Triple

T7861123
Position Surface form Disambiguated ID Type / Status
Subject Adrien-Marie Legendre E182500 entity
Predicate knownFor P22 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: [Adrien-Marie Legendre, knownFor, Legendre symbol]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Legendre symbol
Context triple: [Adrien-Marie Legendre, knownFor, 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. Gauss sum
    A Gauss sum is a finite exponential sum, often involving characters such as the Legendre symbol, that plays a central role in number theory and the study of quadratic and higher-order residues.
  • 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_69ca82887fd48190975896bf38c4596b completed March 30, 2026, 2:02 p.m.
NER Named-entity recognition batch_69cb36bcb5cc8190a8a384ce0f020b9f completed March 31, 2026, 2:51 a.m.
NED1 Entity disambiguation (via context triple) batch_69cb5b4138d081908a5ff16b79f0a0c8 completed March 31, 2026, 5:27 a.m.
Created at: March 30, 2026, 4:53 p.m.