Triple

T13894069
Position Surface form Disambiguated ID Type / Status
Subject Hadamard three-circle theorem E334042 entity
Predicate relatedTo P37 FINISHED
Object Hadamard three-lines theorem E334042 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: Hadamard three-lines theorem | Statement: [Hadamard three-circle theorem, relatedTo, Hadamard three-lines theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hadamard three-lines theorem
Context triple: [Hadamard three-circle theorem, relatedTo, Hadamard three-lines theorem]
  • A. Hadamard three-circle theorem chosen
    The Hadamard three-circle theorem is a result in complex analysis that describes how the maximum modulus of a holomorphic function behaves logarithmically between three concentric circles in the complex plane.
  • B. Inequalities for analytic functions
    "Inequalities for analytic functions" is a mathematical work by Gábor Szegő that develops fundamental bounds and estimates for complex analytic functions, particularly in the context of complex analysis and approximation theory.
  • C. Corona theorem
    The Corona theorem is a fundamental result in complex analysis that characterizes when bounded analytic functions on the unit disk can be solved in a certain type of division problem, showing that the maximal ideal space of the disk algebra has no "corona."
  • D. Lempert function on convex domains
    The Lempert function on convex domains is a complex-analytic invariant that coincides with the Kobayashi distance and provides an extremal characterization of holomorphic mappings between convex domains in several complex variables.
  • E. Schwarz–Pick theorem
    The Schwarz–Pick theorem is a fundamental result in complex analysis that characterizes holomorphic self-maps of the unit disk by showing they are distance-decreasing with respect to the hyperbolic (Poincaré) metric.
  • 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.