Triple

T1862413
Position Surface form Disambiguated ID Type / Status
Subject Helmut Hasse E34844 entity
Predicate notableWork P4 FINISHED
Object Hasse–Minkowski theorem E207311 NE FINISHED

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: Hasse–Minkowski theorem | Statement: [Helmut Hasse, notableWork, Hasse–Minkowski theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hasse–Minkowski theorem
Context triple: [Helmut Hasse, notableWork, Hasse–Minkowski theorem]
  • A. Hasse principle chosen
    The Hasse principle is a concept in number theory stating that a Diophantine equation has a rational solution if and only if it has solutions in all completions of the rationals, such as the real numbers and p-adic numbers.
  • B. Hasse–Arf theorem
    The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
  • C. Kronecker–Weber theorem
    The Kronecker–Weber theorem is a fundamental result in algebraic number theory stating that every finite abelian extension of the rational numbers is contained in a cyclotomic field generated by roots of unity.
  • D. Fermat's theorem on sums of two squares
    Fermat's theorem on sums of two squares is a result in number theory stating exactly which prime numbers (and, more generally, which integers) can be expressed as the sum of two perfect squares.
  • E. Hasse invariant
    The Hasse invariant is an arithmetic invariant in number theory and algebraic geometry that classifies structures such as quadratic forms or elliptic curves over local and global fields, playing a key role in local-global principles.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69a88600b2f88190bc09303e68ab517e completed March 4, 2026, 7:20 p.m.
NER Named-entity recognition batch_69abb09e714881909cef0f7e77b5b3b9 completed March 7, 2026, 4:59 a.m.
NED1 Entity disambiguation (via context triple) batch_69addf4ecdc08190a264b358d3883f70 completed March 8, 2026, 8:42 p.m.
Created at: March 4, 2026, 7:34 p.m.