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.