Triple

T9843389
Position Surface form Disambiguated ID Type / Status
Subject Hardy Z-function E239280 entity
Predicate relatedTo P37 FINISHED
Object Riemann–Siegel theta function E239279 NE 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: Riemann–Siegel theta function | Statement: [Hardy Z-function, relatedTo, Riemann–Siegel theta function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riemann–Siegel theta function
Context triple: [Hardy Z-function, relatedTo, Riemann–Siegel theta function]
  • A. Riemann–Siegel theta function chosen
    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.
  • B. 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.
  • C. Riemann zeta function
    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.
  • D. Jacobi theta functions
    Jacobi theta functions are special functions in complex analysis and number theory that encode modular and elliptic properties, playing a central role in the theory of elliptic functions, modular forms, and various applications in mathematical physics.
  • 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.

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_69ca84e3f0c48190ada72a65ebd50efd completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb35c8e348190aa090c71bf6f30eb completed April 2, 2026, 12:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1d5dda4b0819092703270e87bee5a completed April 5, 2026, 3:24 a.m.
Created at: March 30, 2026, 8:33 p.m.