Triple
T7871551
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Carl Gustav Jacob Jacobi |
E182747
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object | Jacobi symbol |
E182750
|
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: Jacobi symbol | Statement: [Carl Gustav Jacob Jacobi, knownFor, Jacobi symbol]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Jacobi symbol Context triple: [Carl Gustav Jacob Jacobi, knownFor, Jacobi symbol]
-
A.
Jacobi symbol
chosen
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.
-
B.
Legendre symbol
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.
-
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.
Jacobi
Jacobi is a German surname most famously associated with the 19th-century mathematician Carl Gustav Jacob Jacobi, known for his foundational work in elliptic functions and number theory.
-
E.
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.
- 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_69ca82894d9081908a832bfce71a4714 |
completed | March 30, 2026, 2:02 p.m. |
| NER | Named-entity recognition | batch_69cb39a5950481908399211c5dfe2569 |
completed | March 31, 2026, 3:04 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69cb5b6bc7248190adbf4377c52e16a9 |
completed | March 31, 2026, 5:28 a.m. |
Created at: March 30, 2026, 4:56 p.m.