Triple

T32258721
Position Surface form Disambiguated ID Type / Status
Subject matrix-tree theorem E824090 entity
Predicate generalizationOf P2372 FINISHED
Object Cayley’s formula for the number of labeled trees
Cayley’s formula for the number of labeled trees is a classical result in combinatorics stating that there are \(n^{n-2}\) distinct labeled trees on \(n\) vertices.
 E2000690 NE FINISHED

How this triple was built (2 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: Cayley’s formula for the number of labeled trees | Statement: [matrix-tree theorem, generalizationOf, Cayley’s formula for the number of labeled trees]
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: Cayley’s formula for the number of labeled trees
Triple: [matrix-tree theorem, generalizationOf, Cayley’s formula for the number of labeled trees]
Generated description
Cayley’s formula for the number of labeled trees is a classical result in combinatorics stating that there are \(n^{n-2}\) distinct labeled trees on \(n\) vertices.

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_69f3490db0748190bfef6e50c95d39d3 completed April 30, 2026, 12:20 p.m.
NER Named-entity recognition batch_69f6bc5652e08190b519631b7d497e75 completed May 3, 2026, 3:09 a.m.
NED1 Entity disambiguation (via context triple) batch_6a2f46d7d4388190bb7fed8881336a35 completed June 15, 2026, 12:27 a.m.
NEDg Description generation batch_6a2f47d66a34819082bc75aaf3f2b197 completed June 15, 2026, 12:31 a.m.
NED2 Entity disambiguation (via description) batch_6a301ae519348190a8563be3d2c124d0 completed June 15, 2026, 3:31 p.m.
Created at: May 1, 2026, 12:41 a.m.