Triple

T20471195
Position Surface form Disambiguated ID Type / Status
Subject Hermite–Minkowski theorem E502195 entity
Predicate relatedTo P37 FINISHED
Object Minkowski’s 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: Minkowski’s theorem | Statement: [Hermite–Minkowski theorem, relatedTo, Minkowski’s theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Minkowski’s theorem
Context triple: [Hermite–Minkowski theorem, relatedTo, Minkowski’s theorem]
  • 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. 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.
  • C. Mazur’s theorem on convex sets
    Mazur’s theorem on convex sets is a fundamental result in functional analysis that characterizes the structure and approximation properties of convex sets in Banach spaces, particularly via convex combinations of sequences.
  • D. Jarník–Besicovitch theorem
    The Jarník–Besicovitch theorem is a fundamental result in metric number theory that determines the Hausdorff dimension of sets of real numbers that are very well approximable by rationals.
  • E. Carathéodory’s theorem in convex geometry
    Carathéodory’s theorem in convex geometry is a fundamental result stating that any point in the convex hull of a set in ℝⁿ can be expressed as a convex combination of at most n+1 points from that set.
  • 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.