Triple
T25920196
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | shape operator |
E653147
|
entity |
| Predicate | relationToSecondFundamentalForm |
P140208
|
FINISHED |
| Object | second fundamental form II(X,Y) = ⟨S(X),Y⟩ |
—
|
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: second fundamental form II(X,Y) = ⟨S(X),Y⟩ | Statement: [shape operator, relationToSecondFundamentalForm, second fundamental form II(X,Y) = ⟨S(X),Y⟩]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: relationToSecondFundamentalForm Context triple: [shape operator, relationToSecondFundamentalForm, second fundamental form II(X,Y) = ⟨S(X),Y⟩]
-
A.
associatedQuadraticForm
chosen
Indicates that one mathematical object (such as a bilinear form, matrix, or linear operator) is linked to or determines a specific quadratic form derived from it.
-
B.
associatedQuadraticFormProperty
Indicates that a quadratic form is linked to, or characterized by, a specific property or attribute related to its structure or behavior.
-
C.
RicciTensor
Indicates the curvature relationship between nearby geodesics in a space(time), summarizing how matter or energy causes volumes to converge or diverge through the contraction of the Riemann curvature tensor.
-
D.
RiemannTensor
Indicates how much and in what way a manifold’s geometry deviates from flatness by describing the curvature through the failure of parallel-transported vectors to return unchanged.
-
E.
isConformallyRelatedTo
Indicates that one entity can be transformed into the other by a conformal (angle-preserving) mapping, preserving local shapes but not necessarily sizes or distances.
- 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_69e7ab3e025c819086771607157f0015 |
completed | April 21, 2026, 4:52 p.m. |
| NER | Named-entity recognition | batch_69fd6f9d600c8190acf495b7fc632e4b |
completed | May 8, 2026, 5:07 a.m. |
| PD | Predicate disambiguation | batch_69fd6e98a2948190a9f78c415ad23b8c |
completed | May 8, 2026, 5:03 a.m. |
Created at: April 22, 2026, 8:32 a.m.