Triple

T23372407
Position Surface form Disambiguated ID Type / Status
Subject SU(n) E593508 entity
Predicate specialCase P7025 FINISHED
Object SU(2) is isomorphic to the group of unit quaternions 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: SU(2) is isomorphic to the group of unit quaternions | Statement: [SU(n), specialCase, SU(2) is isomorphic to the group of unit quaternions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: SU(2) is isomorphic to the group of unit quaternions
Context triple: [SU(n), specialCase, SU(2) is isomorphic to the group of unit quaternions]
  • A. rotation group SU(2)
    The rotation group SU(2) is the Lie group of 2×2 unitary matrices with determinant 1 that serves as the double cover of the three-dimensional rotation group SO(3) and underlies the quantum theory of angular momentum and spin.
  • B. Quaternions chosen
    Quaternions are a number system that extends complex numbers to four dimensions and is widely used to represent and compute 3D rotations in mathematics, physics, and computer graphics.
  • C. special unitary group SU(n)
    The special unitary group SU(n) is a fundamental compact Lie group consisting of n×n unitary matrices with determinant 1, central in mathematics and physics, especially in quantum theory and gauge symmetries.
  • D. Hurwitz quaternions
    Hurwitz quaternions are a specific lattice of quaternions with integer and half-integer components that form a maximal order in the quaternion algebra and provide a natural algebraic framework for understanding representations of integers as sums of four squares.
  • E. Hamiltonian quaternion notation
    Hamiltonian quaternion notation is the classical symbolic system introduced by William Rowan Hamilton to represent quaternions using a scalar part and three imaginary units i, j, k with specific multiplication rules.
  • 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_69e25d2593c88190bcdf4a716a94ccb2 completed April 17, 2026, 4:17 p.m.
NER Named-entity recognition batch_69f1a3af45ec8190a32aa4e5f04f6756 completed April 29, 2026, 6:22 a.m.
Created at: April 17, 2026, 5:32 p.m.