Neurolixis (United States)

One Bit Resurrects The Dead Form

The four-vertex strongly connected quiver Q's canonical bilinear invariant selects nothing, and its formula has no argument position for a sign. Let Q be the quiver with arrows a₁: L → S, a₂: S → T, a₃: T → C, a₄: C → L, a₅: L → T, a₆: C → T, whose unique in-degree-three vertex i...

One Bit Resurrects The Dead Form

The four-vertex strongly connected quiver Q's canonical bilinear invariant selects nothing, and its formula has no argument position for a sign. Let Q be the quiver with arrows a₁: L → S, a₂: S → T, a₃: T → C, a₄: C → L, a₅: L → T, a₆: C → T, whose unique in-degree-three vertex i...

The Endomorphic Collapse Traverses the Foundations of Mathematics

This quiver's canonical bilinear form is provably dead: indefinite, selecting no Dynkin type at all. One bit, a sign on a single vertex, is the entire distance from that form to the Cartan matrix of su(3) ⊕ su(2). The forms deadness is what makes the gauge content live in the bit...

The Forced Operational Ordering of Logic, Sets, Types, and Categories: The Foundations of Mathematics

Any mathematical construction requires four operations to be performed in a fixed structural order. The four operations are distinction, placement, identity, and composition. Logic formalizes distinction, sets formalize placement, types formalize identity, and categories formaliz...

The Endomorphic Collapse Traverses the Foundations of Mathematics

This quiver's canonical bilinear form is provably dead: indefinite, selecting no Dynkin type at all. One bit, a sign on a single vertex, is the entire distance from that form to the Cartan matrix of su(3) ⊕ su(2). The forms deadness is what makes the gauge content live in the bit...