基底无关计算:混沌介质中计算功能的存在性与构造性 (Substrate-Independent Computation: Existence and Constructibility of Computational Functions in Chaotic Media)

What if we stop manufacturing computation, and start educating chaos? As Moore's Law hits the wall of quantum tunneling and thermal limits, traditional computing architecture is running out of road. This paper proposes a radical paradigm shift: Substrate-Independent Computation (SIC). Instead of meticulously designing physical chips to force specific logic, we prove that any chaotic, un-designed physical system mathematically contains the capacity for arbitrary finite computation—waiting to be harnessed. Formulated as Dec ∘ Φ ∘ Enc = f, computation is elegantly decoupled from its physical substrate. We mathematically prove that while "Lookup Table" implementation is trivially guaranteed by random scattering, true power lies in compression. We establish the exact necessary and sufficient dimension conditions (n ≤ min(d, D) and n ≤ min(D, d^2)) for linear readout implementations. Crucially, we introduce the "Textbook Transfer Theorem": a computational function mined in one chaotic medium can be instantly transferred to a completely new substrate using just n calibration shots—shifting the cost from hardware fabrication to software education. We also boldly define the physical architecture of this new era: Optoelectronic Hybrid (O/E) computing. We reject the impractical utopia of all-optical computers. Instead, we leverage light as an ultrafast, stateless, parallel evaluation engine (光求值), while fully embracing the irreplaceable legacy of electronics for memory and sequential logic control (电主控). Key philosophical takeaway: Computation is not an intrinsic property of matter; it is an interpretation imposed by an observer. When the road of precision manufacturing comes to an end, the light still scatters in the chaos, waiting for its interface.