Triple

T2815406
Position Surface form Disambiguated ID Type / Status
Subject Euler’s totient function φ(n) E54269 entity
Predicate OEIS P43794 FINISHED
Object OEIS sequence A000010 E54269 NE FINISHED

How this triple was built (3 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: OEIS sequence A000010 | Statement: [Euler’s totient function φ(n), OEIS, OEIS sequence A000010]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: OEIS sequence A000010
Context triple: [Euler’s totient function φ(n), OEIS, OEIS sequence A000010]
  • A. Euler’s totient function φ(n) chosen
    Euler’s totient function φ(n) is a fundamental arithmetic function in number theory that counts the positive integers up to n that are relatively prime to n and plays a key role in topics such as modular arithmetic and cryptography.
  • B. OEIS A064988
    OEIS A064988 is the entry in the On-Line Encyclopedia of Integer Sequences that records the decimal expansion of Gauss’s constant, a notable mathematical constant arising in elliptic integrals and number theory.
  • C. Look-and-say sequence
    The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
  • D. Ulam sequence
    The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
  • E. Fibonacci sequence
    The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: OEIS
Context triple: [Euler’s totient function φ(n), OEIS, OEIS sequence A000010]
  • A. associatedConjecture
    Indicates that one entity is linked or connected to a particular conjecture, typically as its subject, source, or relevant context.
  • B. relatedConjecture
    Indicates that one conjecture is connected or associated with another conjecture, such as by similarity, dependency, or thematic relation.
  • C. EuclideanFunction
    Indicates a relationship defined by a Euclidean distance–based function, typically mapping entities or their attributes to values derived from Euclidean metric properties.
  • D. number
    Indicates that one entity is associated with a specific numerical value or count in relation to another entity or context.
  • E. notableNumber
    Indicates that a number associated with an entity is distinguished or significant in some notable way (e.g., record-setting, symbolic, or otherwise remarkable).
  • F. None of above. chosen

Provenance (5 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.
NED1 Entity disambiguation (via context triple) batch_69afce9f964081909e422aaf1f026dbb completed March 10, 2026, 7:56 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.