Triple

T11085764
Position Surface form Disambiguated ID Type / Status
Subject Voronin universality theorem E262116 entity
Predicate mainObject P18495 FINISHED
Object Riemann zeta function E47609 NE FINISHED

How this triple was built (3 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: Riemann zeta function | Statement: [Voronin universality theorem, mainObject, Riemann zeta function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riemann zeta function
Context triple: [Voronin universality theorem, mainObject, Riemann zeta function]
  • A. Riemann zeta function chosen
    The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
  • B. Riemann xi function
    The Riemann xi function is an entire, symmetrized version of the Riemann zeta function that encodes its nontrivial zeros and plays a central role in the study of the Riemann Hypothesis and related analytic number theory.
  • C. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • D. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • E. Dirichlet eta function
    The Dirichlet eta function is an alternating Dirichlet series closely related to the Riemann zeta function and used in analytic number theory, particularly for studying series convergence and analytic continuation.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: mainObject
Context triple: [Voronin universality theorem, mainObject, Riemann zeta function]
  • A. mainBase
    Indicates that one entity serves as the primary or central base or headquarters for another entity.
  • B. mainFunctions chosen
    Indicates that the subject serves as the primary or central functional component or role for the object.
  • C. mainSingle
    Indicates that an entity is the primary or sole main instance among a set of related entities.
  • D. mainRite
    Indicates that one ritual, ceremony, or rite is the primary or central rite associated with a given context, entity, or event.
  • E. mainStartingPoint
    Indicates the primary location or position from which an event, process, or path begins.
  • F. None of above.

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_69d6aa9983c08190b0ef61603b69feac completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d799c2c7d4819087ac793153340178 completed April 9, 2026, 12:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69e3e7a6dfa8819096f822294eb64dd1 completed April 18, 2026, 8:20 p.m.
PD Predicate disambiguation batch_69d744185a5881909ba4cf151d1798ec completed April 9, 2026, 6:15 a.m.
Created at: April 8, 2026, 9:27 p.m.