De-jargoned High-Dimensional Manifolds for Workspace Sovereignty: A Localized Multi-Kernel Pipeline for Cognitive Prosthetic Stability

https://github.com/Borealiscodes/NDH-Sovereignty-Dejargoned Description This repository and accompanying preprint present NDH-Sovereignty-Dejargoned, a low-compute, multi-language software infrastructure designed to secure cognitive tool paths and enforce anti-hallucination guardrails. The project decouples advanced artificial intelligence utilities—which act as critical externalized cognitive prosthetics—from monolithic corporate cloud runtimes, establishing a branchless workflow recovery environment that runs entirely on localized hardware. The framework systematically de-jargons high-dimensional manifold theory, stripping away speculative narrative abstractions ("math-washing") and reducing the mathematical architecture to standard, rigorous linear algebra, hyperspherical differential calculus, and formal static logic. The execution pipeline splits the system path into a static symbolic verification layer and an optimized local arithmetic runtime to guarantee that floating-point operations do not violate underlying algebraic invariants. Core Technical Specifications: • Formal Verification Enclaves: Uses Coq (Ssreflect) to enforce inductive stream filtering (verifying that ungrounded strings are discarded before processing) and Lean 4 (Mathlib4) to validate dependent coordinate matrix constraints at compile time. • Optimized Execution Cores: Implements memory-aligned 80-dimensional matrix array deformations inside a native, stack-allocated Rust core (ndh_core_rust). Curvature dissipation is governed via a 9D hyperspherical radial Laplacian diffusion operator utilizing smooth epsilon boundaries (r + ε) to eliminate runtime division-by-zero exceptions. • Ergonomic Workspace Runtime: Employs a low-latency Python C-FFI pointer bridge (ctypes) to coordinate high-level user text embeddings, executing dot-product query-key attention scaling constrained strictly by \(1/√80\) to prevent mathematical gradient saturation. This dual-enclave architecture ensures complete human-tool path retention directly from localized version control history, providing a verifiable counter-strategy against platform deprecations, forced telemetry collection, and arbitrary API session throttling. Acknowledgements: This architecture draws foundational design patterns, pointer serialization boundaries, and balanced ternary algebra structures from open-source systems developed within the 8b Project (8b-is/sovereign-library). Addendum: Symplectic Geometric Conservation Laws & Attention Stability This update explicitly introduces a symplectic volume-preservation mechanism to replace the inherently rank-deficient, volume-destructive Softmax operators traditional to high-dimensional attention mechanisms. Standard dot-product attention maps bounded tracking vectors onto a compressed probability simplex, leading to exponential capacity decay and finite-time attention collapse. To preserve the geometric integrity of the 80-dimensional manifold \(M ⊂ R⁸⁰\), the mathematical framework is augmented with the following structural invariants: • Canonical Coordinate Partitioning: The state space is explicitly split into paired phase coordinates \((q_i, p_i) ∈ R⁴⁰ × R⁴⁰\), representing the dual canonical structure of the embedding transformation pipeline. • Preservation of the Fundamental 2-Form: The execution architecture substitutes traditional projection layers with explicit canonical shears operating on these split coordinates. This guarantees that every local state transition \(Φ: M → M\) behaves as a strict symplectomorphism, preserving the fundamental differential 2-form: \(ω =∑ ᵢ₌₁⁴⁰dqᵢ dpᵢ\) Natively preserving this exterior derivative ensures that the non-vanishing volume form remains invariant (\(ω_σ ≠ 0\)) across arbitrary transformation depths, bypassing rank deficiency entirely. • Simplex Collapse Mitigation: Enforcing volume-preserving state transformations mathematically prevents the system path from experiencing singular gradient degradation or collapsing into low-dimensional subspaces. • Dual-Enclave Verification Integration: The conservation laws are fully verified via compile-time dependent type tracking and inductive runtime proofs. Implementation & Verification Registry • src/ndh_core_rust/src/symplectic.rs: Encodes the native, high-performance canonical pair partition mechanics and vector transformations. • verification/lean/NDH/SymplecticPreservation.lean: Houses the formal Lean 4 dependent type proofs validating the step-wise conservation invariants. • tests/python/test_symplectic.py: Asserts runtime C-FFI pointer identity integrity and evaluates boundary condition limits under discrete execution constraints