Triple

T9243189
Position Surface form Disambiguated ID Type / Status
Subject Pavel Florensky E222115 entity
Predicate notableWork P4 FINISHED
Object Imaginary Numbers in Geometry
"Imaginary Numbers in Geometry" is a seminal mathematical-philosophical work by Pavel Florensky that explores the geometric interpretation and deeper conceptual meaning of imaginary numbers.
E786846 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: Imaginary Numbers in Geometry | Statement: [Pavel Florensky, notableWork, Imaginary Numbers in Geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Imaginary Numbers in Geometry
Context triple: [Pavel Florensky, notableWork, Imaginary Numbers in Geometry]
  • A. The Beauty of Geometry
    The Beauty of Geometry is a classic mathematical book by H. S. M. Coxeter that explores elegant geometric ideas and configurations through clear exposition and rich illustrations.
  • B. Gaussian integers
    Gaussian integers are complex numbers whose real and imaginary parts are both integers, forming a lattice in the complex plane with important applications in number theory and algebra.
  • C. Möbius geometry
    Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
  • D. Gaussian rationals ℚ(i)
    Gaussian rationals ℚ(i) are the field of complex numbers whose real and imaginary parts are rational, formed by adjoining the imaginary unit i to the rational numbers.
  • E. Euler’s formula for complex exponentials
    Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
  • 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: Imaginary Numbers in Geometry
Triple: [Pavel Florensky, notableWork, Imaginary Numbers in Geometry]
Generated description
"Imaginary Numbers in Geometry" is a seminal mathematical-philosophical work by Pavel Florensky that explores the geometric interpretation and deeper conceptual meaning of imaginary numbers.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Imaginary Numbers in Geometry
Target entity description: "Imaginary Numbers in Geometry" is a seminal mathematical-philosophical work by Pavel Florensky that explores the geometric interpretation and deeper conceptual meaning of imaginary numbers.
  • A. The Beauty of Geometry
    The Beauty of Geometry is a classic mathematical book by H. S. M. Coxeter that explores elegant geometric ideas and configurations through clear exposition and rich illustrations.
  • B. Gaussian integers
    Gaussian integers are complex numbers whose real and imaginary parts are both integers, forming a lattice in the complex plane with important applications in number theory and algebra.
  • C. Möbius geometry
    Möbius geometry is a branch of geometry that studies properties of figures invariant under Möbius (conformal) transformations of the extended complex plane or higher-dimensional spheres.
  • D. Gaussian rationals ℚ(i)
    Gaussian rationals ℚ(i) are the field of complex numbers whose real and imaginary parts are rational, formed by adjoining the imaginary unit i to the rational numbers.
  • E. Euler’s formula for complex exponentials
    Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
  • F. None of above. chosen

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_69ca83ee26cc81909ac624e190597d6d completed March 30, 2026, 2:08 p.m.
NER Named-entity recognition batch_69cd03ec23ec8190993003a826372d40 completed April 1, 2026, 11:39 a.m.
NED1 Entity disambiguation (via context triple) batch_69d077e977c48190ba46a48850a3da0a completed April 4, 2026, 2:31 a.m.
NEDg Description generation batch_69d07c3d6c1881908b267c2947b360d6 completed April 4, 2026, 2:49 a.m.
NED2 Entity disambiguation (via description) batch_69d07ca8bad48190a0d36c6deb96610f completed April 4, 2026, 2:51 a.m.
Created at: March 30, 2026, 7:30 p.m.