Triple
T21783730
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Serge Lang |
E537781
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object | Algebraic Number Theory |
—
|
NE NERFINISHED |
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: Algebraic Number Theory | Statement: [Serge Lang, notableWork, Algebraic Number Theory]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Algebraic Number Theory Context triple: [Serge Lang, notableWork, Algebraic Number Theory]
-
A.
algebraic number theory
chosen
Algebraic number theory is a branch of mathematics that studies algebraic structures related to algebraic integers and number fields, focusing on properties of integers through tools from abstract algebra.
-
B.
Cassels–Fröhlich: Algebraic Number Theory
Cassels–Fröhlich: Algebraic Number Theory is a classic graduate-level textbook that provides a comprehensive and rigorous introduction to algebraic number theory and its foundational results.
-
C.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
-
D.
Neukirch: Algebraic Number Theory
"Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.
-
E.
Iwasawa theory
Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69e0c47198f881908cb0d237266c10e9 |
completed | April 16, 2026, 11:13 a.m. |
| NER | Named-entity recognition | batch_69f046303d54819096b3fab4ab5678e6 |
completed | April 28, 2026, 5:31 a.m. |
Created at: April 16, 2026, 6:52 p.m.