Triple

T20471197
Position Surface form Disambiguated ID Type / Status
Subject Hermite–Minkowski theorem E502195 entity
Predicate relatedTo P37 FINISHED
Object geometry of numbers 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: geometry of numbers | Statement: [Hermite–Minkowski theorem, relatedTo, geometry of numbers]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: geometry of numbers
Context triple: [Hermite–Minkowski theorem, relatedTo, geometry of numbers]
  • A. geometry of numbers chosen
    Geometry of numbers is a branch of number theory that studies the properties of integers and Diophantine equations using the geometry of lattices and convex bodies in Euclidean space.
  • B. Diophantine approximation
    Diophantine approximation is a branch of number theory that studies how closely real numbers can be approximated by rational numbers, often with quantitative bounds on the quality of approximation.
  • C. Diophantine geometry
    Diophantine geometry is the branch of number theory that studies solutions to polynomial equations with integer or rational coefficients using geometric methods, particularly those from algebraic geometry.
  • D. Hermite constant
    The Hermite constant is a number in each dimension that measures the densest possible lattice sphere packing, playing a central role in the geometry of numbers and lattice theory.
  • E. An Introduction to Diophantine Approximation
    "An Introduction to Diophantine Approximation" is a classic mathematical monograph that systematically develops the theory of approximating real numbers by rationals, aimed at advanced undergraduates and researchers in number theory.
  • 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_69e0b4ae5f1081908768b0c9a3a0bf38 completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e699608d7c8190910217817e789915 completed April 20, 2026, 9:23 p.m.
Created at: April 16, 2026, 11:33 a.m.