Triple

T11971700
Position Surface form Disambiguated ID Type / Status
Subject Ilya Piatetski-Shapiro E284934 entity
Predicate notableWork P4 FINISHED
Object Euler Products E304347 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: Euler Products | Statement: [Ilya Piatetski-Shapiro, notableWork, Euler Products]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Euler Products
Context triple: [Ilya Piatetski-Shapiro, notableWork, Euler Products]
  • A. Euler product formula for the Riemann zeta function
    The Euler product formula for the Riemann zeta function is a fundamental identity in analytic number theory that expresses the zeta function as an infinite product over all prime numbers, revealing a deep connection between primes and the distribution of integers.
  • B. Euler products for automorphic L-functions chosen
    Euler products for automorphic L-functions are infinite product expansions attached to automorphic representations that encode deep arithmetic information and generalize the classical Euler product of the Riemann zeta function to a broad class of L-functions in the Langlands program.
  • C. Euler’s theorem
    Euler’s theorem is a fundamental result in number theory stating that for any integer a coprime to n, a raised to the power of φ(n) is congruent to 1 modulo n.
  • D. Euler’s identity for sine product
    Euler’s identity for sine product is a classical formula expressing the sine function as an infinite product, foundational in the theory of infinite products and special functions.
  • E. Euler’s reflection formula
    Euler’s reflection formula is a fundamental identity in complex analysis that relates the values of the Gamma function at z and 1−z through the sine function, revealing a deep symmetry of the Gamma function.
  • 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_69d6ab2eaeb881909f7914758f859413 completed April 8, 2026, 7:23 p.m.
NER Named-entity recognition batch_69d9037d32e88190b1509285dc907d29 completed April 10, 2026, 2:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69f4597cf818819089b0d897c236b87b completed May 1, 2026, 7:42 a.m.
Created at: April 8, 2026, 9:46 p.m.