Triple
T1489717
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Gauss’s lemma (number theory) |
E29548
|
entity |
| Predicate | statement |
P4223
|
FINISHED |
| Object | Let p be an odd prime and a an integer coprime to p. Consider the numbers a,2a,3a,…,((p−1)/2)a reduced modulo p into the interval (−p/2,p/2]. Let n be the number of these residues that are negative. Then (a|p) = (−1)^n, where (a|p) is the Legendre symbol. |
—
|
LITERAL FINISHED |
How this triple was built (1 step)
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: Let p be an odd prime and a an integer coprime to p. Consider the numbers a,2a,3a,…,((p−1)/2)a reduced modulo p into the interval (−p/2,p/2]. Let n be the number of these residues that are negative. Then (a|p) = (−1)^n, where (a|p) is the Legendre symbol. | Statement: [Gauss’s lemma (number theory), statement, Let p be an odd prime and a an integer coprime to p. Consider the numbers a,2a,3a,…,((p−1)/2)a reduced modulo p into the interval (−p/2,p/2]. Let n be the number of these residues that are negative. Then (a|p) = (−1)^n, where (a|p) is the Legendre symbol.]
Provenance (2 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_69a498da82e08190ba833330d05f380f |
completed | March 1, 2026, 7:51 p.m. |
| NER | Named-entity recognition | batch_69a4c6c233ec819087e1233af02aabfc |
completed | March 1, 2026, 11:07 p.m. |
Created at: March 1, 2026, 8:12 p.m.