Triple

T17872455
Position Surface form Disambiguated ID Type / Status
Subject Richard Laver E446867 entity
Predicate notableFor P22 FINISHED
Object Laver tables
Laver tables are finite algebraic structures arising in set theory and large cardinal research, known for their role in studying self-distributive operations and the foundations of mathematics.
E1294482 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: Laver tables | Statement: [Richard Laver, notableFor, Laver tables]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Laver tables
Context triple: [Richard Laver, notableFor, Laver tables]
  • A. Tarski’s theorem on amenable groups
    Tarski’s theorem on amenable groups is a fundamental result in group theory and measure theory that characterizes amenable groups as precisely those that do not admit Banach–Tarski-type paradoxical decompositions.
  • B. Lattice
    Lattice is a software company that provides people management and performance review tools to help organizations develop and engage their employees.
  • C. Knuth–Bendix completion algorithm
    The Knuth–Bendix completion algorithm is a procedure in term rewriting and automated theorem proving that transforms a set of equations into a confluent rewriting system, enabling decision of word problems in algebraic structures.
  • D. Dehn’s decision problems in group theory
    Dehn’s decision problems in group theory are foundational early 20th-century problems that introduced algorithmic questions about the solvability of word, conjugacy, and isomorphism problems in finitely presented groups, helping launch the field of algorithmic group theory.
  • E. Birkhoff’s representation theorem for finite distributive lattices
    Birkhoff’s representation theorem for finite distributive lattices is a fundamental result in lattice theory that characterizes every finite distributive lattice as isomorphic to the lattice of lower (order) ideals of a finite poset.
  • 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: Laver tables
Triple: [Richard Laver, notableFor, Laver tables]
Generated description
Laver tables are finite algebraic structures arising in set theory and large cardinal research, known for their role in studying self-distributive operations and the foundations of mathematics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Laver tables
Target entity description: Laver tables are finite algebraic structures arising in set theory and large cardinal research, known for their role in studying self-distributive operations and the foundations of mathematics.
  • A. Tarski’s theorem on amenable groups
    Tarski’s theorem on amenable groups is a fundamental result in group theory and measure theory that characterizes amenable groups as precisely those that do not admit Banach–Tarski-type paradoxical decompositions.
  • B. Lattice
    Lattice is a software company that provides people management and performance review tools to help organizations develop and engage their employees.
  • C. Knuth–Bendix completion algorithm
    The Knuth–Bendix completion algorithm is a procedure in term rewriting and automated theorem proving that transforms a set of equations into a confluent rewriting system, enabling decision of word problems in algebraic structures.
  • D. Dehn’s decision problems in group theory
    Dehn’s decision problems in group theory are foundational early 20th-century problems that introduced algorithmic questions about the solvability of word, conjugacy, and isomorphism problems in finitely presented groups, helping launch the field of algorithmic group theory.
  • E. Birkhoff’s representation theorem for finite distributive lattices
    Birkhoff’s representation theorem for finite distributive lattices is a fundamental result in lattice theory that characterizes every finite distributive lattice as isomorphic to the lattice of lower (order) ideals of a finite poset.
  • 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_69d8b9f4c22c819093c2680434472894 completed April 10, 2026, 8:51 a.m.
NER Named-entity recognition batch_69e49aa3cd248190a13a8209ba44fd3b completed April 19, 2026, 9:04 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0313cdffa8819085ba2ef27abe0700 completed May 12, 2026, 11:49 a.m.
NEDg Description generation batch_6a0314f1f01c8190b4065637716e845f completed May 12, 2026, 11:54 a.m.
NED2 Entity disambiguation (via description) batch_6a0318a4ca1481909f8ec14b9b8cb422 completed May 12, 2026, 12:10 p.m.
Created at: April 10, 2026, 10:18 a.m.