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.