Triple
T12596992
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jordan’s totient functions |
E300758
|
entity |
| Predicate | DirichletSeries |
P70734
|
FINISHED |
| Object | ∑_{n≥1} J_k(n) n^{-s} = ζ(s-k)/ζ(s) |
—
|
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: ∑_{n≥1} J_k(n) n^{-s} = ζ(s-k)/ζ(s) | Statement: [Jordan’s totient functions, DirichletSeries, ∑_{n≥1} J_k(n) n^{-s} = ζ(s-k)/ζ(s)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: DirichletSeries
Context triple: [Jordan’s totient functions, DirichletSeries, ∑_{n≥1} J_k(n) n^{-s} = ζ(s-k)/ζ(s)]
-
A.
domainOfZetaFunction
Indicates the set of complex numbers for which the zeta function is defined (i.e., where it is analytic or meaningfully evaluable).
-
B.
DirichletConvolution
Indicates that two arithmetic functions are combined into a new function by summing the products of their values over all pairs of positive integers whose product equals a given integer.
-
C.
OEIS
Indicates that there is a relationship to the On-Line Encyclopedia of Integer Sequences, typically referencing or identifying a specific integer sequence entry.
-
D.
VoroninUniversality
Indicates that a function or object exhibits Voronin universality, meaning its values approximate those of a wide class of analytic functions arbitrarily well on certain domains.
-
E.
zetaRelation
chosen
Indicates a specialized, context-dependent association between entities whose exact nature is defined by the specific system or theory using the term "zetaRelation".
- 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.