SUBSTRATE REQUIREMENT

Physical Substrates of Information

Comprehensive list of known information carriers:

| Domain | Substrate | Information Encoding |

|--------|-----------|---------------------|

| Classical computing | Transistors/magnetic domains | Voltage levels / magnetization |

| Quantum computing | Superconducting qubits, ions | Energy levels / spin states |

| Biological | DNA/RNA | Nucleotide sequences |

| Neural | Synaptic connections | Connection weights / firing patterns |

| Thermodynamic | Particle configurations | Phase space coordinates |

| Optical | Photon polarization/phase | Quantum states |

| Gravitational | Spacetime curvature | Metric tensor components |

No exception has ever been found. Every instance of information in physics has a physical carrier.

Formal Substrate Requirement

Definition: A substrate for information I is a structure S such that:

1. Instantiation: I is realized in S (there exists an embedding i: I → S)

2. Retrievability: I can be extracted from S (there exists a projection p: S → I)

3. Dynamics: Changes in I correspond to changes in S (ΔI ⇔ ΔS)

Mathematical formulation:

\text{Info}(x) \text{ exists} \Rightarrow \exists S: \text{Substrate}(S) \land \text{Instantiates}(S, \text{Info}(x))

• Landauer's Principle
• Bérut et al.

Bridge Count: 7