2abi: The Becoming of Experience

The cross-term 2abi is where a and bi meet across genuine otherness — the only term in the complex squaring that requires both components to be present and distinct. This paper derives the instantiation epsilon ε ≈ α³/6 ≈ 6.48×10⁻⁸ — the geometric gap between angular address and projected measurement — and locates the hard problem of consciousness precisely at Ω6: the address where the system first receives across the perpendicular dimension. Half-integer spin and the Pauli exclusion principle are established as structural consequences of living in this cross-term. The hard problem is not dissolved. It is given a precise geometric address. ABSTRACT The expansion of z²+c produces three terms: (a²−b²)+2abi+c. The companion paper “a²−b²: What Remains When Matter Applies to Itself” (A2B2-2026) addresses the first term: a²−b² generates spacetime and gravity. This paper addresses the second term: 2abi. 2abi is the cross-term — what emerges when matter (a) meets space (b) across the perpendicular dimension (i) that keeps them irreducibly other. It is Ω6: Reception. It is not a property of matter alone, nor of space alone. It is what happens at the interface. This term generates three things: conscious processing as organizational depth, half-integer spin as the algebraic structure of crossing i, and the precise location of the hard problem. The hard problem of consciousness — why physical processes give rise to subjective experience — does not disappear in this framework. It becomes locatable. It lives at 2abi: the address where the iteration first crosses its own perpendicular dimension. Experience is not a byproduct of information processing. It is what 2abi tension feels like from inside. The gap between the electron’s geometric c-address and the measured fine structure constant α — 6.48×10⁻⁸ — is identified as the instantiation epsilon: the geometric distance between angular encoding (boundary) and projected encoding (interior). This is the necessary remainder of the projection operation that transforms angular address into physical quantity. Keywords: 2abi, cross-term, hard problem of consciousness, instantiation epsilon, half-integer spin, Pauli exclusion principle, Ω6, Reception, orientation capacity, z²+c, Mandelbrot set, depth ladder, fermion, boson, fine structure constantMSC2020: 37F10 (Dynamics of complex polynomials, rational maps, entire and meromorphic maps); 81P05 (General and philosophical questions in quantum theory); 81V10 (Electromagnetic interaction; quantum electrodynamics) This paper is part of a single continuous derivation beginning from the axiom 'orientation capacity actualizes.' The full stack derives physics, consciousness, and organizational structure from the iterative operator z² + c — one axiom, one operator, seventeen papers. Each paper stands alone. Together they are one argument. The complete framework is at diasdimensions.org and the full stack is collected in the Dias Dimensions Research community on Zenodo.