Triple

T18266174
Position Surface form Disambiguated ID Type / Status
Subject Leonard Carlitz E437489 entity
Predicate notableFor P22 FINISHED
Object Carlitz q-Bernoulli numbers
The Carlitz q-Bernoulli numbers are a q-analogue of the classical Bernoulli numbers introduced by Leonard Carlitz, playing a key role in q-series, special functions, and number theory.
E1315964 NE FINISHED

How this triple was built (4 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: Carlitz q-Bernoulli numbers | Statement: [Leonard Carlitz, notableFor, Carlitz q-Bernoulli numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Carlitz q-Bernoulli numbers
Context triple: [Leonard Carlitz, notableFor, Carlitz q-Bernoulli numbers]
  • A. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • B. Bernoulli polynomials
    Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
  • C. Jacobi sums
    Jacobi sums are special algebraic number theory constructs formed from character sums over finite fields or residue classes, widely used in primality testing and the study of cyclotomic fields.
  • D. Ono’s partition congruences
    Ono’s partition congruences are modern number-theoretic results that extend Ramanujan’s classical congruences by proving the existence of infinitely many congruence relations for the partition function modulo various primes.
  • E. Rogers–Ramanujan-type identities
    Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Carlitz q-Bernoulli numbers
Triple: [Leonard Carlitz, notableFor, Carlitz q-Bernoulli numbers]
Generated description
The Carlitz q-Bernoulli numbers are a q-analogue of the classical Bernoulli numbers introduced by Leonard Carlitz, playing a key role in q-series, special functions, and number theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Carlitz q-Bernoulli numbers
Target entity description: The Carlitz q-Bernoulli numbers are a q-analogue of the classical Bernoulli numbers introduced by Leonard Carlitz, playing a key role in q-series, special functions, and number theory.
  • A. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • B. Bernoulli polynomials
    Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
  • C. Jacobi sums
    Jacobi sums are special algebraic number theory constructs formed from character sums over finite fields or residue classes, widely used in primality testing and the study of cyclotomic fields.
  • D. Ono’s partition congruences
    Ono’s partition congruences are modern number-theoretic results that extend Ramanujan’s classical congruences by proving the existence of infinitely many congruence relations for the partition function modulo various primes.
  • E. Rogers–Ramanujan-type identities
    Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
  • 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_69d8b913351c8190932b6a426de04b41 completed April 10, 2026, 8:47 a.m.
NER Named-entity recognition batch_69e4ff7af85c81909859e7247738a535 completed April 19, 2026, 4:14 p.m.
NED1 Entity disambiguation (via context triple) batch_6a03b3f6c1b081908fdd0ccb6f1bf633 completed May 12, 2026, 11:12 p.m.
NEDg Description generation batch_6a03b4f0cd188190a9577a3999a5b473 completed May 12, 2026, 11:17 p.m.
NED2 Entity disambiguation (via description) batch_6a03b5c09f4881909fb0ead5fc48895c completed May 12, 2026, 11:20 p.m.
Created at: April 10, 2026, 10:34 a.m.