Triple
T19050898
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Dirichlet convolution |
E466252
|
entity |
| Predicate | inverseExistenceCondition |
P67472
|
FINISHED |
| Object | every arithmetic function with f(1) ≠ 0 has a Dirichlet inverse |
—
|
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: every arithmetic function with f(1) ≠ 0 has a Dirichlet inverse | Statement: [Dirichlet convolution, inverseExistenceCondition, every arithmetic function with f(1) ≠ 0 has a Dirichlet inverse]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: inverseExistenceCondition Context triple: [Dirichlet convolution, inverseExistenceCondition, every arithmetic function with f(1) ≠ 0 has a Dirichlet inverse]
-
A.
existsIf
chosen
Indicates that the existence or validity of one entity or condition depends on the presence or truth of another specified condition.
-
B.
isInverseOf
Indicates that one relation reverses the direction of another, so that if the original relates A to B, its inverse relates B to A.
-
C.
hasExistentiale
Indicates that an entity possesses or is associated with an existential characteristic, condition, or mode of being.
-
D.
concludesExistenceOf
Indicates that one entity determines or infers that another entity exists.
-
E.
proposesExistenceOf
Indicates that one entity puts forward or suggests that another entity should exist or be brought into existence.
- 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_69d8dd040fb881909af2a964f65ad208 |
completed | April 10, 2026, 11:20 a.m. |
| NER | Named-entity recognition | batch_69e5dc02597c8190b39fd2c7b7e42258 |
completed | April 20, 2026, 7:55 a.m. |
| PD | Predicate disambiguation | batch_69e4b99633c8819097988608c278ecf8 |
completed | April 19, 2026, 11:16 a.m. |
Created at: April 10, 2026, 12:03 p.m.