Triple

T2815391
Position Surface form Disambiguated ID Type / Status
Subject Euler’s totient function φ(n) E54269 entity
Predicate asymptoticBehavior P6112 FINISHED
Object φ(n) is typically of size ≈ n · 6/π² 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(n) is typically of size ≈ n · 6/π² | Statement: [Euler’s totient function φ(n), asymptoticBehavior, φ(n) is typically of size ≈ n · 6/π²]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: asymptoticBehavior
Context triple: [Euler’s totient function φ(n), asymptoticBehavior, φ(n) is typically of size ≈ n · 6/π²]
  • A. divergesAt
    Indicates that a process, function, or behavior fails to converge or terminate at a specific point or under specific conditions.
  • B. finiteAt
    Indicates that a function, quantity, or value remains finite (not infinite or undefined) at a specified point or under a given condition.
  • C. asymmetric
    Indicates that the relationship between two entities never holds in both directions simultaneously, so if it holds from A to B it cannot also hold from B to A.
  • D. canBeAnalyticallyContinuedTo
    Indicates that one mathematical object (typically a function) can be extended beyond its original domain in a consistent, analytic way that preserves its defining properties.
  • E. limitBehavior chosen
    Indicates how an entity behaves or changes as it approaches a specified limit or boundary condition.
  • 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.