Triple

T27675185
Position Surface form Disambiguated ID Type / Status
Subject Sturm–Liouville problem E697758 entity
Predicate hasKeyTheorem P72923 FINISHED
Object Sturm oscillation theorem
The Sturm oscillation theorem is a fundamental result in the theory of linear second-order differential equations that relates the number of zeros of eigenfunctions to the ordering of their corresponding eigenvalues.
 E1782171 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: Sturm oscillation theorem | Statement: [Sturm–Liouville problem, hasKeyTheorem, Sturm oscillation 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: Sturm oscillation theorem
Triple: [Sturm–Liouville problem, hasKeyTheorem, Sturm oscillation theorem]
Generated description
The Sturm oscillation theorem is a fundamental result in the theory of linear second-order differential equations that relates the number of zeros of eigenfunctions to the ordering of their corresponding eigenvalues.

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_69ef590d458c81909583290c3cd0478b completed April 27, 2026, 12:39 p.m.
NER Named-entity recognition batch_69f63532e35881909bfe0a8a315e2efe completed May 2, 2026, 5:32 p.m.
NED1 Entity disambiguation (via context triple) batch_6a12daaa22c48190b3f05cc780d85fcf completed May 24, 2026, 11:02 a.m.
NEDg Description generation batch_6a12db425798819097c2f19d2aa6baaa completed May 24, 2026, 11:04 a.m.
NED2 Entity disambiguation (via description) batch_6a12dbac16bc8190aa2c654274fbcb3b completed May 24, 2026, 11:06 a.m.
Created at: April 27, 2026, 2:43 p.m.