Φᵈᶜᵖ: Factoring the Universe through the Web of the Adjacent Possible

The quest to factor large semiprimes has long been the "impenetrable wall" of modern cryptography. Standard methods like the General Number Field Sieve (GNFS) require massive, centralized clusters and sub-exponential time. However, a new paradigm is emerging at the intersection of finitist arithmetic and decentralized computing: the Integer Vector Inversion (IVI) mechanism powered by the Distributive Compute Protocol (DCP). We call this evolution Φᵈᶜᵖ. It is not just an algorithm; it is an expanding web of the "Adjacent Possible," where the mystery of a 2048-bit number is solved one digit at a time across a global fabric of idle processors. This paper presents the theoretical framework, mathematical foundations, and architectural principles of Φᵈᶜᵖ, demonstrating how digit-by-digit propagation combined with decentralized computation transforms factorization from an exponential search problem into a linear, distributable constraint satisfaction task across time and space.