Triple

T13894068
Position Surface form Disambiguated ID Type / Status
Subject Hadamard three-circle theorem E334042 entity
Predicate relatedTo P37 FINISHED
Object Phragmén–Lindelöf principle E518479 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: Phragmén–Lindelöf principle | Statement: [Hadamard three-circle theorem, relatedTo, Phragmén–Lindelöf principle]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Phragmén–Lindelöf principle
Context triple: [Hadamard three-circle theorem, relatedTo, Phragmén–Lindelöf principle]
  • A. Lindelöf theorem in complex analysis chosen
    The Lindelöf theorem in complex analysis is a result that refines the maximum modulus principle by controlling the boundary growth of analytic functions, particularly along paths approaching boundary points of their domain.
  • B. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • C. Schwarz lemma
    Schwarz lemma is a fundamental result in complex analysis that constrains holomorphic self-maps of the unit disk, particularly bounding their magnitude and derivative at the origin.
  • D. Malgrange–Ehrenpreis theorem
    The Malgrange–Ehrenpreis theorem is a fundamental result in the theory of partial differential equations stating that every linear partial differential operator with constant coefficients admits a fundamental solution.
  • E. Montel theorem
    Montel's theorem is a fundamental result in complex analysis stating that a family of holomorphic functions that is uniformly bounded on every compact subset of a domain is a normal family, meaning every sequence in it has a subsequence that converges uniformly on compact sets.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d81c5dd2d48190b7a5fc1e009de936 completed April 9, 2026, 9:38 p.m.
NER Named-entity recognition batch_69de23a741908190bdf46d76c5f1411a completed April 14, 2026, 11:23 a.m.
NED1 Entity disambiguation (via context triple) batch_69f7c71ca8a881908ac02687fbfe62fb completed May 3, 2026, 10:07 p.m.
Created at: April 9, 2026, 10:15 p.m.