Triple

T7420157
Position Surface form Disambiguated ID Type / Status
Subject Legendre symbol E171225 entity
Predicate quadraticReciprocity P76850 FINISHED
Object (p/q)(q/p)=(-1)^{(p-1)(q-1)/4} for odd primes p,q LITERAL 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: (p/q)(q/p)=(-1)^{(p-1)(q-1)/4} for odd primes p,q | Statement: [Legendre symbol, quadraticReciprocity, (p/q)(q/p)=(-1)^{(p-1)(q-1)/4} for odd primes p,q]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: quadraticReciprocity
Context triple: [Legendre symbol, quadraticReciprocity, (p/q)(q/p)=(-1)^{(p-1)(q-1)/4} for odd primes p,q]
  • A. secondCongruenceModulus
    Indicates that the second argument specifies the modulus with respect to which two values are congruent in a modular arithmetic relationship.
  • B. secondCongruence
    Indicates that one entity is congruent to another with respect to a second, distinct congruence relation or modular equivalence condition.
  • C. discriminantOverℚ
    Indicates that the discriminant of the given algebraic object is taken with respect to the field of rational numbers ℚ.
  • D. firstCongruenceModulus
    Indicates that the specified value is the modulus used in the first congruence of a system of modular equations or congruence relations.
  • E. primeInGaussianIntegersCondition
    Indicates that a number remains prime when considered within the ring of Gaussian integers, typically meaning it cannot be factored nontrivially in that domain.
  • F. None of above. chosen

Provenance (4 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_69c68a625d048190af70eb8b63bec5a0 completed March 27, 2026, 1:47 p.m.
NER Named-entity recognition batch_69c6f2ea61248190886e8e55b42ba5f1 completed March 27, 2026, 9:13 p.m.
PD Predicate disambiguation batch_69c6f0345040819094c5756dfa487faf completed March 27, 2026, 9:01 p.m.
PDg Predicate description generation batch_69c6f1c3307481909a7f6bb69d4fddac completed March 27, 2026, 9:08 p.m.
Created at: March 27, 2026, 3:11 p.m.