TR-001: Formal Derivation of the 1.81 Stability Constant (R)

Title: TR-001: Formal Derivation of the 1.81 Stability Constant (R) Document Class: Foundational Proof / Axiomatic Derivation Core Reference: L=12 | σ≈1.382 | R=1.81 Abstract This document provides the formal mathematical and geometric derivation of the 1.81 Stability Constant (R), the fundamental metric utilized by the TR-001-V Verification Engine to audit AI reasoning integrity. The derivation is anchored in the 3D Kissing Number, which establishes the 12-Link Wall (L=12) as the maximum packing density for informational unit spheres surrounding a central grounding anchor. By calculating the Logarithmic Potential (P) of a 12-link chain and normalizing it against the Structural Scaling Factor (σ), we identify the critical equilibrium point of informational expansion. Implementation Note This derivation establishes R=1.81 as the precise "Critical Point" where the expansion of Semantic Entropy (ΔS) is perfectly balanced by the tension of the grounding substrate. Beyond this threshold, the system becomes "Super-Critical," leading to stochastic drift and hallucination. Implementations of the TR-001-V engine must utilize this constant to identify the Grounding Delta required to restore symmetry to recursive reasoning chains. Experimental Verification Guide, please visit the official repository: Github. Current Status: Version 2.0 - Hardened. Peer-validation of the 12th-link collapse is currently underway.