Triple

T11242695
Position Surface form Disambiguated ID Type / Status
Subject Conway circle theorem E266109 entity
Predicate relatedTo P37 FINISHED
Object Miquel circle
The Miquel circle is a notable circle in geometry that passes through the three points where the circumcircles of the triangles formed by choosing three vertices of a quadrilateral intersect.
E913508 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: Miquel circle | Statement: [Conway circle theorem, relatedTo, Miquel circle]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Miquel circle
Context triple: [Conway circle theorem, relatedTo, Miquel circle]
  • A. Soddy circle
    A Soddy circle is one of the circles in a configuration of four mutually tangent circles, central to the geometric problem described by Descartes' circle theorem.
  • B. Conway circle theorem
    The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
  • C. Fermat point
    The Fermat point is a special point inside a triangle that minimizes the total distance to the triangle’s three vertices.
  • D. Malfatti
    Malfatti is an Italian-origin surname notably associated with Brazilian modernist painter Anita Malfatti.
  • E. Tusi couple
    The Tusi couple is a geometric device from medieval Islamic astronomy that generates linear motion from the sum of two circular motions, later influencing Copernican models of planetary motion.
  • 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: Miquel circle
Triple: [Conway circle theorem, relatedTo, Miquel circle]
Generated description
The Miquel circle is a notable circle in geometry that passes through the three points where the circumcircles of the triangles formed by choosing three vertices of a quadrilateral intersect.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Miquel circle
Target entity description: The Miquel circle is a notable circle in geometry that passes through the three points where the circumcircles of the triangles formed by choosing three vertices of a quadrilateral intersect.
  • A. Soddy circle
    A Soddy circle is one of the circles in a configuration of four mutually tangent circles, central to the geometric problem described by Descartes' circle theorem.
  • B. Conway circle theorem
    The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
  • C. Fermat point
    The Fermat point is a special point inside a triangle that minimizes the total distance to the triangle’s three vertices.
  • D. Malfatti
    Malfatti is an Italian-origin surname notably associated with Brazilian modernist painter Anita Malfatti.
  • E. Tusi couple
    The Tusi couple is a geometric device from medieval Islamic astronomy that generates linear motion from the sum of two circular motions, later influencing Copernican models of planetary motion.
  • 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_69d6aac656d48190b275efaa7d6074ee completed April 8, 2026, 7:21 p.m.
NER Named-entity recognition batch_69d7e91b0b808190bc38008bb344d180 completed April 9, 2026, 5:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69e4ad849f70819098a7056fbc4831ff completed April 19, 2026, 10:25 a.m.
NEDg Description generation batch_69e4b12eee348190bee6c84587e4955d completed April 19, 2026, 10:40 a.m.
NED2 Entity disambiguation (via description) batch_69e4be2bb8c88190a21773b0c43b6b99 completed April 19, 2026, 11:36 a.m.
Created at: April 8, 2026, 9:30 p.m.