Information Reconstruction Theory: A Relational Coherence Framework for Asymmetric Compute, Low-Bandwidth Telemetry, and Post-Quantum Empty Signals

Abstract Classical information theory (Shannon, 1948) established the physical limits of transmitting data across noisy channels by assuming a zero-shared-state boundary condition ( 𝑆=∅ ), wherein the physical signal must carry 100% of the recoverable payload ( 𝐼𝑟=𝑡 ). This paper formalizes Information Reconstruction Theory ( 𝐼𝑟=𝑅(𝑡,𝑆) ), a generalized framework that shifts the operational burden of communication from physical channel transport ( 𝑡 ) to local endpoint state synthesis ( 𝑆 ). By modeling reconstructed information as an emergent function of minimal, drifted vector triggers evaluated against pre-existing, compatible endpoint state spaces, we demonstrate two primary paradigms: Bandwidth-Compute Substitution: In physically bandwidth-constrained or deep-space environments (e.g., interplanetary links), systems can trade physical channel throughput ( 𝐵→0 ) for local endpoint storage and energy compute ( 𝑆↑ ), rendering high-complexity operational states locally without heavy payload transport.Post-Payload Interpretation Layered Security (ILS): By decoupling semantic meaning from the physical transport layer, signals passing across the wire remain semantically void ( 𝐻∞(𝐼𝑟∣𝑡)≥𝐵 ). This eliminates the threat of Harvest Now, Decrypt Later (HNDL) attacks through temporal context decay and asymmetric min-entropy gaps, proving that security is an emergent property of relational context rather than computational vault hardness.We validate the framework across heterogeneous robotic execution models, historical linguistic analogues (the Rosetta Stone and Egyptian determinatives), and classical state bootstrapping mechanisms (Interpretation Secure Key Distribution / Shared-State Blackjack).