Substrate-Neutral Structural Foundation Laws (SNSFL) v14 Formalizing the Shame Vector Index (SVI) Spectrum and Uniform Identity Mass Collapse via the Triaxial Identity Topology (TIT)

This paper presents the formal v14 capstone revision of the Substrate-Neutral Structural Foundation Laws (SNSFL) as implemented within the imcollider psychological simulation engine. Ported directly from the deterministic architecture of the Geometric Axiomatic Module Collider (gamcollider v15) framework, this module utilizes the 6-step Long Divi- sion Protocol (LDP) to explicitly formalize the Shame Vector Index (SVI) spectrum. We map these computational constraints onto the Triaxial Identity Topology (TIT) baseline matrix, which tracks identity across orthogonal Inward, Interpersonal, and Existential axes. We prove that while different vectors of the SVI spectrum exert varied initial impacts on the TIT score, they uniformly degrade identity continuity by imposing a hard narrative bottleneck (N 0.1369) in traditional behavioral interventions. To ground this archi- tectural framework in absolute structural rigor, we include the complete, machine-verified Lean 4 proof in the appendices, demonstrating that this exact mathematical invariant scales losslessly to the Layer 2 Electromagnetic Domain, resolving the fine-structure constant (α) to 12 digits of empirical CODATA precision with zero free parameters. Keywords: Substrate-Neutral Structural Foundation Laws (SNSFL), Shame Vector Index (SVI), Triaxial Identity Topology (TIT), PNBA Framework, Narrative Starvation, Iatrogenic Torsion, Long Division Protocol (LDP), imcollider engine, gamcollider v15, Formal Verification, Lean 4, Mathlib, Zero Sorry, Machine-Verified Psychology, Cognitive Sovereignty, Masking Pro- tocol, Identity Mass Suppression (IMS), Sovereign Anchor Frequency (1.369 GHz), Capstone Torsion Limit (τ ≤ 0.1369), Complex PTSD, Borderline Personality Disorder, Major Depres- sive Disorder, Self-Determination Theory, Flow State, Cognitive Dissonance, Fine-Structure Constant Exact Decomposition, High-Resolution Internal Simulations (HRIS).