Triple
T6295462
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Lie bracket |
E141120
|
entity |
| Predicate | JacobiIdentity |
P69850
|
FINISHED |
| Object | [x,[y,z]] + [y,[z,x]] + [z,[x,y]] = 0 |
—
|
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: [x,[y,z]] + [y,[z,x]] + [z,[x,y]] = 0 | Statement: [Lie bracket, JacobiIdentity, [x,[y,z]] + [y,[z,x]] + [z,[x,y]] = 0]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: JacobiIdentity Context triple: [Lie bracket, JacobiIdentity, [x,[y,z]] + [y,[z,x]] + [z,[x,y]] = 0]
-
A.
satisfiesJacobiIdentity
chosen
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.
-
B.
hasLieAlgebra
Indicates that one mathematical structure is associated with, or gives rise to, a specific Lie algebra capturing its infinitesimal or tangent-level structure.
-
C.
bracketIsAntisymmetric
Indicates that the bracket operation changes sign when its two arguments are swapped, so [x, y] = −[y, x].
-
D.
hasCommutationRelations
Indicates that there exist specific commutation relations governing how two operators or elements combine or reorder with respect to each other.
-
E.
isNonassociative
Indicates that a binary operation on three or more elements yields different results when the elements are grouped in different ways, so the associative law does not hold.
- 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_69c008cdf2ac8190bb640c94478fb4ed |
completed | March 22, 2026, 3:20 p.m. |
| NER | Named-entity recognition | batch_69c06439a6908190b0a8ebf426d3ca02 |
completed | March 22, 2026, 9:50 p.m. |
| PD | Predicate disambiguation | batch_69c060df0d8881908215575862ef6831 |
completed | March 22, 2026, 9:36 p.m. |
Created at: March 22, 2026, 4:27 p.m.