Triple

T1615227
Position Surface form Disambiguated ID Type / Status
Subject Carl Gustav Jacob Jacobi E34700 entity
Predicate notableWork P4 FINISHED
Object Jacobi’s triple product identity E182749 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: Jacobi’s triple product identity | Statement: [Carl Gustav Jacob Jacobi, notableWork, Jacobi’s triple product identity]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Jacobi’s triple product identity
Context triple: [Carl Gustav Jacob Jacobi, notableWork, Jacobi’s triple product identity]
  • A. Jacobi triple product chosen
    The Jacobi triple product is a fundamental identity in number theory and complex analysis that expresses an infinite product as an infinite sum, playing a key role in the theory of theta functions and q-series.
  • B. Jacobi’s four-square theorem
    Jacobi’s four-square theorem is a fundamental result in number theory that gives a precise formula for the number of ways an integer can be expressed as a sum of four squares.
  • C. Rogers–Ramanujan-type identities
    Rogers–Ramanujan-type identities are a class of deep q-series and partition identities generalizing the classical Rogers–Ramanujan identities, with rich connections to combinatorics, number theory, and modular forms.
  • D. Ramanujan partition congruences
    Ramanujan partition congruences are remarkable number-theoretic results discovered by Srinivasa Ramanujan that describe surprising modular patterns in the partition function, such as specific arithmetic progressions where the number of integer partitions of an integer is divisible by a given prime.
  • E. Hardy–Ramanujan asymptotic formula
    The Hardy–Ramanujan asymptotic formula is a landmark result in number theory that gives an approximate expression for the partition function p(n), describing how the number of integer partitions of n grows rapidly with n.
  • 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_69a885ffc5ec819091afa325d5f9611c completed March 4, 2026, 7:20 p.m.
NER Named-entity recognition batch_69a9099049e0819099763ecb09fb4f57 completed March 5, 2026, 4:41 a.m.
NED1 Entity disambiguation (via context triple) batch_69ad58c6d7e88190b9fc0e34a007a2f5 completed March 8, 2026, 11:08 a.m.
Created at: March 4, 2026, 7:28 p.m.