The Needham Scaling Constant as a Stability-Derived Invariant from Vacuum Suppression

This work presents a stability-based derivation of the Needham Scaling Constant (NSC) as an emergent invariant arising from extreme vacuum energy suppression between the Planck scale and observable matter scales. The constant is not assumed, fitted, or constructed from symbolic mathematical constants. Instead, it emerges from physical requirements of locality, causality, and recursive stability across a vast hierarchy of scales. The framework shows that stable matter can only persist if vacuum suppression occurs through finite, iterated steps rather than a single discontinuous transition. Enforcing overlap preservation between adjacent scales constrains the effective per-step scaling factor to a narrow admissible window. Numerical tests across multiple independent matter anchors demonstrate that the empirically observed NSC lies naturally within this stability window. The paper carefully distinguishes origin from representation: the NSC is fixed by stability constraints, while any later appearance of familiar mathematical constants is treated as descriptive rather than generative. The results are fully reproducible and supported by an explicit computational validation, but the present version is released solely to establish authorship, priority, and conceptual structure pending further refinement. nsc_stability_paper