Arthur Stewart

The Witness Ordinance: The Manner by Which a Matter Is Established

A structural claim is established when two or more independent constructions, sharing no premises and passing through none of each other's steps, are each complete on their own terms and agree on the object. One construction is a result. Agreement of independent constructions is...

Cognitive Bias as Default Setting: An Architectural Argument

A person's biases are the person. They are the accumulated content the person's judgment is based on, present at every moment, shaping every output, observable in how the person judges anything they meet. The cognitive-bias literature has treated bias as something else, an error...

The Subconscious Circuit: A Neural Framework for Execution, Automaticity, and Flow

Three execution systems and one gate whose suppression enables them (the cerebellum, basal ganglia, and locus coeruleus, and the hippocampus) are the subconscious infrastructure for skilled execution, automaticity, and flow. During flow, the cerebellum, basal ganglia, and locus c...

The Subconscious Circuit: A Neural Framework for Execution, Automaticity, and Flow

Three execution systems and one gate whose suppression enables them (the cerebellum, basal ganglia, and locus coeruleus, and the hippocampus) are the subconscious infrastructure for skilled execution, automaticity, and flow. During flow, the cerebellum, basal ganglia, and locus c...

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 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...