Triple

T16614856
Position Surface form Disambiguated ID Type / Status
Subject Peano curve E403670 entity
Predicate relatedTo P37 FINISHED
Object Lebesgue space-filling curve
The Lebesgue space-filling curve is a classic continuous mapping from a one-dimensional interval onto a multi-dimensional region that, like the Peano curve, demonstrates how a line can completely fill an area.
E403670 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: Lebesgue space-filling curve | Statement: [Peano curve, relatedTo, Lebesgue space-filling curve]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lebesgue space-filling curve
Context triple: [Peano curve, relatedTo, Lebesgue space-filling curve]
  • A. 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.
  • B. Sierpiński arrowhead curve
    The Sierpiński arrowhead curve is a self-similar fractal curve that recursively forms a triangular, dragon-like pattern and is closely related to the Sierpiński triangle.
  • 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. Schwarz–Christoffel mapping
    The Schwarz–Christoffel mapping is a conformal transformation that maps the upper half-plane (or unit disk) onto polygonal regions, playing a central role in complex analysis and applications such as fluid dynamics and electrostatics.
  • E. Unique Forms of Continuity in Space
    Unique Forms of Continuity in Space is a seminal Futurist bronze sculpture by Umberto Boccioni that dynamically depicts a striding human figure dissolving into flowing, aerodynamic forms to evoke speed and modernity.
  • 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: Lebesgue space-filling curve
Triple: [Peano curve, relatedTo, Lebesgue space-filling curve]
Generated description
The Lebesgue space-filling curve is a classic continuous mapping from a one-dimensional interval onto a multi-dimensional region that, like the Peano curve, demonstrates how a line can completely fill an area.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lebesgue space-filling curve
Target entity description: The Lebesgue space-filling curve is a classic continuous mapping from a one-dimensional interval onto a multi-dimensional region that, like the Peano curve, demonstrates how a line can completely fill an area.
  • A. Peano curve chosen
    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.
  • B. Sierpiński arrowhead curve
    The Sierpiński arrowhead curve is a self-similar fractal curve that recursively forms a triangular, dragon-like pattern and is closely related to the Sierpiński triangle.
  • 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. Schwarz–Christoffel mapping
    The Schwarz–Christoffel mapping is a conformal transformation that maps the upper half-plane (or unit disk) onto polygonal regions, playing a central role in complex analysis and applications such as fluid dynamics and electrostatics.
  • E. Unique Forms of Continuity in Space
    Unique Forms of Continuity in Space is a seminal Futurist bronze sculpture by Umberto Boccioni that dynamically depicts a striding human figure dissolving into flowing, aerodynamic forms to evoke speed and modernity.
  • F. None of above.

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_69d883897eb481909eaaa088ba9918d9 completed April 10, 2026, 4:58 a.m.
NER Named-entity recognition batch_69e3609935a88190baa56f3a42b2ecd1 completed April 18, 2026, 10:44 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0075aeaa9881908bdef0f9f2b52e60 completed May 10, 2026, 12:10 p.m.
NEDg Description generation batch_6a007705f57881908b07a20ae8957c64 completed May 10, 2026, 12:16 p.m.
NED2 Entity disambiguation (via description) batch_6a007b18f0b08190a9ddc6ad7358d6b8 completed May 10, 2026, 12:33 p.m.
Created at: April 10, 2026, 5:17 a.m.