Triple

T7871678
Position Surface form Disambiguated ID Type / Status
Subject Jacobi symbol E182750 entity
Predicate relatedTo P37 FINISHED
Object Legendre symbol E171225 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: Legendre symbol | Statement: [Jacobi symbol, relatedTo, Legendre symbol]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Legendre symbol
Context triple: [Jacobi symbol, relatedTo, Legendre symbol]
  • A. Legendre symbol chosen
    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.
  • B. Jacobi symbol
    The Jacobi symbol is a number-theoretic function that generalizes the Legendre symbol and plays a key role in quadratic residues and primality testing in modular arithmetic.
  • C. Euler criterion
    Euler criterion is a number-theoretic result that characterizes quadratic residues modulo an odd prime using exponentiation, providing a practical way to evaluate the Legendre symbol.
  • D. quadratic reciprocity law
    The quadratic reciprocity law is a fundamental theorem in number theory that characterizes when a quadratic equation modulo one odd prime has solutions in terms of solvability modulo another, revealing a deep symmetry between primes.
  • E. Hilbert symbol
    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.
  • 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_69ca82894d9081908a832bfce71a4714 completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb39a5950481908399211c5dfe2569 completed March 31, 2026, 3:04 a.m.
NED1 Entity disambiguation (via context triple) batch_69cbdf844f24819091cb8757d29a4a3f completed March 31, 2026, 2:51 p.m.
Created at: March 30, 2026, 4:56 p.m.