Triple

T8454719
Position Surface form Disambiguated ID Type / Status
Subject Menger curvature E199891 entity
Predicate invariantUnder P4235 FINISHED
Object Euclidean isometries E121354 NE 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: Euclidean isometries | Statement: [Menger curvature, invariantUnder, Euclidean isometries]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Euclidean isometries
Context triple: [Menger curvature, invariantUnder, Euclidean isometries]
  • A. Euclidean group chosen
    The Euclidean group is the group of all distance-preserving transformations of Euclidean space, consisting of rotations, reflections, and translations.
  • B. Euclidean space
    Euclidean space is the standard flat, n-dimensional geometric setting of classical geometry and vector calculus, characterized by straight lines, right angles, and the usual distance and dot product.
  • C. Euclidean metric
    The Euclidean metric is the standard distance function on Euclidean space, defined by the square root of the sum of squared coordinate differences between two points.
  • D. Euclidean geometry
    Euclidean geometry is the classical mathematical system that studies flat space and shapes using axioms about points, lines, and angles, forming the foundation of much of traditional mathematics and physics.
  • E. Lie sphere group
    The Lie sphere group is the continuous symmetry group that preserves the incidence and contact relations of spheres, planes, and points in Lie sphere geometry.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69ca8318231881908fd1bc1c4d45d286 completed March 30, 2026, 2:05 p.m.
NER Named-entity recognition batch_69cbe48ca9988190b60ebd09a135194d completed March 31, 2026, 3:13 p.m.
NED1 Entity disambiguation (via context triple) batch_69ce1de232508190803fd2dad21e677f completed April 2, 2026, 7:42 a.m.
Created at: March 30, 2026, 6:10 p.m.