4 problems

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The Level Conjecture for finite field-realized quaternionic structures
Level Conjecture. All finite quaternionic structures coming from fields have level in
Conjecturerefutedquadratic-forms quaternionic-structuresarXiv posted 2 days ago
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The weak Elementary Type Conjecture for field-realized quaternionic structures
Weak Elementary Type Conjecture. Every finite quaternionic structure that is realized by a field is of elementary type.
Conjecturerefutedquaternionic-structures witt-ringsarXiv posted 2 days ago
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The Elementary Type Conjecture for finite quaternionic structures
Elementary Type Conjecture. Every finite quaternionic structure is of elementary type.
Conjecturerefutedquaternionic-structures witt-ringsarXiv posted 2 days ago
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The Elementary Type Conjecture for finitely generated Witt rings
Elementary Type Conjecture. Every finitely generated Witt ring is of elementary type.
Conjecturerefutedquaternionic-structures witt-ringsarXiv posted 2 days ago

The Level Conjecture for finite field-realized quaternionic structures