Triple
T1489710
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Gauss’s lemma (number theory) |
E29548
|
entity |
| Predicate | relates |
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: [Gauss’s lemma (number theory), relates, Legendre symbol]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Legendre symbol Context triple: [Gauss’s lemma (number theory), relates, 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.
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.
-
C.
Gauss’s lemma in number theory
Gauss’s lemma in number theory is a result that relates the Legendre symbol to the number of sign changes in a certain sequence of multiples, providing a practical criterion for determining quadratic residues modulo an odd prime.
-
D.
Pochhammer symbol
The Pochhammer symbol is a mathematical notation representing rising factorials, widely used in series expansions, special functions, and hypergeometric functions.
-
E.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
- 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_69a498da82e08190ba833330d05f380f |
completed | March 1, 2026, 7:51 p.m. |
| NER | Named-entity recognition | batch_69a4c6c233ec819087e1233af02aabfc |
completed | March 1, 2026, 11:07 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ad232f4b80819095a608816d4d2a34 |
completed | March 8, 2026, 7:20 a.m. |
Created at: March 1, 2026, 8:12 p.m.