Triple

T15860215
Position Surface form Disambiguated ID Type / Status
Subject Hilbert–Schmidt operator E384562 entity
Predicate hasDuality P31338 FINISHED
Object dual of Hilbert–Schmidt space is itself via Hilbert–Schmidt inner product — 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: dual of Hilbert–Schmidt space is itself via Hilbert–Schmidt inner product | Statement: [Hilbert–Schmidt operator, hasDuality, dual of Hilbert–Schmidt space is itself via Hilbert–Schmidt inner product]
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: hasDuality
Context triple: [Hilbert–Schmidt operator, hasDuality, dual of Hilbert–Schmidt space is itself via Hilbert–Schmidt inner product]
  • A. haveDualityProperty
    Indicates that an entity possesses a characteristic or state that inherently consists of two complementary, contrasting, or coexisting aspects.
  • B. dualPair chosen
    Indicates that two entities form a dual pair, standing in a mathematically defined dual relationship where each is the dual counterpart of the other.
  • C. dualLicensed
    Indicates that an entity is simultaneously licensed under two distinct licenses or licensing regimes.
  • D. hasTwinFeature
    Indicates that two entities share an identical or nearly identical feature, characteristic, or component, as if they are twins in that respect.
  • E. dualHattedAs
    Indicates that a single individual simultaneously holds two distinct official roles, positions, or responsibilities.
  • 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_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.
Created at: April 10, 2026, 4:50 a.m.