Triple
T12597010
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jordan’s totient functions |
E300758
|
entity |
| Predicate | relationToEulerPhi |
P105604
|
FINISHED |
| Object | J_1(n) = φ(n) |
—
|
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: J_1(n) = φ(n) | Statement: [Jordan’s totient functions, relationToEulerPhi, J_1(n) = φ(n)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: relationToEulerPhi Context triple: [Jordan’s totient functions, relationToEulerPhi, J_1(n) = φ(n)]
-
A.
EuclideanFunction
Indicates a relationship defined by a Euclidean distance–based function, typically mapping entities or their attributes to values derived from Euclidean metric properties.
-
B.
primeNumberTheoremRelation
Indicates the asymptotic relationship between the distribution of prime numbers and the logarithmic growth of integers, as formalized by the prime number theorem.
-
C.
multiplicativeInverse
Indicates that one quantity is the multiplicative inverse of another, meaning their product equals the multiplicative identity (typically 1).
-
D.
quadraticReciprocity
Indicates that a specified relationship between two integers reflects the law of quadratic reciprocity, describing how the solvability of one integer as a quadratic residue modulo the other is reciprocally related.
-
E.
EulerCriterion
Indicates that a number satisfies Euler’s criterion, meaning its power modulo a prime determines whether it is a quadratic residue or non-residue relative to that prime.
- 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_69d7bdea2ca881908f379526c13b1145 |
completed | April 9, 2026, 2:55 p.m. |
| NER | Named-entity recognition | batch_69d954e6e20481908bca684c4b497c48 |
completed | April 10, 2026, 7:52 p.m. |
| PD | Predicate disambiguation | batch_69d95416cbd88190b2c65196162349bc |
completed | April 10, 2026, 7:48 p.m. |
| PDg | Predicate description generation | batch_69d954e351f88190869220d46e0ce282 |
completed | April 10, 2026, 7:52 p.m. |
Created at: April 9, 2026, 5:08 p.m.