Triple

T15860187
Position Surface form Disambiguated ID Type / Status
Subject Hilbert–Schmidt operator E384562 entity
Predicate elementOf P11236 FINISHED
Object Schatten class S2 E384562 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: Schatten class S2 | Statement: [Hilbert–Schmidt operator, elementOf, Schatten class S2]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Schatten class S2
Context triple: [Hilbert–Schmidt operator, elementOf, Schatten class S2]
  • A. Fefferman–Phong inequality
    The Fefferman–Phong inequality is a fundamental result in harmonic analysis and partial differential equations that provides weighted \(L^2\) estimates controlling functions by their gradients and associated potentials.
  • B. Singular Integrals and Differentiability Properties of Functions
    "Singular Integrals and Differentiability Properties of Functions" is a landmark mathematical monograph by Elias M. Stein that developed the modern theory of singular integral operators and their role in harmonic analysis and differentiability.
  • C. Schwartz space
    Schwartz space is the function space of rapidly decreasing smooth functions on Euclidean space, fundamental in distribution theory and Fourier analysis.
  • D. Schwarzschild S
    Schwarzschild S is a small satellite impact crater on the far side of the Moon, located near the larger walled plain Schwarzschild.
  • E. Hilbert–Schmidt operators chosen
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • 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.