Triple
T21858391
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Artin’s conjecture on L-functions |
E539691
|
entity |
| Predicate | approach |
P1717
|
FINISHED |
| Object | Langlands functoriality |
—
|
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: Langlands functoriality | Statement: [Artin’s conjecture on L-functions, approach, Langlands functoriality]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Langlands functoriality Context triple: [Artin’s conjecture on L-functions, approach, Langlands functoriality]
-
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.
Automorphic Forms and Representations
Automorphic Forms and Representations is a foundational mathematical monograph that develops the theory of automorphic forms and their connections to representation theory and number theory.
-
C.
Langlands classification
The Langlands classification is a fundamental framework in representation theory that systematically describes all irreducible admissible representations of a real or p-adic reductive group in terms of data from its parabolic subgroups and their characters.
-
D.
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.
-
E.
Euler products for automorphic L-functions
Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
- 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_69e0c47829648190bbe2d1d7033768ec |
completed | April 16, 2026, 11:14 a.m. |
| NER | Named-entity recognition | batch_69f0d638721c8190918fc6ad9c5d5bf6 |
completed | April 28, 2026, 3:46 p.m. |
Created at: April 16, 2026, 6:56 p.m.