Holonomery: Parallel Transport, SIMD Ternary Vectorization, and Soft-Gate Relaxation Theorems

Holonomery: Parallel Transport, SIMD Ternary Vectorization, and Soft-Gate Relaxation Theorems — A Differential Geometric and Machine-Checked Formal Framework for Zero-Deadlock Autonomous Decision Surfaces.

This monograph presents the formal architecture of Holonomery, unifying parallel transport holonomy trace deficits on curved decision manifolds with 2-bit packed SIMD balanced ternary logic, deterministic AST dual proposition generation (&mathcal;D(P)), and the machine-checked Soft-Gate Relaxation Theorem (τ_eff).

Key Breakthroughs:

• Parallel Transport Logic: Holonomy trace deficit R = 1 - tr(Hol¹⁴)/tr(I) measuring curvature-induced logical tension.
• 2-Bit SIMD Vectorization: Bitwise hardware gates (trit_and, trit_or) evaluating 32 parallel decision channels per 64-bit word execution.
• Deterministic AST Dual Generator &mathcal;D(P): Zero-shot hallucination elimination via chiral asymmetry scoring ΔS.
• Machine-Checked Soft-Gate Relaxation (τ_eff): Lean 4 verified theorem proving zero-deadlock execution under model entropy.