Triple

T2815394
Position Surface form Disambiguated ID Type / Status
Subject Euler’s totient function φ(n) E54269 entity
Predicate minimumOnInterval P4229 FINISHED
Object For n ≥ 3, φ(n) attains its minimum at prime powers 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: For n ≥ 3, φ(n) attains its minimum at prime powers | Statement: [Euler’s totient function φ(n), minimumOnInterval, For n ≥ 3, φ(n) attains its minimum at prime powers]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: minimumOnInterval
Context triple: [Euler’s totient function φ(n), minimumOnInterval, For n ≥ 3, φ(n) attains its minimum at prime powers]
  • A. isMinimumWhen chosen
    Indicates that a value or state is at its smallest or least level precisely under certain specified conditions or circumstances.
  • B. minimumNumber
    Indicates that the associated value is the smallest or least quantity allowed, required, or observed within a given set or context.
  • C. lowerLimit
    Indicates that one value serves as the minimum or smallest allowable bound or threshold for another value or range.
  • D. minimumWidth
    Indicates that there is a specified smallest allowable or required width for something in the relationship.
  • E. lowestPoint
    Indicates that one entity is the point with the minimum vertical position or value relative to another entity or within a specified context.
  • 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_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.
Created at: March 6, 2026, 9:59 p.m.