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.