Triple

T18397363
Position Surface form Disambiguated ID Type / Status
Subject Brahmagupta E449902 entity
Predicate knownFor P22 FINISHED
Object Brahmagupta’s theorem
Brahmagupta’s theorem is a classical result in Euclidean geometry that characterizes a special property of cyclic quadrilaterals whose diagonals are perpendicular, relating the orthocenter of the triangle formed by three vertices to the fourth vertex.
E1322031 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: Brahmagupta’s theorem | Statement: [Brahmagupta, knownFor, Brahmagupta’s theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Brahmagupta’s theorem
Context triple: [Brahmagupta, knownFor, Brahmagupta’s theorem]
  • A. Thales’ theorem
    Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
  • B. Brahmagupta–Fibonacci identity
    The Brahmagupta–Fibonacci identity is a classical algebraic formula showing that the product of two sums of two squares can itself be expressed as a sum of two squares, fundamental in number theory and the study of quadratic forms.
  • C. 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.
  • D. Miquel point
    The Miquel point is a notable point in triangle geometry defined as the common intersection of the circumcircles of three triangles formed by choosing one point on each side of a reference triangle.
  • E. Pythagorean theorem
    The Pythagorean theorem is a fundamental principle of geometry stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
  • 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: Brahmagupta’s theorem
Triple: [Brahmagupta, knownFor, Brahmagupta’s theorem]
Generated description
Brahmagupta’s theorem is a classical result in Euclidean geometry that characterizes a special property of cyclic quadrilaterals whose diagonals are perpendicular, relating the orthocenter of the triangle formed by three vertices to the fourth vertex.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Brahmagupta’s theorem
Target entity description: Brahmagupta’s theorem is a classical result in Euclidean geometry that characterizes a special property of cyclic quadrilaterals whose diagonals are perpendicular, relating the orthocenter of the triangle formed by three vertices to the fourth vertex.
  • A. Thales’ theorem
    Thales’ theorem is a fundamental result in Euclidean geometry stating that any angle inscribed in a semicircle is a right angle.
  • B. Brahmagupta–Fibonacci identity
    The Brahmagupta–Fibonacci identity is a classical algebraic formula showing that the product of two sums of two squares can itself be expressed as a sum of two squares, fundamental in number theory and the study of quadratic forms.
  • C. 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.
  • D. Miquel point
    The Miquel point is a notable point in triangle geometry defined as the common intersection of the circumcircles of three triangles formed by choosing one point on each side of a reference triangle.
  • E. Pythagorean theorem
    The Pythagorean theorem is a fundamental principle of geometry stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
  • 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_69d8b9fab8a8819086a9ddc0871715e0 completed April 10, 2026, 8:51 a.m.
NER Named-entity recognition batch_69e5184777548190818365ee52ac88b7 completed April 19, 2026, 6 p.m.
NED1 Entity disambiguation (via context triple) batch_6a03e2427c448190b3562d7cb0313d5a completed May 13, 2026, 2:30 a.m.
NEDg Description generation batch_6a03e2ca62f881908122f2d2fe3b937d completed May 13, 2026, 2:32 a.m.
NED2 Entity disambiguation (via description) batch_6a03e33718f481909377eeff33332f33 completed May 13, 2026, 2:34 a.m.
Created at: April 10, 2026, 10:46 a.m.