Triple

T2566431
Position Surface form Disambiguated ID Type / Status
Subject Johann Heinrich Lambert E57361 entity
Predicate knownFor P22 FINISHED
Object Lambert W function (later named in his honor)
The Lambert W function is a special multivalued function that solves equations where a variable appears both inside and outside an exponential, defined as the inverse of f(w) = w e^w and widely used in mathematics, physics, and engineering.
E279121 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: Lambert W function (later named in his honor) | Statement: [Johann Heinrich Lambert, knownFor, Lambert W function (later named in his honor)]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lambert W function (later named in his honor)
Context triple: [Johann Heinrich Lambert, knownFor, Lambert W function (later named in his honor)]
  • A. Ackermann function
    The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
  • B. Lindemann–Weierstrass theorem precursor
    The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.
  • C. Halley’s method for solving equations
    Halley’s method for solving equations is an iterative numerical algorithm, related to and faster-converging than Newton’s method, used to find approximate roots of equations.
  • D. Hardy Z-function
    The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
  • E. 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.
  • 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: Lambert W function (later named in his honor)
Triple: [Johann Heinrich Lambert, knownFor, Lambert W function (later named in his honor)]
Generated description
The Lambert W function is a special multivalued function that solves equations where a variable appears both inside and outside an exponential, defined as the inverse of f(w) = w e^w and widely used in mathematics, physics, and engineering.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lambert W function (later named in his honor)
Target entity description: The Lambert W function is a special multivalued function that solves equations where a variable appears both inside and outside an exponential, defined as the inverse of f(w) = w e^w and widely used in mathematics, physics, and engineering.
  • A. Ackermann function
    The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
  • B. Lindemann–Weierstrass theorem precursor
    The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.
  • C. Halley’s method for solving equations
    Halley’s method for solving equations is an iterative numerical algorithm, related to and faster-converging than Newton’s method, used to find approximate roots of equations.
  • D. Hardy Z-function
    The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
  • E. 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.
  • 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_69ab4a4ef9008190a0e6d4422b9418b7 completed March 6, 2026, 9:42 p.m.
NER Named-entity recognition batch_69abd35ef22c8190966612cc75f69eca completed March 7, 2026, 7:27 a.m.
NED1 Entity disambiguation (via context triple) batch_69af6565e05081909dc12aa3240de5f2 completed March 10, 2026, 12:27 a.m.
NEDg Description generation batch_69af667c6b008190b3960f29f5e07653 completed March 10, 2026, 12:31 a.m.
NED2 Entity disambiguation (via description) batch_69af6740cd2c8190a76309238340bd22 completed March 10, 2026, 12:35 a.m.
Created at: March 6, 2026, 9:48 p.m.