Triple
T19050899
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Dirichlet convolution |
E466252
|
entity |
| Predicate | inverseRecurrence |
P105602
|
FINISHED |
| Object | f^{-1}(1)=1/f(1) and f^{-1}(n) = -(1/f(1)) ∑_{d|n, d<n} f(d) f^{-1}(n/d) |
—
|
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: f^{-1}(1)=1/f(1) and f^{-1}(n) = -(1/f(1)) ∑_{d|n, d<n} f(d) f^{-1}(n/d) | Statement: [Dirichlet convolution, inverseRecurrence, f^{-1}(1)=1/f(1) and f^{-1}(n) = -(1/f(1)) ∑_{d|n, d<n} f(d) f^{-1}(n/d)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: inverseRecurrence
Context triple: [Dirichlet convolution, inverseRecurrence, f^{-1}(1)=1/f(1) and f^{-1}(n) = -(1/f(1)) ∑_{d|n, d<n} f(d) f^{-1}(n/d)]
-
A.
inverseConvolution
chosen
Indicates the operation that reverses or undoes a prior convolution, recovering an original signal or function from its convolved form.
-
B.
recurrence
Indicates that an event, condition, or state happens again or repeatedly over time, often after a period of absence or resolution.
-
C.
inverseFourierTransform
Indicates the mathematical operation that converts a frequency-domain representation of a signal or function back into its corresponding time- or spatial-domain form.
-
D.
inverseImage
Indicates the mapping from a set of outputs back to all inputs that are related to those outputs under a given function or relation.
-
E.
multiplicativeInverse
Indicates that one quantity is the multiplicative inverse of another, meaning their product equals the multiplicative identity (typically 1).
- 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.