Triple

T6150018
Position Surface form Disambiguated ID Type / Status
Subject Enrico Bombieri E137175 entity
Predicate knownFor P22 FINISHED
Object Bombieri norm
The Bombieri norm is a mathematical norm on polynomials, introduced by Enrico Bombieri, that is particularly useful in analytic number theory and the study of polynomial inequalities.
E571013 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: Bombieri norm | Statement: [Enrico Bombieri, knownFor, Bombieri norm]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Bombieri norm
Context triple: [Enrico Bombieri, knownFor, Bombieri norm]
  • A. Banach–Mazur distance
    The Banach–Mazur distance is a numerical measure in functional analysis that quantifies how "far apart" two finite-dimensional normed vector spaces are up to linear isomorphism.
  • 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. Minkowski inequality
    The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
  • D. Bernstein inequalities
    Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
  • E. Fefferman–Phong inequality
    The Fefferman–Phong inequality is a fundamental result in harmonic analysis and partial differential equations that provides weighted \(L^2\) estimates controlling functions by their gradients and associated potentials.
  • 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: Bombieri norm
Triple: [Enrico Bombieri, knownFor, Bombieri norm]
Generated description
The Bombieri norm is a mathematical norm on polynomials, introduced by Enrico Bombieri, that is particularly useful in analytic number theory and the study of polynomial inequalities.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Bombieri norm
Target entity description: The Bombieri norm is a mathematical norm on polynomials, introduced by Enrico Bombieri, that is particularly useful in analytic number theory and the study of polynomial inequalities.
  • A. Banach–Mazur distance
    The Banach–Mazur distance is a numerical measure in functional analysis that quantifies how "far apart" two finite-dimensional normed vector spaces are up to linear isomorphism.
  • 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. Minkowski inequality
    The Minkowski inequality is a fundamental result in functional analysis and measure theory that generalizes the triangle inequality to L^p spaces, providing a key tool for studying norms and integrable functions.
  • D. Bernstein inequalities
    Bernstein inequalities are fundamental results in approximation theory and probability that provide bounds on the derivatives or deviations of functions and random variables under certain smoothness or moment conditions.
  • E. Fefferman–Phong inequality
    The Fefferman–Phong inequality is a fundamental result in harmonic analysis and partial differential equations that provides weighted \(L^2\) estimates controlling functions by their gradients and associated potentials.
  • 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_69c008a2c6308190a56519b22d55d083 completed March 22, 2026, 3:20 p.m.
NER Named-entity recognition batch_69c05ce329648190a03ba0233df841fa completed March 22, 2026, 9:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69c13608944481909e22df6131a06e41 completed March 23, 2026, 12:46 p.m.
NEDg Description generation batch_69c13679dd58819099036d1119fa370b completed March 23, 2026, 12:47 p.m.
NED2 Entity disambiguation (via description) batch_69c1376db6a0819087c0d0aebc2e2b3e completed March 23, 2026, 12:51 p.m.
Created at: March 22, 2026, 4:16 p.m.