Triple

T20523458
Position Surface form Disambiguated ID Type / Status
Subject Helge von Koch E503870 entity
Predicate hasWork P6260 FINISHED
Object On a continuous curve without tangents, constructible from elementary geometry
"On a continuous curve without tangents, constructible from elementary geometry" is the 1904 paper by Swedish mathematician Helge von Koch in which he introduced the now-famous Koch snowflake, one of the earliest and most iconic examples of a fractal curve.
E1435906 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: On a continuous curve without tangents, constructible from elementary geometry | Statement: [Helge von Koch, hasWork, On a continuous curve without tangents, constructible from elementary geometry]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: On a continuous curve without tangents, constructible from elementary geometry
Context triple: [Helge von Koch, hasWork, On a continuous curve without tangents, constructible from elementary geometry]
  • A. Jordan curve theorem
    The Jordan curve theorem is a fundamental result in topology stating that any simple closed curve in the plane divides the plane into exactly two distinct regions, an "inside" and an "outside."
  • B. On the Art of Measurement with the Compass and Ruler
    "On the Art of Measurement with the Compass and Ruler" is a foundational Renaissance treatise by Albrecht Dürer that systematizes the use of geometry and proportion in artistic design and representation.
  • C. Random Curves
    Random Curves is a mathematics book by Neal Koblitz that explores probabilistic and heuristic methods in number theory and algebraic geometry, particularly in relation to elliptic curves and cryptographic applications.
  • D. Frey curve construction
    The Frey curve construction is a method in number theory that associates an elliptic curve to a putative solution of Fermat’s Last Theorem, playing a key role in the proof by linking the theorem to modularity.
  • E. Peano curve
    The Peano curve is a space-filling fractal curve that continuously maps a one-dimensional interval onto a two-dimensional area, demonstrating that a line can completely fill a square.
  • 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: On a continuous curve without tangents, constructible from elementary geometry
Triple: [Helge von Koch, hasWork, On a continuous curve without tangents, constructible from elementary geometry]
Generated description
"On a continuous curve without tangents, constructible from elementary geometry" is the 1904 paper by Swedish mathematician Helge von Koch in which he introduced the now-famous Koch snowflake, one of the earliest and most iconic examples of a fractal curve.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: On a continuous curve without tangents, constructible from elementary geometry
Target entity description: "On a continuous curve without tangents, constructible from elementary geometry" is the 1904 paper by Swedish mathematician Helge von Koch in which he introduced the now-famous Koch snowflake, one of the earliest and most iconic examples of a fractal curve.
  • A. Jordan curve theorem
    The Jordan curve theorem is a fundamental result in topology stating that any simple closed curve in the plane divides the plane into exactly two distinct regions, an "inside" and an "outside."
  • B. On the Art of Measurement with the Compass and Ruler
    "On the Art of Measurement with the Compass and Ruler" is a foundational Renaissance treatise by Albrecht Dürer that systematizes the use of geometry and proportion in artistic design and representation.
  • C. Random Curves
    Random Curves is a mathematics book by Neal Koblitz that explores probabilistic and heuristic methods in number theory and algebraic geometry, particularly in relation to elliptic curves and cryptographic applications.
  • D. Frey curve construction
    The Frey curve construction is a method in number theory that associates an elliptic curve to a putative solution of Fermat’s Last Theorem, playing a key role in the proof by linking the theorem to modularity.
  • E. Peano curve
    The Peano curve is a space-filling fractal curve that continuously maps a one-dimensional interval onto a two-dimensional area, demonstrating that a line can completely fill a square.
  • 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_69e0b4b3a6e08190ae663701f50fab8e completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e69f471f18819091e8a57161fe0225 completed April 20, 2026, 9:48 p.m.
NED1 Entity disambiguation (via context triple) batch_6a089d43c6588190a4be58521ca67698 completed May 16, 2026, 4:37 p.m.
NEDg Description generation batch_6a089e00cde081908dca3893f03e3398 completed May 16, 2026, 4:40 p.m.
NED2 Entity disambiguation (via description) batch_6a089e8a05488190b3470f4ffb5927ce completed May 16, 2026, 4:42 p.m.
Created at: April 16, 2026, 11:36 a.m.