Triple
T12597005
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jordan’s totient functions |
E300758
|
entity |
| Predicate | sumOverDivisorsIdentity |
P43790
|
FINISHED |
| Object | ∑_{d|n} J_k(d) = n^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: ∑_{d|n} J_k(d) = n^k | Statement: [Jordan’s totient functions, sumOverDivisorsIdentity, ∑_{d|n} J_k(d) = n^k]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: sumOverDivisorsIdentity
Context triple: [Jordan’s totient functions, sumOverDivisorsIdentity, ∑_{d|n} J_k(d) = n^k]
-
A.
isSumOf
Indicates that one quantity is the result of adding together two or more other quantities.
-
B.
DirichletConvolution
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.
-
C.
hasMinimalSumOfReciprocals
Indicates that the related entities are arranged or selected such that the sum of the reciprocals of certain associated values is as small as possible compared to alternatives.
-
D.
summatoryIdentity
chosen
Indicates that two expressions are identically equal when summed over a specified range, typically expressing an equality between a summation and an equivalent closed-form or alternative summation.
-
E.
usesDivisor
Indicates that one entity employs another entity as a divisor in a division or modular arithmetic operation.
- 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.