}} (up to equivalent standard forms)]
-
A.
isProductOf
Indicates that one entity is the result or outcome produced by another entity or process.
-
B.
hasWeierstrassProduct
chosen
Indicates that one mathematical object is represented or characterized by a Weierstrass product expansion in terms of another.
-
C.
hasInfiniteSumSide
Indicates that one side of a relationship or equation involves an infinite sum or series rather than a finite quantity.
-
D.
hasIntegralRepresentation
Indicates that one entity can be expressed or represented as an integral involving the other entity.
-
E.
continuedFraction
Indicates that one quantity is represented as, or related to another through, a continued fraction expansion (an expression built from a sequence of nested fractions).
- 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_69d85cd53a7c819080f5b9042c4c199e |
completed | April 10, 2026, 2:13 a.m. |
| NER | Named-entity recognition | batch_69e03fcc5bb88190b8a9a81419a9a38b |
completed | April 16, 2026, 1:47 a.m. |
| PD | Predicate disambiguation | batch_69ded2896a9c8190a8b9627deb3c17b4 |
completed | April 14, 2026, 11:49 p.m. |
Created at: April 10, 2026, 3:54 a.m.