Triple
T29436247
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Riesz transforms |
E746579
|
entity |
| Predicate | isSkewAdjoint |
P167178
|
FINISHED |
| Object | true on L^2(R^n) |
—
|
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: true on L^2(R^n) | Statement: [Riesz transforms, isSkewAdjoint, true on L^2(R^n)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: isSkewAdjoint Context triple: [Riesz transforms, isSkewAdjoint, true on L^2(R^n)]
-
A.
isSkewSymmetric
Indicates that a relation or matrix changes sign when its arguments or indices are swapped, i.e., R(x, y) = −R(y, x), with all diagonal/self-relations being zero.
-
B.
isSelfAdjoint
Indicates that an operator is equal to its own adjoint (conjugate transpose), meaning it has the same effect as its Hermitian transpose in the given inner product space.
-
C.
hasAdjointRepresentation
Indicates that a mathematical object (typically a Lie group or Lie algebra) is associated with its adjoint representation, describing how it acts on its own Lie algebra via the adjoint action.
-
D.
isHermitian
Indicates that an operator or matrix is equal to its own conjugate transpose, ensuring real eigenvalues and orthogonal eigenvectors.
-
E.
satisfiesJacobiIdentity
Indicates that a given binary operation on elements of an algebraic structure obeys the Jacobi identity, i.e., the specific cyclic sum of nested operations always equals zero.
- F. None of above. chosen
Provenance (4 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_69f0a7a180e48190ae775e40047dbcb5 |
completed | April 28, 2026, 12:27 p.m. |
| NER | Named-entity recognition | batch_69f66accf77c81908f0f4c1a67e05e47 |
completed | May 2, 2026, 9:21 p.m. |
| PD | Predicate disambiguation | batch_69f66339175c819080bd70f0ff7057b1 |
completed | May 2, 2026, 8:48 p.m. |
| PDg | Predicate description generation | batch_69f663ff176c8190aaadb475f75daee4 |
completed | May 2, 2026, 8:52 p.m. |
Created at: April 28, 2026, 3:16 p.m.