Triple

T10991327
Position Surface form Disambiguated ID Type / Status
Subject Montgomery's pair correlation conjecture E259758 entity
Predicate hasMathematicalExpression P12675 FINISHED
Object pair correlation function R_2(x) = 1 - (sin(πx)/(πx))^2 for the scaled 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: pair correlation function R_2(x) = 1 - (sin(πx)/(πx))^2 for the scaled zeros | Statement: [Montgomery's pair correlation conjecture, hasMathematicalExpression, pair correlation function R_2(x) = 1 - (sin(πx)/(πx))^2 for the scaled zeros]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: hasMathematicalExpression
Context triple: [Montgomery's pair correlation conjecture, hasMathematicalExpression, pair correlation function R_2(x) = 1 - (sin(πx)/(πx))^2 for the scaled zeros]
  • A. mathematicallyExpressedBy chosen
    Indicates that something (such as a concept, quantity, or relationship) is represented or captured using a specific mathematical expression or formulation.
  • B. hasMathematicalProperty
    Indicates that one entity possesses or exhibits a specific mathematical property or characteristic.
  • C. mathematicallyUses
    Indicates that one entity employs or applies another entity within a mathematical context, such as in a formula, proof, computation, or theoretical framework.
  • D. hasExpression
    Indicates that an entity displays or possesses a particular facial or emotional expression.
  • E. mathematicallyFormulatedIn
    Indicates that something is expressed, defined, or represented using mathematical formulas, equations, or formal mathematical structures within a given context.
  • 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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
PD Predicate disambiguation batch_69d72e93ac648190b46c5d12bf3eb1e9 completed April 9, 2026, 4:44 a.m.
Created at: April 8, 2026, 9:24 p.m.