Triple

T15977116
Position Surface form Disambiguated ID Type / Status
Subject Cauchy functional equation E387476 entity
Predicate relatedTo P37 FINISHED
Object Jensen inequality
Jensen's inequality is a fundamental result in convex analysis and probability theory that bounds the value of a convex (or concave) function of an expectation by the expectation of the function.
E87727 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: Jensen inequality | Statement: [Cauchy functional equation, relatedTo, Jensen inequality]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Jensen inequality
Context triple: [Cauchy functional equation, relatedTo, Jensen inequality]
  • A. Seča
    Seča is a small coastal settlement in southwestern Slovenia, situated near the town of Piran on the Adriatic Sea.
  • B. Gejiu
    Gejiu is a city in Yunnan Province, China, historically known as one of the country’s major tin-mining centers.
  • C. Jesenwang
    Jesenwang is a small municipality in Upper Bavaria, Germany, situated within the Fürstenfeldbruck district west of Munich.
  • D. Sijilmasa
    Sijilmasa was a medieval Moroccan oasis city that flourished as a key commercial hub linking North Africa with sub-Saharan gold and trade networks.
  • E. Jiu
    Jiu is the Yale romanization of the Cantonese pronunciation of the Chinese surname 趙.
  • 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: Jensen inequality
Triple: [Cauchy functional equation, relatedTo, Jensen inequality]
Generated description
Jensen's inequality is a fundamental result in convex analysis and probability theory that bounds the value of a convex (or concave) function of an expectation by the expectation of the function.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Jensen inequality
Target entity description: Jensen's inequality is a fundamental result in convex analysis and probability theory that bounds the value of a convex (or concave) function of an expectation by the expectation of the function.
  • A. Jensen inequality chosen
    Jensen's inequality is a fundamental result in convex analysis and probability theory that relates the value of a convex (or concave) function of an expectation to the expectation of the function, providing bounds that underlie many other inequalities and convergence results.
  • B. Seča
    Seča is a small coastal settlement in southwestern Slovenia, situated near the town of Piran on the Adriatic Sea.
  • C. Gejiu
    Gejiu is a city in Yunnan Province, China, historically known as one of the country’s major tin-mining centers.
  • D. Jesenwang
    Jesenwang is a small municipality in Upper Bavaria, Germany, situated within the Fürstenfeldbruck district west of Munich.
  • E. Sijilmasa
    Sijilmasa was a medieval Moroccan oasis city that flourished as a key commercial hub linking North Africa with sub-Saharan gold and trade networks.
  • F. None of above.

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_69d86da94ccc819083d187f5dc6a123e completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e157521f6c8190a54023b5ee6fc033 completed April 16, 2026, 9:40 p.m.
NED1 Entity disambiguation (via context triple) batch_69ffbe8e4124819084c2937f532f5ab5 completed May 9, 2026, 11:09 p.m.
NEDg Description generation batch_69ffbf1948708190975024577e58a211 completed May 9, 2026, 11:11 p.m.
NED2 Entity disambiguation (via description) batch_69ffbf745f788190abae3ba723c3a564 completed May 9, 2026, 11:12 p.m.
Created at: April 10, 2026, 4:54 a.m.