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.