Triple
T27562818
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Legendre polynomials |
E695818
|
entity |
| Predicate | satisfyOrthogonalityRelation |
P76852
|
FINISHED |
| Object | ∫_{-1}^1 P_m(x)P_n(x) dx = 2/(2n+1) δ_{mn} |
—
|
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 P_m(x)P_n(x) dx = 2/(2n+1) δ_{mn} | Statement: [Legendre polynomials, satisfyOrthogonalityRelation, ∫_{-1}^1 P_m(x)P_n(x) dx = 2/(2n+1) δ_{mn}]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: satisfyOrthogonalityRelation
Context triple: [Legendre polynomials, satisfyOrthogonalityRelation, ∫_{-1}^1 P_m(x)P_n(x) dx = 2/(2n+1) δ_{mn}]
-
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.
nonOrthogonality
Indicates that two vectors, directions, or subspaces are not orthogonal, meaning their inner product is nonzero and they are not mutually perpendicular.
-
D.
areEigenfunctionsOf
Indicates that certain functions serve as eigenfunctions corresponding to a specified operator or transformation.
-
E.
isParallelWithRespectTo
Indicates that two or more entities maintain a constant separation and never intersect within a specified reference or coordinate system.
- 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_69ef53891af88190a193c5e2a1dac9b1 |
completed | April 27, 2026, 12:16 p.m. |
| NER | Named-entity recognition | batch_69f63894e5848190aec428392562ab06 |
completed | May 2, 2026, 5:47 p.m. |
| PD | Predicate disambiguation | batch_69f6370c8c7c8190a02ea82847bb6e76 |
completed | May 2, 2026, 5:40 p.m. |
Created at: April 27, 2026, 1:40 p.m.