Triple

T18897002
Position Surface form Disambiguated ID Type / Status
Subject Cassels–Fröhlich: Algebraic Number Theory E462233 entity
Predicate topic P261 FINISHED
Object Minkowski theory 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: Minkowski theory | Statement: [Cassels–Fröhlich: Algebraic Number Theory, topic, Minkowski theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Minkowski theory
Context triple: [Cassels–Fröhlich: Algebraic Number Theory, topic, Minkowski theory]
  • A. Minkowski’s theorem on convex sets chosen
    Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
  • B. Minkowski space-time
    Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
  • C. Hermite–Minkowski theorem
    The Hermite–Minkowski theorem is a fundamental result in algebraic number theory that gives a finiteness bound on the number of number fields of a given degree and discriminant.
  • D. Erlangen Program
    The Erlangen Program is Felix Klein’s influential 1872 framework that classifies and studies geometries based on their underlying symmetry groups and transformation properties.
  • E. Lorentzian geometry
    Lorentzian geometry is the branch of differential geometry that studies manifolds equipped with metrics of Lorentzian signature, providing the mathematical framework for general relativity and spacetime physics.
  • 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_69d8dcfd05bc819088903cca13cc2846 completed April 10, 2026, 11:20 a.m.
NER Named-entity recognition batch_69e5c47f6c948190918ade08bb88f1fd completed April 20, 2026, 6:15 a.m.
Created at: April 10, 2026, 11:58 a.m.