Triple
T22150702
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bourgain–Tzafriri restricted invertibility principle |
E547403
|
entity |
| Predicate | hasGeneralization |
P2372
|
FINISHED |
| Object |
Spielman–Srivastava restricted invertibility results
The Spielman–Srivastava restricted invertibility results are refined theorems in functional analysis and matrix theory that strengthen and generalize the Bourgain–Tzafriri restricted invertibility principle by providing sharper bounds and more flexible conditions for extracting well-invertible submatrices or coordinate restrictions.
|
E1522136
|
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: Spielman–Srivastava restricted invertibility results | Statement: [Bourgain–Tzafriri restricted invertibility principle, hasGeneralization, Spielman–Srivastava restricted invertibility results]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Spielman–Srivastava restricted invertibility results Context triple: [Bourgain–Tzafriri restricted invertibility principle, hasGeneralization, Spielman–Srivastava restricted invertibility results]
-
A.
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.
-
B.
Gowers–Hatami stability theorem
The Gowers–Hatami stability theorem is a result in functional analysis and group theory that characterizes when approximate representations of finite groups are close to genuine representations, providing a quantitative form of stability for such structures.
-
C.
Alon–Boppana bound
The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
-
D.
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.
-
E.
Babai–Fortnow–Lund–Safra–Szegedy theorem
The Babai–Fortnow–Lund–Safra–Szegedy theorem is a landmark result in computational complexity theory that characterizes the power of multi-prover interactive proofs by showing they capture exactly the class of nondeterministic exponential-time problems.
- 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: Spielman–Srivastava restricted invertibility results Triple: [Bourgain–Tzafriri restricted invertibility principle, hasGeneralization, Spielman–Srivastava restricted invertibility results]
Generated description
The Spielman–Srivastava restricted invertibility results are refined theorems in functional analysis and matrix theory that strengthen and generalize the Bourgain–Tzafriri restricted invertibility principle by providing sharper bounds and more flexible conditions for extracting well-invertible submatrices or coordinate restrictions.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Spielman–Srivastava restricted invertibility results Target entity description: The Spielman–Srivastava restricted invertibility results are refined theorems in functional analysis and matrix theory that strengthen and generalize the Bourgain–Tzafriri restricted invertibility principle by providing sharper bounds and more flexible conditions for extracting well-invertible submatrices or coordinate restrictions.
-
A.
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.
-
B.
Gowers–Hatami stability theorem
The Gowers–Hatami stability theorem is a result in functional analysis and group theory that characterizes when approximate representations of finite groups are close to genuine representations, providing a quantitative form of stability for such structures.
-
C.
Alon–Boppana bound
The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
-
D.
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.
-
E.
Babai–Fortnow–Lund–Safra–Szegedy theorem
The Babai–Fortnow–Lund–Safra–Szegedy theorem is a landmark result in computational complexity theory that characterizes the power of multi-prover interactive proofs by showing they capture exactly the class of nondeterministic exponential-time problems.
- 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_69e11e3b52088190ad5df386d01eb2fb |
completed | April 16, 2026, 5:36 p.m. |
| NER | Named-entity recognition | batch_69f129f37dac8190a7cecb12f4271515 |
completed | April 28, 2026, 9:43 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a0a9704f4988190b03783c006929ad7 |
completed | May 18, 2026, 4:35 a.m. |
| NEDg | Description generation | batch_6a0a97e509a88190a7f316cf340d010a |
completed | May 18, 2026, 4:39 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a0a987daa208190bab5b7adec1913e8 |
completed | May 18, 2026, 4:41 a.m. |
Created at: April 16, 2026, 8:33 p.m.