A Proposal for a Mathematical Theory of Physical Reconstruction (MTPR)

This paper introduces the Mathematical Theory of Physical Reconstruction (MTPR) — a conceptual framework extending Claude Shannon’s 1948 Mathematical Theory of Communication into the physical domain of fabrication and reconstruction. MTPR seeks to quantify how much information is required to reproduce a physical object within a target fidelity. It defines key quantities such as Object Entropy (H_obj), Teleportation Fidelity Index (TFI), and Physical Channel Capacity (C_m), and models reconstruction as a multi-stage information channel involving scanning, encoding, transmission, decoding, and verification. The theory proposes an Error-Corrected Physical Teleportation (EC–PT) model to describe redundancy and semantic parity in physical reproduction, and suggests an experimental framework using 3D scanning and printing to empirically measure rate–fidelity tradeoffs. This paper is released to ensure that the question — “How much information is required to reconstitute matter within a target fidelity?” — exists in the scientific record and can be refined by future researchers.