Triple

T10732936
Position Surface form Disambiguated ID Type / Status
Subject Cohomologie Galoisienne E253118 entity
Predicate topic P261 FINISHED
Object Hilbert symbol E697755 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: Hilbert symbol | Statement: [Cohomologie Galoisienne, topic, Hilbert symbol]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hilbert symbol
Context triple: [Cohomologie Galoisienne, topic, Hilbert symbol]
  • A. Hilbert symbol chosen
    The Hilbert symbol is a local arithmetic invariant in number theory that encodes whether a quadratic form represents zero over a given local field, playing a central role in local class field theory and reciprocity laws.
  • B. Hasse invariant
    The Hasse invariant is an arithmetic invariant in number theory and algebraic geometry that classifies structures such as quadratic forms or elliptic curves over local and global fields, playing a key role in local-global principles.
  • C. Hasse norm theorem
    The Hasse norm theorem is a fundamental result in algebraic number theory that characterizes when an element of a global field is a norm from a cyclic extension by relating this property to its behavior in all completions of the field.
  • D. Legendre symbol
    The Legendre symbol is a number-theoretic function that indicates whether an integer is a quadratic residue modulo an odd prime, taking values 1, −1, or 0 accordingly.
  • E. Hilbert class field
    The Hilbert class field of a number field is its maximal unramified abelian extension, central in class field theory as it corresponds to the field’s ideal class group.
  • 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_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.
Created at: April 8, 2026, 9:14 p.m.