Triple

T1382050
Position Surface form Disambiguated ID Type / Status
Subject Theorema Egregium E29359 entity
Predicate relatedTo P37 FINISHED
Object Gauss map E30376 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: Gauss map | Statement: [Theorema Egregium, relatedTo, Gauss map]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Gauss map
Context triple: [Theorema Egregium, relatedTo, Gauss map]
  • A. Gauss map chosen
    The Gauss map is a differential geometry concept that assigns to each point on a surface the corresponding point on the unit sphere determined by the surface’s normal vector at that point.
  • B. Gaussian curvature
    Gaussian curvature is a fundamental concept in differential geometry that measures how a surface bends at a point by combining its principal curvatures into a single intrinsic quantity.
  • C. Theorema Egregium
    Theorema Egregium is Gauss’s celebrated theorem in differential geometry showing that the Gaussian curvature of a surface is an intrinsic property independent of how the surface is embedded in space.
  • D. Gauss–Bonnet theorem (early form)
    The Gauss–Bonnet theorem (early form) is an early version of the fundamental result in differential geometry that links the total curvature of a surface to its topological characteristics, originally developed by Carl Friedrich Gauss.
  • E. Poincaré map
    The Poincaré map is a mathematical tool in dynamical systems theory that reduces continuous-time dynamics to a discrete map by tracking intersections of trajectories with a lower-dimensional surface.
  • 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_69a498d883a48190bfdca525296ef7ee completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c3361bf08190b3f6bbf82e17685b completed March 1, 2026, 10:52 p.m.
NED1 Entity disambiguation (via context triple) batch_69acd48c41f4819092f7e1302d803662 completed March 8, 2026, 1:44 a.m.
Created at: March 1, 2026, 7:59 p.m.