Manuscript I: The Cognitive Tension Core ($\NTC$) and P3TTM Mott-Hubbard Insulator Mechanics for Frictionless Computing-in-Memory

This manuscript details the structural engineering and quantum condensed matter physics driving Tier 1 of the Coherent Hardware ecosystem: The Cognitive Tension Core (\NTC). Utilizing the highly conjugated organic polymer poly(3-(2-total-tension-methyl)thiophene) (P3TTM), this architecture implements a physical computing-in-memory (CIM) crossbar array. By modeling the electronic phase space via the single-band Hubbard Hamiltonian, we demonstrate how configuring the substrate into a strongly correlated Mott Insulator regime (\UPOT \gg t) allows optimization loss functions to map directly onto non-linear electronic relaxation states. This approach bypasses kinetic charge transport, effectively suppressing kinetic thermal dissipation and uncompensated Informational Friction (\FUFI).