Triple

T16150954
Position Surface form Disambiguated ID Type / Status
Subject Dirac operator E391906 entity
Predicate squareRelatesTo P37 FINISHED
Object Bochner Laplacian E577497 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: Bochner Laplacian | Statement: [Dirac operator, squareRelatesTo, Bochner Laplacian]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Bochner Laplacian
Context triple: [Dirac operator, squareRelatesTo, Bochner Laplacian]
  • A. Bochner–Kodaira–Nakano identity
    The Bochner–Kodaira–Nakano identity is a fundamental formula in complex differential geometry relating the Laplacian on differential forms to curvature terms, with key applications to vanishing theorems and Hodge theory.
  • B. Bochner technique in Riemannian geometry
    The Bochner technique in Riemannian geometry is a method that uses Bochner-type identities and curvature conditions to derive vanishing theorems and rigidity results for differential forms and harmonic maps on manifolds.
  • C. Bochner–Martinelli formula
    The Bochner–Martinelli formula is a fundamental integral representation in several complex variables that generalizes the Cauchy integral formula to higher dimensions.
  • D. Laplace operator
    The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
  • E. Hodge Laplacian chosen
    The Hodge Laplacian is a differential operator on differential forms of a Riemannian manifold that combines the exterior derivative and its adjoint to study harmonic forms and de Rham cohomology.
  • 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_69d87f1c65e48190aa2b4c472e9bafc4 completed April 10, 2026, 4:39 a.m.
NER Named-entity recognition batch_69e21d9724808190a8332987583a345a completed April 17, 2026, 11:46 a.m.
NED1 Entity disambiguation (via context triple) batch_69fff7a9ebf08190aa21cdff051f4ba2 completed May 10, 2026, 3:12 a.m.
Created at: April 10, 2026, 5:01 a.m.