Triple

T2815382
Position Surface form Disambiguated ID Type / Status
Subject Euler’s totient function φ(n) E54269 entity
Predicate primePowerFormula P43787 FINISHED
Object φ(p^k) = p^k − p^{k−1} for prime p and integer k ≥ 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: φ(p^k) = p^k − p^{k−1} for prime p and integer k ≥ 1 | Statement: [Euler’s totient function φ(n), primePowerFormula, φ(p^k) = p^k − p^{k−1} for prime p and integer k ≥ 1]
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: primePowerFormula
Context triple: [Euler’s totient function φ(n), primePowerFormula, φ(p^k) = p^k − p^{k−1} for prime p and integer k ≥ 1]
  • 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. expandsPowersOf
    Indicates that one entity increases, extends, or enhances the authority, capabilities, or influence held by another entity.
  • C. primeNumberTheoremRelation
    Indicates the asymptotic relationship between the distribution of prime numbers and the logarithmic growth of integers, as formalized by the prime number theorem.
  • D. powerBy
    Indicates that one entity operates, functions, or is made possible through the energy, resources, or enabling capabilities provided by another entity.
  • E. notableExponents
    Indicates that certain entities are especially prominent, influential, or exemplary practitioners or representatives of a given field, movement, or activity.
  • F. None of above. chosen

Provenance (4 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_69ab49de0af08190b3da69683be1e728 completed March 6, 2026, 9:40 p.m.
NER Named-entity recognition batch_69abde4d29488190a32461906dd9ea7e completed March 7, 2026, 8:14 a.m.
PD Predicate disambiguation batch_69abdd0740208190911dc9c9546a79ae completed March 7, 2026, 8:08 a.m.
PDg Predicate description generation batch_69abde0f4c648190b9812e64f30c39da completed March 7, 2026, 8:13 a.m.
Created at: March 6, 2026, 9:59 p.m.