Triple

T37258872
Position Surface form Disambiguated ID Type / Status
Subject Borg–Marchenko theorem E924204 entity
Predicate generalizes P2372 FINISHED
Object Borg’s uniqueness result for Sturm–Liouville problems
Borg’s uniqueness result for Sturm–Liouville problems is a foundational theorem in inverse spectral theory stating that, under suitable conditions, the potential in a Sturm–Liouville operator is uniquely determined by its spectral data.
E924204 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: Borg’s uniqueness result for Sturm–Liouville problems | Statement: [Borg–Marchenko theorem, generalizes, Borg’s uniqueness result for Sturm–Liouville problems]
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: Borg’s uniqueness result for Sturm–Liouville problems
Triple: [Borg–Marchenko theorem, generalizes, Borg’s uniqueness result for Sturm–Liouville problems]
Generated description
Borg’s uniqueness result for Sturm–Liouville problems is a foundational theorem in inverse spectral theory stating that, under suitable conditions, the potential in a Sturm–Liouville operator is uniquely determined by its spectral data.

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_69f76eabd6c481909d414a80a1345c98 completed May 3, 2026, 3:50 p.m.
NER Named-entity recognition batch_69fb372da9248190bab2b04711f839f4 completed May 6, 2026, 12:42 p.m.
NED1 Entity disambiguation (via context triple) batch_6a4043d8d2e481908c363980e133e824 completed June 27, 2026, 9:42 p.m.
NEDg Description generation batch_6a40448854a88190852646c14a8f9864 completed June 27, 2026, 9:45 p.m.
NED2 Entity disambiguation (via description) batch_6a404505b4048190bfadd456a3214fe1 completed June 27, 2026, 9:47 p.m.
Created at: May 3, 2026, 4:15 p.m.