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.