Triple

T31631
Position Surface form Disambiguated ID Type / Status
Subject Nash embedding theorem E631 entity
Predicate statesThat P34 FINISHED
Object every smooth Riemannian manifold admits an isometric embedding into some Euclidean space 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: every smooth Riemannian manifold admits an isometric embedding into some Euclidean space | Statement: [Nash embedding theorem, statesThat, every smooth Riemannian manifold admits an isometric embedding into some Euclidean space]
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: statesThat
Context triple: [Nash embedding theorem, statesThat, every smooth Riemannian manifold admits an isometric embedding into some Euclidean space]
  • A. states chosen
    Indicates that an entity formally declares, expresses, or asserts a fact, opinion, or condition about another entity or situation.
  • B. numberOfStates
    Indicates the total count of distinct states or conditions associated with an entity or system.
  • C. conventionState
    Indicates that an entity is in a particular formal status or phase within a convention or agreed procedural framework.
  • D. homeState
    Indicates that a person or organization has their primary residence, registration, or official base in a particular state.
  • E. sovereignState
    Indicates that an entity is recognized as an independent, self-governing state with ultimate authority over its territory and not subject to any higher political power.
  • F. None of above.

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_69a2479dec388190967ba648663442c9 completed Feb. 28, 2026, 1:40 a.m.
NER Named-entity recognition batch_69a249ec0d288190ac3a0939db61813b completed Feb. 28, 2026, 1:50 a.m.
PD Predicate disambiguation batch_69a24870417081909c7c01e400c94716 completed Feb. 28, 2026, 1:44 a.m.
Created at: Feb. 28, 2026, 1:44 a.m.