Triple
T2815386
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler’s totient function φ(n) |
E54269
|
entity |
| Predicate | DirichletConvolution |
P43789
|
FINISHED |
| Object | φ * 1 = id where id(n) = 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: φ * 1 = id where id(n) = n | Statement: [Euler’s totient function φ(n), DirichletConvolution, φ * 1 = id where id(n) = n]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: DirichletConvolution Context triple: [Euler’s totient function φ(n), DirichletConvolution, φ * 1 = id where id(n) = 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.
primeFactorization
Indicates that one entity is the decomposition of another entity into a multiset or sequence of prime factors whose product equals the original.
-
C.
isQuotientOf
Indicates that one quantity is the result of dividing another quantity by a specified divisor.
-
D.
bitLengthFactorization
Indicates a relationship where the bit-length of a number is determined or constrained by the factorization of that number.
-
E.
domainOfZetaFunction
Indicates the set of complex numbers for which the zeta function is defined (i.e., where it is analytic or meaningfully evaluable).
- 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_69ab49de0af08190b3da69683be1e728 |
completed | March 6, 2026, 9:40 p.m. |
| NER | Named-entity recognition | batch_69abde4d29488190a32461906dd9ea7e |
completed | March 7, 2026, 8:14 a.m. |
| PD | Predicate disambiguation | batch_69abdd0740208190911dc9c9546a79ae |
completed | March 7, 2026, 8:08 a.m. |
| PDg | Predicate description generation | batch_69abde0f4c648190b9812e64f30c39da |
completed | March 7, 2026, 8:13 a.m. |
Created at: March 6, 2026, 9:59 p.m.