A QMU-Ledger Derivation of the Nuclear Binding Length: Holonomic Twist as the Origin of the Mass Deficit (QMU)

This paper presents a purely holonomic derivation of the nuclear binding energy using the Quantum Measurement Units (QMU) and the Aether Physics Model (APM). In this framework, the nuclear mass deficit is not interpreted as a loss of mass but as a geometric projection effect: a portion of each nucleon's 5-dimensional loxodromic mass-string is rotated out of the 4-dimensional projection by Aether curl. The resulting "Nuclear Binding Length" is the QMU ledger index that quantifies the total holonomic twist stored in the 5-dimensional Aether. The central result is a linear holonomy binding-length functional,\[Bₗₑₙ =C₀\,Bκ+C₁\,Δ Bκ+C₂\,Φₚₐᵣₜᵢₐₗ+C₃\,ΦCoul+C₄\,A ,\]whose QMU binding energy is\[EbindQMU =Aᵤ\,Bₗₑₙ .\] This functional depends only on holonomic curvature depth \((Bκ)\), curvature imbalance \((Δ Bκ)\), partial-shell twist tension \((Φₚₐᵣₜᵢₐₗ)\), Coulomb opposition \((ΦCoul)\), and the nucleon ledger \(A = Z+N\). No liquid-drop volume, surface, asymmetry, pairing, or radius-scaling assumptions are invoked. Using evaluated binding-energy data for 2,927 nuclei, the MeV-calibrated SI version of the model is\[EbindSI(Z,N) =C₀SI\,Bκ+C₁SI\,Δ Bκ+C₂SI\,Φₚₐᵣₜᵢₐₗ+C₃SI\,{Z(Z-1)}{Sdom}+C₄SI\,(Z+N),\]with fitted coefficients\[C₀SI=-0.125391, ₁SI=-0.112268, ₂SI=-16.905587, ₃SI=+0.201416, ₄SI=+8.849416 .\] The global fit achieves\[R² = 0.9998141782, = 16.18~MeV,\]matching or surpassing the performance of many Skyrme and Gogny mean-field parameterizations while being derived from a simpler, fully geometric QMU ledger. The Nuclear Binding Length provides a new physical interpretation of the mass deficit as conserved holonomic twist, rather than energy "lost" from the nucleus. Magic numbers arise naturally from the vanishing of curvature imbalance and partial-shell twist, \(Δ Bκ=0\) and \(Φₚₐᵣₜᵢₐₗ=0\), giving a geometric explanation for shell closures. The model is further validated by predicting representative magic nuclei such as \(⁴⁸Ca\), \(⁵⁶Ni\), \(¹⁰⁰Sn\), \(¹³²Sn\), and \(²⁰⁸Pb\) with high accuracy. All holonomy invariants, curvature ledgers, residuals, and scripts used for the results in this paper are included. The GitHub repository contains the full analysis code, Python holonomy ledger generator, and plotting tools:\[https://github.com/aetherwizard/Nuclear-Binding-Length.\] This work is part of the Quantum AetherDynamics Institute (QADI) program developing a unified metrological foundation for nuclear, gravitational, and electromagnetic phenomena in terms of Aether geometry and QMU.