Triple

T36932178
Position Surface form Disambiguated ID Type / Status
Subject Miquel point E913507 entity
Predicate theoremStates P186750 FINISHED
Object for any triangle and any choice of one point on each side, the three circumcircles of the triangles formed by the vertices and these points are concurrent at the Miquel point LITERAL FINISHED

How this triple was built (2 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: for any triangle and any choice of one point on each side, the three circumcircles of the triangles formed by the vertices and these points are concurrent at the Miquel point | Statement: [Miquel point, theoremStates, for any triangle and any choice of one point on each side, the three circumcircles of the triangles formed by the vertices and these points are concurrent at the Miquel point]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: theoremStates
Context triple: [Miquel point, theoremStates, for any triangle and any choice of one point on each side, the three circumcircles of the triangles formed by the vertices and these points are concurrent at the Miquel point]
  • A. hasTheorem
    Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.
  • B. stateDoctrine
    Indicates that a state or government officially endorses, promotes, or is guided by a particular doctrine, ideology, or set of principles.
  • C. symbolicallyStates
    Indicates that one entity expresses or asserts something in a symbolic or representational form rather than in a direct or literal manner.
  • D. proposition3States
    Indicates that a third proposition articulates, asserts, or formally states a particular claim, condition, or content.
  • E. firstTheoremStates
    Indicates that the content of the first theorem asserts or expresses a particular statement or claim.
  • F. None of above. chosen

Provenance (4 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_69f76e896c988190880c130e01303dd4 completed May 3, 2026, 3:49 p.m.
NER Named-entity recognition batch_69fa0a7b00948190a257273d9968c5d7 completed May 5, 2026, 3:19 p.m.
PD Predicate disambiguation batch_69f9fec9c9488190ae2a349651a02782 completed May 5, 2026, 2:29 p.m.
PDg Predicate description generation batch_69fa0a799b9081909bfa8293a22c4b00 completed May 5, 2026, 3:19 p.m.
Created at: May 3, 2026, 4:13 p.m.