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.