Triple

T7978918
Position Surface form Disambiguated ID Type / Status
Subject Carl Gustav Jacob Jacobi E185515 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. Euler pentagonal number theorem
    The Euler pentagonal number theorem is a fundamental result in number theory and combinatorics that gives a remarkable infinite product expansion for the generating function of partition numbers, involving exponents given by generalized pentagonal numbers.
  • D. 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.
  • E. 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.
  • 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_69ca829851908190b4e03829353ee7c3 completed March 30, 2026, 2:03 p.m.
NER Named-entity recognition batch_69cb3bf84b1081908e60a556d984aad6 completed March 31, 2026, 3:14 a.m.
NED1 Entity disambiguation (via context triple) batch_69cc5677968881908835169157244962 completed March 31, 2026, 11:19 p.m.
Created at: March 30, 2026, 5:14 p.m.