Triple

T7290653
Position Surface form Disambiguated ID Type / Status
Subject Weingarten map E164383 entity
Predicate alsoKnownAs P39 FINISHED
Object shape operator
The shape operator is a linear map in differential geometry that describes how a surface curves in different directions by relating changes in its normal vector to directions in the tangent plane.
 E653147 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: shape operator | Statement: [Weingarten map, alsoKnownAs, shape operator]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: shape operator
Context triple: [Weingarten map, alsoKnownAs, shape operator]
  • A. Shape
    Shape is a health and fitness magazine and digital brand focused on exercise, nutrition, and wellness content, owned by Dotdash Meredith.
  • B. SHAPE
    SHAPE is the central military command headquarters of NATO responsible for planning and executing the alliance’s collective defense operations in Europe.
  • C. Geometric Shapes Extended block
    Geometric Shapes Extended block is a Unicode block that adds additional geometric symbols and shapes beyond those found in the original Geometric Shapes block.
  • D. Square
    Square is a financial technology company best known for its mobile payment solutions and point-of-sale hardware that enable businesses to accept card payments easily.
  • E. ctangle
    ctangle is a CWEB tool that converts literate CWEB source files into compilable C code by extracting and tangling the program fragments.
  • 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: shape operator
Triple: [Weingarten map, alsoKnownAs, shape operator]
Generated description
The shape operator is a linear map in differential geometry that describes how a surface curves in different directions by relating changes in its normal vector to directions in the tangent plane.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07 
Target entity: shape operator
Target entity description: The shape operator is a linear map in differential geometry that describes how a surface curves in different directions by relating changes in its normal vector to directions in the tangent plane.
  • A. Shape
    Shape is a health and fitness magazine and digital brand focused on exercise, nutrition, and wellness content, owned by Dotdash Meredith.
  • B. SHAPE
    SHAPE is the central military command headquarters of NATO responsible for planning and executing the alliance’s collective defense operations in Europe.
  • C. Geometric Shapes Extended block
    Geometric Shapes Extended block is a Unicode block that adds additional geometric symbols and shapes beyond those found in the original Geometric Shapes block.
  • D. Square
    Square is a financial technology company best known for its mobile payment solutions and point-of-sale hardware that enable businesses to accept card payments easily.
  • E. ctangle
    ctangle is a CWEB tool that converts literate CWEB source files into compilable C code by extracting and tangling the program fragments.
  • 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_69c6887a499881909dd23341399c59d8 completed March 27, 2026, 1:39 p.m.
NER Named-entity recognition batch_69c6eb6d4e308190af6b8c237988d7d8 completed March 27, 2026, 8:41 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7db4a31608190ba465e22e7a81782 completed March 28, 2026, 1:44 p.m.
NEDg Description generation batch_69c7dbf65fb08190ae8a9c4e57d42e97 completed March 28, 2026, 1:47 p.m.
NED2 Entity disambiguation (via description) batch_69c7dc6af4b08190be165856d216f2ae completed March 28, 2026, 1:49 p.m.
Created at: March 27, 2026, 3 p.m.