Triple
T12597001
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jordan’s totient functions |
E300758
|
entity |
| Predicate | multiplicativeFactor |
P71174
|
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, multiplicativeFactor, J_k(n)/n^k = ∏_{p|n}(1 - p^{-k})]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: multiplicativeFactor
Context triple: [Jordan’s totient functions, multiplicativeFactor, J_k(n)/n^k = ∏_{p|n}(1 - p^{-k})]
-
A.
isProportionalityFactorIn
Indicates that one quantity serves as the proportionality factor (constant of proportionality) in a specified proportional relationship or equation.
-
B.
hasMultiplicationFormula
chosen
Indicates that there exists a specific multiplication-based formula or rule that defines or computes the value or behavior of the related entity.
-
C.
transmissionFactor
Indicates how strongly or efficiently something is passed or transmitted from one entity to another.
-
D.
multiplicity
Indicates the number of instances of one entity that can or must be associated with a single instance of another entity within a relationship.
-
E.
contractMultiplier
Indicates the standardized number of underlying units (e.g., shares, commodities) that one contract represents in a derivatives or futures agreement.
- 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.