Triple
T12596995
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jordan’s totient functions |
E300758
|
entity |
| Predicate | multiplicativeDefinition |
P71174
|
FINISHED |
| Object | J_k(mn) = J_k(m)J_k(n) if gcd(m,n)=1 |
—
|
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(mn) = J_k(m)J_k(n) if gcd(m,n)=1 | Statement: [Jordan’s totient functions, multiplicativeDefinition, J_k(mn) = J_k(m)J_k(n) if gcd(m,n)=1]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: multiplicativeDefinition Context triple: [Jordan’s totient functions, multiplicativeDefinition, J_k(mn) = J_k(m)J_k(n) if gcd(m,n)=1]
-
A.
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.
-
B.
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.
-
C.
isProductOf
Indicates that one entity is the result or outcome produced by another entity or process.
-
D.
multiplicativeInverse
Indicates that one quantity is the multiplicative inverse of another, meaning their product equals the multiplicative identity (typically 1).
-
E.
isAdditiveFor
Indicates that one entity can be combined with another in a way that their effects or quantities sum together to produce a cumulative result.
- 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.