Triple

T15860142
Position Surface form Disambiguated ID Type / Status
Subject Schmidt decomposition E384561 entity
Predicate hasComponent P35 FINISHED
Object Schmidt basis E384561 NE 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: Schmidt basis | Statement: [Schmidt decomposition, hasComponent, Schmidt basis]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Schmidt basis
Context triple: [Schmidt decomposition, hasComponent, Schmidt basis]
  • A. Schmidt orthogonalization
    Schmidt orthogonalization is a mathematical procedure, also known as the Gram–Schmidt process, that converts a set of linearly independent vectors into an orthonormal set spanning the same subspace.
  • B. Schmidt decomposition chosen
    The Schmidt decomposition is a mathematical technique in functional analysis and quantum information theory that expresses a bipartite vector (such as a quantum state) as a sum of orthogonal product states with nonnegative coefficients, revealing its entanglement structure.
  • C. Schauder basis
    A Schauder basis is a sequence in a Banach space such that every element of the space can be uniquely represented as a convergent infinite linear combination of the sequence’s vectors.
  • D. Clebsch–Gordan coefficients
    Clebsch–Gordan coefficients are numerical factors in quantum mechanics and representation theory that describe how to combine two angular momenta (or group representations) into a single resultant one.
  • E. Riesz basis
    A Riesz basis is a sequence in a Hilbert space that is complete and behaves like an orthonormal basis up to a bounded, invertible linear transformation, allowing stable and unique expansions of vectors.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

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_69d86da422088190aac39e32e6c68429 completed April 10, 2026, 3:25 a.m.
NER Named-entity recognition batch_69e1555a1f008190bb3f03b0f35ed8a4 completed April 16, 2026, 9:32 p.m.
NED1 Entity disambiguation (via context triple) batch_69ffa14da7ac8190bbef49a1602a76fe completed May 9, 2026, 9:04 p.m.
Created at: April 10, 2026, 4:50 a.m.