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.