Triple
T12597003
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jordan’s totient functions |
E300758
|
entity |
| Predicate | convolutionExplanation |
P43789
|
FINISHED |
| Object | J_k(n) = ∑_{d|n} μ(d)(n/d)^k |
—
|
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: J_k(n) = ∑_{d|n} μ(d)(n/d)^k | Statement: [Jordan’s totient functions, convolutionExplanation, J_k(n) = ∑_{d|n} μ(d)(n/d)^k]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: convolutionExplanation
Context triple: [Jordan’s totient functions, convolutionExplanation, J_k(n) = ∑_{d|n} μ(d)(n/d)^k]
-
A.
convolutionIdentity
Indicates that one element acts as the identity under convolution, leaving the other element unchanged when convolved with it.
-
B.
hasConvolutionProperty
Indicates that one entity possesses a convolution-related characteristic or behavior in relation to another entity or operation.
-
C.
inceptionApproximation
Indicates an approximate or estimated starting point or origin of something, rather than an exact inception time.
-
D.
DirichletConvolution
chosen
Indicates that two arithmetic functions are combined into a new function by summing the products of their values over all pairs of positive integers whose product equals a given integer.
-
E.
inverseFourierTransform
Indicates the mathematical operation that converts a frequency-domain representation of a signal or function back into its corresponding time- or spatial-domain form.
- 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_69d7bdea2ca881908f379526c13b1145 |
completed | April 9, 2026, 2:55 p.m. |
| NER | Named-entity recognition | batch_69d954e6e20481908bca684c4b497c48 |
completed | April 10, 2026, 7:52 p.m. |
| PD | Predicate disambiguation | batch_69d95416cbd88190b2c65196162349bc |
completed | April 10, 2026, 7:48 p.m. |
Created at: April 9, 2026, 5:08 p.m.