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.