Triple
T18729840
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Neumann boundary conditions in potential theory |
E458005
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Green's identities |
—
|
NE NERFINISHED |
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: Green's identities | Statement: [Neumann boundary conditions in potential theory, relatedTo, Green's identities]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Green's identities Context triple: [Neumann boundary conditions in potential theory, relatedTo, Green's identities]
-
A.
Green's identities
chosen
Green's identities are a set of integral formulas in vector calculus that relate functions and their Laplacians over a region to their behavior on the region’s boundary, forming a foundation for potential theory and partial differential equations.
-
B.
Green's functions
Green's functions are mathematical tools used in physics and engineering to solve inhomogeneous differential equations and describe the propagation of fields or particles in space and time.
-
C.
Wirtinger relations
Wirtinger relations are algebraic relations among generators in a knot group presentation that encode how strands of a knot interact at each crossing.
-
D.
Green's theorem
Green's theorem is a fundamental result in vector calculus that relates a line integral around a simple closed curve in the plane to a double integral over the region it encloses.
-
E.
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.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (2 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_69d8d393ba9c8190a8b03b04ddbb0a09 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e56d7660488190b4f70db963d05ef6 |
completed | April 20, 2026, 12:04 a.m. |
Created at: April 10, 2026, 11:50 a.m.