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.