Triple
T12597009
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jordan’s totient functions |
E300758
|
entity |
| Predicate | coprimalityCondition |
P64870
|
FINISHED |
| Object | J_k(n) counts k-tuples whose gcd with n is 1 in a suitable sense |
—
|
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_k(n) counts k-tuples whose gcd with n is 1 in a suitable sense | Statement: [Jordan’s totient functions, coprimalityCondition, J_k(n) counts k-tuples whose gcd with n is 1 in a suitable sense]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: coprimalityCondition Context triple: [Jordan’s totient functions, coprimalityCondition, J_k(n) counts k-tuples whose gcd with n is 1 in a suitable sense]
-
A.
coprimeProperty
chosen
Indicates that two numbers share no common positive integer divisors greater than 1, i.e., their greatest common divisor is 1.
-
B.
primeCondition
Indicates that a condition or requirement is primary, fundamental, or of highest priority within a given context.
-
C.
firstCongruenceModulus
Indicates that the specified value is the modulus used in the first congruence of a system of modular equations or congruence relations.
-
D.
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.
-
E.
firstCongruence
Indicates that one entity is the initial or primary instance in a set of congruent (equivalent in form or measure) entities or relationships.
- F. None of above.
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_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. |
Created at: April 9, 2026, 5:08 p.m.