Triple

T15961280
Position Surface form Disambiguated ID Type / Status
Subject Joseph B. Kruskal E387063 entity
Predicate knownFor P22 FINISHED
Object Kruskal's tree theorem
Kruskal's tree theorem is a fundamental result in combinatorics and mathematical logic stating that finite trees are well-quasi-ordered under homeomorphic embedding, with deep implications in proof theory and computer science.
E1187022 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: Kruskal's tree theorem | Statement: [Joseph B. Kruskal, knownFor, Kruskal's tree theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Kruskal's tree theorem
Context triple: [Joseph B. Kruskal, knownFor, Kruskal's tree theorem]
  • A. Tarski–Mostowski–Robinson theorem
    The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
  • B. Kesten’s theorem
    Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
  • C. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • D. Mazurkiewicz–Sierpiński theorem
    The Mazurkiewicz–Sierpiński theorem is a result in topology and measure theory that characterizes certain properties of measurable sets and mappings, particularly concerning continuous images of sets in Euclidean spaces.
  • E. Graham–Rothschild theorem
    The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
  • 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: Kruskal's tree theorem
Triple: [Joseph B. Kruskal, knownFor, Kruskal's tree theorem]
Generated description
Kruskal's tree theorem is a fundamental result in combinatorics and mathematical logic stating that finite trees are well-quasi-ordered under homeomorphic embedding, with deep implications in proof theory and computer science.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Kruskal's tree theorem
Target entity description: Kruskal's tree theorem is a fundamental result in combinatorics and mathematical logic stating that finite trees are well-quasi-ordered under homeomorphic embedding, with deep implications in proof theory and computer science.
  • A. Tarski–Mostowski–Robinson theorem
    The Tarski–Mostowski–Robinson theorem is a fundamental result in model theory that characterizes when a class of structures is first-order axiomatizable, linking definability properties with closure under ultraproducts and isomorphisms.
  • B. Kesten’s theorem
    Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
  • C. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • D. Mazurkiewicz–Sierpiński theorem
    The Mazurkiewicz–Sierpiński theorem is a result in topology and measure theory that characterizes certain properties of measurable sets and mappings, particularly concerning continuous images of sets in Euclidean spaces.
  • E. Graham–Rothschild theorem
    The Graham–Rothschild theorem is a fundamental result in Ramsey theory that generalizes classical partition theorems to higher-dimensional combinatorial structures.
  • 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_69d86da882448190a82ea962fe343b79 completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e156ff4cdc81908db31394eaa191bc completed April 16, 2026, 9:39 p.m.
NED1 Entity disambiguation (via context triple) batch_69ffbe827d248190adbfd41f55638ebd completed May 9, 2026, 11:08 p.m.
NEDg Description generation batch_69ffbffcbd748190a666eca28cf44ad5 completed May 9, 2026, 11:15 p.m.
NED2 Entity disambiguation (via description) batch_69ffc09df25481908674f306b0f96f95 completed May 9, 2026, 11:17 p.m.
Created at: April 10, 2026, 4:53 a.m.