Triple

T32308228
Position Surface form Disambiguated ID Type / Status
Subject Cauchy’s mean value theorem E825423 entity
Predicate hasSpecialCase P7025 FINISHED
Object Lagrange’s mean value theorem
Lagrange’s mean value theorem is a fundamental result in calculus that guarantees, for a differentiable function on a closed interval, the existence of at least one point where the instantaneous rate of change equals the average rate of change over that interval.
E2001744 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: Lagrange’s mean value theorem | Statement: [Cauchy’s mean value theorem, hasSpecialCase, Lagrange’s mean value theorem]
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: Lagrange’s mean value theorem
Triple: [Cauchy’s mean value theorem, hasSpecialCase, Lagrange’s mean value theorem]
Generated description
Lagrange’s mean value theorem is a fundamental result in calculus that guarantees, for a differentiable function on a closed interval, the existence of at least one point where the instantaneous rate of change equals the average rate of change over that interval.

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_69f3491213b88190a57094d8697a7455 completed April 30, 2026, 12:20 p.m.
NER Named-entity recognition batch_69f6bd8835588190b562ff2832f98acf completed May 3, 2026, 3:14 a.m.
NED1 Entity disambiguation (via context triple) batch_6a305712a02c81908eaa9aad47fe3236 completed June 15, 2026, 7:48 p.m.
NEDg Description generation batch_6a305ad097f481908935fa484b3aba59 completed June 15, 2026, 8:04 p.m.
NED2 Entity disambiguation (via description) batch_6a305b7872348190aaa5fd5c7eb1a955 completed June 15, 2026, 8:07 p.m.
Created at: May 1, 2026, 12:45 a.m.