Triple

T9931759
Position Surface form Disambiguated ID Type / Status
Subject Neal Koblitz E192662 entity
Predicate authorOf P4244 FINISHED
Object 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.
E831067 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: Random Curves | Statement: [Neal Koblitz, authorOf, Random Curves]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Random Curves
Context triple: [Neal Koblitz, authorOf, Random Curves]
  • 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. Bezier curves
    Bézier curves are mathematically defined parametric curves widely used in computer graphics and digital design to model smooth, scalable shapes and paths.
  • C. Page curve
    The Page curve is a theoretical prediction in black hole physics that describes how the entanglement entropy of Hawking radiation should rise and then fall over time if black hole evaporation is ultimately unitary.
  • D. Ulam spiral
    The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
  • E. "On types of knotted curves"
    "On types of knotted curves" is a 1926 mathematical paper by J. W. Alexander and G. B. Briggs that introduced a systematic classification and notation for mathematical knots.
  • 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: Random Curves
Triple: [Neal Koblitz, authorOf, Random Curves]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Random Curves
Target entity description: 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.
  • 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. Bezier curves
    Bézier curves are mathematically defined parametric curves widely used in computer graphics and digital design to model smooth, scalable shapes and paths.
  • C. Page curve
    The Page curve is a theoretical prediction in black hole physics that describes how the entanglement entropy of Hawking radiation should rise and then fall over time if black hole evaporation is ultimately unitary.
  • D. Ulam spiral
    The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
  • E. "On types of knotted curves"
    "On types of knotted curves" is a 1926 mathematical paper by J. W. Alexander and G. B. Briggs that introduced a systematic classification and notation for mathematical knots.
  • 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_69ca82dd978c8190947124ab0d3315ac completed March 30, 2026, 2:04 p.m.
NER Named-entity recognition batch_69cdb5b54f348190b8e70e7beff6098a completed April 2, 2026, 12:17 a.m.
NED1 Entity disambiguation (via context triple) batch_69d228d1620c8190ac7125b268dd6832 completed April 5, 2026, 9:18 a.m.
NEDg Description generation batch_69d22c3a6fc0819083a376736325a04e completed April 5, 2026, 9:32 a.m.
NED2 Entity disambiguation (via description) batch_69d22cabf39881908f45667751384df5 completed April 5, 2026, 9:34 a.m.
Created at: March 30, 2026, 8:43 p.m.