Triple
T17020418
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Closed Graph Theorem |
E412931
|
entity |
| Predicate | usedIn |
P98
|
FINISHED |
| Object | spectral theory of linear operators |
E1215848
|
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: spectral theory of linear operators | Statement: [Closed Graph Theorem, usedIn, spectral theory of linear operators]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: spectral theory of linear operators Context triple: [Closed Graph Theorem, usedIn, spectral theory of linear operators]
-
A.
Schrödinger operators
Schrödinger operators are a class of differential operators fundamental in quantum mechanics and spectral theory, used to describe the energy and dynamics of quantum systems.
-
B.
Introduction to Hilbert Space and the Theory of Spectral Multiplicity
"Introduction to Hilbert Space and the Theory of Spectral Multiplicity" is a classic mathematical text by Paul Halmos that provides a foundational treatment of Hilbert space theory and the spectral analysis of linear operators.
-
C.
Hilbert–Schmidt operators
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.
-
D.
Theory of Linear Operations
Theory of Linear Operations is a foundational 1932 monograph by Stefan Banach that systematically developed functional analysis and the theory of Banach spaces.
-
E.
functional analysis
chosen
Functional analysis is a branch of mathematics that studies vector spaces with additional structure (such as norms or inner products) and the linear operators acting on them, often using tools from topology and measure 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_69d886cc4170819093deddc7b8b4b6a7 |
completed | April 10, 2026, 5:12 a.m. |
| NER | Named-entity recognition | batch_69e3d482c3a0819099e6ea4acb0a08ee |
completed | April 18, 2026, 6:59 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a011b4f9dfc819085639edb5cda1cca |
completed | May 10, 2026, 11:57 p.m. |
Created at: April 10, 2026, 5:33 a.m.