Triple
T12596997
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jordan’s totient functions |
E300758
|
entity |
| Predicate | primePowerFactorization |
P43787
|
FINISHED |
| Object | J_k(n) = n^k ∏_{p|n}(1 - p^{-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) = n^k ∏_{p|n}(1 - p^{-k}) | Statement: [Jordan’s totient functions, primePowerFactorization, J_k(n) = n^k ∏_{p|n}(1 - p^{-k})]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: primePowerFactorization
Context triple: [Jordan’s totient functions, primePowerFactorization, J_k(n) = n^k ∏_{p|n}(1 - p^{-k})]
-
A.
primeFactorization
Indicates that one entity is the decomposition of another entity into a multiset or sequence of prime factors whose product equals the original.
-
B.
primePowerFormula
chosen
Indicates that a value is computed using a formula specifically involving powers of prime numbers.
-
C.
hasPrimeDecomposition
Indicates that an entity is associated with the factorization of a number into its constituent prime factors.
-
D.
numberOfPrimeMovers
Indicates the quantity of entities that serve as primary initiators or driving forces in a given context.
-
E.
hasPrimeDivisors
Indicates that one entity (typically a number) has the other entity or entities as its prime divisors.
- 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.