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 NE NERFINISHED

How this triple was built (3 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.
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 (2 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.
Created at: April 16, 2026, 8:33 p.m.