Triple
T10732863
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Serre’s conjecture on Galois representations |
E253116
|
entity |
| Predicate | involves |
P1256
|
FINISHED |
| Object |
Serre level
Serre level is an invariant attached to a mod p Galois representation that measures its conductor and ramification behavior, playing a central role in the precise formulation of Serre’s conjecture on modularity.
|
E253116
|
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: Serre level | Statement: [Serre’s conjecture on Galois representations, involves, Serre level]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Serre level Context triple: [Serre’s conjecture on Galois representations, involves, Serre level]
-
A.
Serre
The Serre is a river in northern France that flows through the Aisne and Oise departments before joining the Oise River.
-
B.
Serre’s conjecture on Galois representations
Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
-
C.
Serrean
A Serrean is a resident or native of Serres, a city in northern Greece.
-
D.
Serre spectral sequence
The Serre spectral sequence is a fundamental tool in algebraic topology that relates the homology or cohomology of a fibration to that of its base and fiber, enabling complex computations in a systematic way.
-
E.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
- 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: Serre level Triple: [Serre’s conjecture on Galois representations, involves, Serre level]
Generated description
Serre level is an invariant attached to a mod p Galois representation that measures its conductor and ramification behavior, playing a central role in the precise formulation of Serre’s conjecture on modularity.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Serre level Target entity description: Serre level is an invariant attached to a mod p Galois representation that measures its conductor and ramification behavior, playing a central role in the precise formulation of Serre’s conjecture on modularity.
-
A.
Serre
The Serre is a river in northern France that flows through the Aisne and Oise departments before joining the Oise River.
-
B.
Serre’s conjecture on Galois representations
chosen
Serre’s conjecture on Galois representations is a landmark statement in number theory that predicts which two-dimensional mod p Galois representations of the absolute Galois group of the rationals arise from modular forms.
-
C.
Serrean
A Serrean is a resident or native of Serres, a city in northern Greece.
-
D.
Serre spectral sequence
The Serre spectral sequence is a fundamental tool in algebraic topology that relates the homology or cohomology of a fibration to that of its base and fiber, enabling complex computations in a systematic way.
-
E.
Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
- F. None of above.
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_69d6aa5d8be481909a43218b2bfdbe95 |
completed | April 8, 2026, 7:19 p.m. |
| NER | Named-entity recognition | batch_69d7101ff9808190a27fcc06da097ea3 |
completed | April 9, 2026, 2:34 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69de22bb62e481909544c87801012df3 |
completed | April 14, 2026, 11:19 a.m. |
| NEDg | Description generation | batch_69de271ca4f081908d78a20b25ebd25c |
completed | April 14, 2026, 11:38 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69de2ccee0cc8190acd24d5c225f7cde |
completed | April 14, 2026, 12:02 p.m. |
Created at: April 8, 2026, 9:14 p.m.