Triple

T15860205
Position Surface form Disambiguated ID Type / Status
Subject Hilbert–Schmidt operator E384562 entity
Predicate adjointProperty P120794 FINISHED
Object adjoint of a Hilbert–Schmidt operator is Hilbert–Schmidt — 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: adjoint of a Hilbert–Schmidt operator is Hilbert–Schmidt | Statement: [Hilbert–Schmidt operator, adjointProperty, adjoint of a Hilbert–Schmidt operator is Hilbert–Schmidt]
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: adjointProperty
Context triple: [Hilbert–Schmidt operator, adjointProperty, adjoint of a Hilbert–Schmidt operator is Hilbert–Schmidt]
  • A. hasAdjointRepresentation
    Indicates that a mathematical object (typically a Lie group or Lie algebra) is associated with its adjoint representation, describing how it acts on its own Lie algebra via the adjoint action.
  • B. determinantProperty
    Indicates that one property or factor determines, governs, or decisively influences another property or outcome.
  • C. isSelfAdjoint
    Indicates that an operator is equal to its own adjoint (conjugate transpose), meaning it has the same effect as its Hermitian transpose in the given inner product space.
  • D. conjugateVariable
    Indicates that one variable is the conjugate counterpart of another, typically related by a conjugation operation such as complex, algebraic, or canonical conjugation.
  • E. algorithmicProperty
    Indicates that a subject possesses a specific characteristic, behavior, or quality defined in terms of an algorithm or computational procedure.
  • F. None of above. chosen

Provenance (4 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_69e174de2cd48190ab18e48c9f051a2a completed April 16, 2026, 11:46 p.m.
PD Predicate disambiguation batch_69e142b976c081908d3ba3e705419f3a completed April 16, 2026, 8:12 p.m.
PDg Predicate description generation batch_69e174da2c2c819099ec46616798245a completed April 16, 2026, 11:46 p.m.
Created at: April 10, 2026, 4:50 a.m.