Triple

T6355610
Position Surface form Disambiguated ID Type / Status
Subject John Wallis E142981 entity
Predicate notableConcept P201 FINISHED
Object Wallis product
The Wallis product is an infinite product formula for π/2, discovered by John Wallis in the 17th century and notable as one of the earliest infinite product representations of π.
E587242 NE FINISHED

How this triple was built (4 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: Wallis product | Statement: [John Wallis, notableConcept, Wallis product]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Wallis product
Context triple: [John Wallis, notableConcept, Wallis product]
  • A. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • B. Sylvester sequence
    The Sylvester sequence is an integer sequence defined recursively where each term is one more than the product of all previous terms, yielding rapidly growing, pairwise coprime numbers closely related to Egyptian fraction representations.
  • C. Khinchin's constant
    Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
  • D. 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.
  • E. Jacobi triple product
    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.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Wallis product
Triple: [John Wallis, notableConcept, Wallis product]
Generated description
The Wallis product is an infinite product formula for π/2, discovered by John Wallis in the 17th century and notable as one of the earliest infinite product representations of π.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Wallis product
Target entity description: The Wallis product is an infinite product formula for π/2, discovered by John Wallis in the 17th century and notable as one of the earliest infinite product representations of π.
  • A. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • B. Sylvester sequence
    The Sylvester sequence is an integer sequence defined recursively where each term is one more than the product of all previous terms, yielding rapidly growing, pairwise coprime numbers closely related to Egyptian fraction representations.
  • C. Khinchin's constant
    Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
  • D. 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.
  • E. Jacobi triple product
    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.
  • F. None of above. chosen

Provenance (5 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_69c008d7a9c4819098d647ec47776917 completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c067e22c00819089bc68efb85bc2c8 completed March 22, 2026, 10:06 p.m.
NED1 Entity disambiguation (via context triple) batch_69c6045e03e88190a8607e5d73c812bc completed March 27, 2026, 4:15 a.m.
NEDg Description generation batch_69c6057466ec8190afe96107862bb40a completed March 27, 2026, 4:20 a.m.
NED2 Entity disambiguation (via description) batch_69c6060a113881909b424d0c47c2107e completed March 27, 2026, 4:22 a.m.
Created at: March 22, 2026, 4:31 p.m.