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.