Triple
T7871825
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jacobi polynomials |
E182753
|
entity |
| Predicate | hasOrthogonalityRelation |
P76852
|
FINISHED |
| Object | ∫_{-1}^1 (1-x)^α (1+x)^β P_m^{(α,β)}(x) P_n^{(α,β)}(x) dx = 0 for m ≠ 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: ∫_{-1}^1 (1-x)^α (1+x)^β P_m^{(α,β)}(x) P_n^{(α,β)}(x) dx = 0 for m ≠ n | Statement: [Jacobi polynomials, hasOrthogonalityRelation, ∫_{-1}^1 (1-x)^α (1+x)^β P_m^{(α,β)}(x) P_n^{(α,β)}(x) dx = 0 for m ≠ n]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasOrthogonalityRelation
Context triple: [Jacobi polynomials, hasOrthogonalityRelation, ∫_{-1}^1 (1-x)^α (1+x)^β P_m^{(α,β)}(x) P_n^{(α,β)}(x) dx = 0 for m ≠ n]
-
A.
orthogonalityProperty
chosen
Indicates that one entity possesses the property of being orthogonal (i.e., at right angles or having zero inner product) with respect to another entity or a given reference.
-
B.
orthonormalityRelation
Indicates that a set of vectors are mutually orthogonal and each has unit length with respect to a given inner product.
-
C.
isParallelWithRespectTo
Indicates that two or more entities maintain a constant separation and never intersect within a specified reference or coordinate system.
-
D.
hasCommutationRelations
Indicates that there exist specific commutation relations governing how two operators or elements combine or reorder with respect to each other.
-
E.
hasRelation
Indicates that there exists some specified relationship or association between two entities.
- 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_69ca82894d9081908a832bfce71a4714 |
completed | March 30, 2026, 2:02 p.m. |
| NER | Named-entity recognition | batch_69cb39a5950481908399211c5dfe2569 |
completed | March 31, 2026, 3:04 a.m. |
| PD | Predicate disambiguation | batch_69cae928e1b88190b0620f4c4f03bc7d |
completed | March 30, 2026, 9:20 p.m. |
Created at: March 30, 2026, 4:56 p.m.