Triple
T10991129
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Dirichlet L-functions |
E259755
|
entity |
| Predicate | hasEulerProduct |
P96490
|
FINISHED |
| Object | L(s,χ)=∏_{p}(1−χ(p)p^{-s})^{-1} for Re(s)>1 |
—
|
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: L(s,χ)=∏_{p}(1−χ(p)p^{-s})^{-1} for Re(s)>1 | Statement: [Dirichlet L-functions, hasEulerProduct, L(s,χ)=∏_{p}(1−χ(p)p^{-s})^{-1} for Re(s)>1]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasEulerProduct
Context triple: [Dirichlet L-functions, hasEulerProduct, L(s,χ)=∏_{p}(1−χ(p)p^{-s})^{-1} for Re(s)>1]
-
A.
hasWeierstrassProduct
Indicates that one mathematical object is represented or characterized by a Weierstrass product expansion in terms of another.
-
B.
EulerCriterion
Indicates that a number satisfies Euler’s criterion, meaning its power modulo a prime determines whether it is a quadratic residue or non-residue relative to that prime.
-
C.
hasPrimeDecomposition
Indicates that an entity is associated with the factorization of a number into its constituent prime factors.
-
D.
hasMultiplicationFormula
Indicates that there exists a specific multiplication-based formula or rule that defines or computes the value or behavior of the related entity.
-
E.
EuclideanFunction
Indicates a relationship defined by a Euclidean distance–based function, typically mapping entities or their attributes to values derived from Euclidean metric properties.
- 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_69d6aa8a6a548190a750f944ccdc8064 |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d787b8d7088190b7d6b63c3bac4ad1 |
completed | April 9, 2026, 11:04 a.m. |
| PD | Predicate disambiguation | batch_69d72e9055908190b438f039574aaaaf |
completed | April 9, 2026, 4:44 a.m. |
| PDg | Predicate description generation | batch_69d732242fdc8190be77d1f730a42935 |
completed | April 9, 2026, 4:59 a.m. |
Created at: April 8, 2026, 9:24 p.m.