Triple
T8640755
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Frigyes Riesz |
E204639
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Riesz–Thorin interpolation theorem
The Riesz–Thorin interpolation theorem is a fundamental result in functional analysis that provides bounds for linear operators between Lᵖ spaces by interpolating their behavior between two known endpoint estimates.
|
E746578
|
NE FINISHED |
How this triple was built (4 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: Riesz–Thorin interpolation theorem | Statement: [Frigyes Riesz, knownFor, Riesz–Thorin interpolation theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Riesz–Thorin interpolation theorem Context triple: [Frigyes Riesz, knownFor, Riesz–Thorin interpolation theorem]
-
A.
Riesz–Fischer theorem
The Riesz–Fischer theorem is a fundamental result in functional analysis that establishes the equivalence between square-summable sequences and square-integrable functions, providing the foundation for the Hilbert space structure of L² spaces.
-
B.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
C.
Bourgain–Tzafriri restricted invertibility principle
The Bourgain–Tzafriri restricted invertibility principle is a fundamental result in functional analysis and operator theory that guarantees the existence of large, well-invertible submatrices within certain classes of linear operators.
-
D.
Banach–Stone theorem
The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
-
E.
Gagliardo–Nirenberg interpolation inequalities
The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Riesz–Thorin interpolation theorem Triple: [Frigyes Riesz, knownFor, Riesz–Thorin interpolation theorem]
Generated description
The Riesz–Thorin interpolation theorem is a fundamental result in functional analysis that provides bounds for linear operators between Lᵖ spaces by interpolating their behavior between two known endpoint estimates.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Riesz–Thorin interpolation theorem Target entity description: The Riesz–Thorin interpolation theorem is a fundamental result in functional analysis that provides bounds for linear operators between Lᵖ spaces by interpolating their behavior between two known endpoint estimates.
-
A.
Riesz–Fischer theorem
The Riesz–Fischer theorem is a fundamental result in functional analysis that establishes the equivalence between square-summable sequences and square-integrable functions, providing the foundation for the Hilbert space structure of L² spaces.
-
B.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
C.
Bourgain–Tzafriri restricted invertibility principle
The Bourgain–Tzafriri restricted invertibility principle is a fundamental result in functional analysis and operator theory that guarantees the existence of large, well-invertible submatrices within certain classes of linear operators.
-
D.
Banach–Stone theorem
The Banach–Stone theorem is a fundamental result in functional analysis that characterizes compact Hausdorff spaces via isometric isomorphisms between their spaces of continuous real- or complex-valued functions.
-
E.
Gagliardo–Nirenberg interpolation inequalities
The Gagliardo–Nirenberg interpolation inequalities are fundamental results in functional analysis and partial differential equations that bound intermediate norms of functions by combinations of lower and higher order norms, playing a key role in regularity theory and nonlinear analysis.
- F. None of above. chosen
Provenance (5 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_69ca834ca1c88190a11ffb0200342fac |
completed | March 30, 2026, 2:06 p.m. |
| NER | Named-entity recognition | batch_69cc47944d1c819081f448f14d04bf9d |
completed | March 31, 2026, 10:15 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69cebc340528819085c80b69d6d32a34 |
completed | April 2, 2026, 6:57 p.m. |
| NEDg | Description generation | batch_69cebcdb197881908eeb6c5e4b225a2c |
completed | April 2, 2026, 7 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69cebd85ad8481909518afd02dbc5358 |
completed | April 2, 2026, 7:03 p.m. |
Created at: March 30, 2026, 6:28 p.m.