Triple
T32258618
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Riemann xi function |
E824087
|
entity |
| Predicate | hasHadamardProduct |
P176983
|
FINISHED |
| Object | ξ(s) = ξ(0) ∏_ρ (1 - s/ρ) where ρ runs over zeros |
—
|
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: ξ(s) = ξ(0) ∏_ρ (1 - s/ρ) where ρ runs over zeros | Statement: [Riemann xi function, hasHadamardProduct, ξ(s) = ξ(0) ∏_ρ (1 - s/ρ) where ρ runs over zeros]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasHadamardProduct Context triple: [Riemann xi function, hasHadamardProduct, ξ(s) = ξ(0) ∏_ρ (1 - s/ρ) where ρ runs over zeros]
-
A.
hasMultiplicationFormula
Indicates that there exists a specific multiplication-based formula or rule that defines or computes the value or behavior of the related entity.
-
B.
hasJordanForm
Indicates that one mathematical object (typically a matrix or linear operator) possesses a specific Jordan normal form associated with it.
-
C.
hasEulerProduct
Indicates that a mathematical function or object can be expressed as an infinite product over prime numbers (an Euler product), typically reflecting a multiplicative structure.
-
D.
isProductOf
Indicates that one entity is the result or outcome produced by another entity or process.
-
E.
isHermitian
Indicates that an operator or matrix is equal to its own conjugate transpose, ensuring real eigenvalues and orthogonal eigenvectors.
- 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_69f3490db0748190bfef6e50c95d39d3 |
completed | April 30, 2026, 12:20 p.m. |
| NER | Named-entity recognition | batch_69f6f85bfba48190aba95b40642a8ca7 |
completed | May 3, 2026, 7:25 a.m. |
| PD | Predicate disambiguation | batch_69f6f6619404819084662aef1238261c |
completed | May 3, 2026, 7:16 a.m. |
| PDg | Predicate description generation | batch_69f6f814fcf48190ae4504154d1b2c05 |
completed | May 3, 2026, 7:24 a.m. |
Created at: May 1, 2026, 12:41 a.m.