Triple

T22150693
Position Surface form Disambiguated ID Type / Status
Subject Bourgain–Tzafriri restricted invertibility principle E547403 entity
Predicate typeOf P4224 FINISHED
Object restricted invertibility theorem — NE NERFINISHED

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: restricted invertibility theorem | Statement: [Bourgain–Tzafriri restricted invertibility principle, typeOf, restricted invertibility theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: restricted invertibility theorem
Context triple: [Bourgain–Tzafriri restricted invertibility principle, typeOf, restricted invertibility theorem]
  • A. Banach inverse mapping theorem
    The Banach inverse mapping theorem is a fundamental result in functional analysis stating that a bijective bounded linear operator between Banach spaces has a bounded linear inverse.
  • B. Bourgain–Tzafriri restricted invertibility principle chosen
    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.
  • C. inverse function theorem
    The inverse function theorem is a fundamental result in calculus and differential geometry that gives conditions under which a differentiable function has a locally defined differentiable inverse near a point where its derivative is invertible.
  • D. Subspace theorem
    The Subspace theorem is a fundamental result in Diophantine approximation that describes how solutions to certain inequalities involving linear forms over algebraic numbers must lie in a finite union of proper subspaces.
  • E. 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.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

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.