Triple
T9297056
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Chebotarev density theorem |
E223663
|
entity |
| Predicate | isToolFor |
P1129
|
FINISHED |
| Object | Langlands program |
E753154
|
NE 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: Langlands program | Statement: [Chebotarev density theorem, isToolFor, Langlands program]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Langlands program Context triple: [Chebotarev density theorem, isToolFor, Langlands program]
-
A.
Langlands program
chosen
The Langlands program is a far-reaching web of conjectures and theories in number theory and representation theory that seeks deep connections between Galois groups and automorphic forms, unifying many areas of modern mathematics.
-
B.
Galois representations
Galois representations are homomorphisms from Galois groups of field extensions into matrix groups that encode deep arithmetic information and link number theory with algebraic geometry and modular forms.
-
C.
Representation Theory and Automorphic Functions
"Representation Theory and Automorphic Functions" is a seminal mathematical work by Israel Gelfand that develops the connections between representation theory of groups and the theory of automorphic forms, with deep applications in number theory and harmonic analysis.
-
D.
Weil conjectures
The Weil conjectures are a set of deep statements about the zeta functions of algebraic varieties over finite fields that guided the development of modern algebraic geometry and were ultimately proved using étale cohomology.
-
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 (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_69ca8423edb08190bc0c91287a484768 |
completed | March 30, 2026, 2:09 p.m. |
| NER | Named-entity recognition | batch_69cd089c9c588190967404c9eb938dfb |
completed | April 1, 2026, 11:59 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d0b251c4148190a94fafdc23a601d6 |
completed | April 4, 2026, 6:40 a.m. |
Created at: March 30, 2026, 7:36 p.m.