A Topological Intermediate Representation, Lattice Vector Quantizer, and Cellular Sheaf Consensus Runtime for Edge-to-Workstation Heterogenous Computing {Aegis Cascade Topology}

Deploying multi-model neural inference and deterministic state machines across heterogeneous, memory-constrained hardware—spanning workstation GPUs and mobile NPU/CPU edge nodes—faces three persistent bottlenecks: non-deterministic concurrency hazards across foreign function boundaries, severe quantization distortion below 2 bits per weight, and split-brain state divergence during distributed execution. We present ACT-Omega (ACT-Ω) and Vesper, a unified polyglot systems architecture implemented in Rust, C++23, and Deno/TypeScript that resolves these bottlenecks by mapping algebraic topology and high-dimensional sphere packing directly to bare-metal compiler and systems primitives. First, we introduce BraidIR, a non-commutative Static Single Assignment (SSA) dependency graph modeled on the Artin Braid Group (Bn). BraidIR encodes sequential read-after-write hazards as non-commutative braid crossings (ii+1i+1i), exposes lock-free data parallelism via far-commuting strands (ij=ji for i-j ≥ 2), and executes compile-time dead-code and idempotency elimination via Reidemeister Type II collapses (ii-1e). Second, we detail the Sovereign Harmonic (SH4Z) memory layer, a zero-copy, page-aligned Tag-Length-Value (mmap TLV) serialization format pairing Conway-Sloane E8 Lattice Vector Quantization (E8R8) and 24-dimensional Leech Lattice codebooks (24) with 1.58-bit ternary execution ({-1,0,+1}), significantly lowering mean-squared quantization error (MSQE) near the Shannon rate-distortion bound while replacing floating-point multiply-accumulate (FMA) operations with integer additions. Third, we formalize the Vesper Routing Engine, which models distributed memory shards as stalks on a Cellular Sheaf (F). By evaluating the coboundary operator across interface restriction maps, Vesper enforces strong global state linearizability when the first sheaf cohomology vanishes (H1(X;F)=0) and triggers a four-phase control-theoretic circuit breaker with write-ahead snapshot rollback whenever cohomological obstructions (H1(X;F)0) arise. We demonstrate the viability of this architecture across a heterogeneous tri-silicon cluster combining an x86_64 workstation host and ARM64 mobile edge nodes connected via QUIC peer-to-peer telemetry streams. 1. Introduction Modern local AI orchestration and high-assurance systems engineering increasingly require multiple specialized models and native execution runtimes to collaborate across heterogeneous silicon. A typical edge-to-host topology must coordinate high-throughput tensor kernels on discrete workstation GPUs (e.g., NVIDIA Ampere/Ada architectures via WebGPU/CubeCL) alongside low-power NPU/CPU pipelines on mobile edge devices (e.g., ARM64 Tensor architectures) over asynchronous peer-to-peer networks. However, conventional software stacks treat compiler scheduling, weight compression, and distributed state verification as isolated problems: Control-Flow Entanglement and IPC Hazards: Polyglot runtimes bridging C++23 memory buffers, Rust borrowing semantics, and high-level TypeScript state graphs routinely suffer from subtle race conditions, cyclic lock contention, and redundant serialization overhead across Foreign Function Interfaces (FFI). Sub-2-Bit Quantization Collapse: Standard scalar quantization methods (such as independent INT4/INT2 rounding) treat weights as statistically independent variables, ignoring high-dimensional geometric correlations and suffering severe perplexity degradation at extreme compression ratios (2 bits/weight). Distributed State Divergence: When multiple local language models or asynchronous state shards operate in a chained cascade, hallucinations, schema violations, or packet drops propagate downstream without a formal mathematical invariant capable of detecting and isolating split-brain inconsistencies in real time. In this paper, we argue that these three systems challenges—dependency scheduling, rate-distortion weight compression, and distributed linearizability—are fundamentally geometric and topological problems. We introduce ACT-Omega (ACT-Ω) and the Vesper State-Space Framework, a zero-Python, bare-metal software architecture that establishes a rigorous 1-to-1 isomorphism between topological invariants and concrete computer science primitives. 1.1 Topological Intermediate Representation (BraidIR) Rather than representing program execution as a flat control-flow graph, ACT-Omega compiles execution traces and inter-process communication (IPC) channels into BraidIR, an intermediate representation grounded in the n-strand Artin Braid Group (Bn). In BraidIR, each strand i ∈ \1 n\ represents an isolated register, memory ring, or execution thread. When two operations share a memory boundary or exhibit a sequential happens-before dependency (), they are encoded as adjacent non-commutative braid generators (ii+1i+1i). Conversely, operations acting on disjoint memory regions are encoded as far-commuting generators (ij=ji for i-j ≥ 2), allowing the compiler to provably schedule lock-free parallel execution across threads. Furthermore, topological equivalence moves directly drive compiler optimization passes: Reidemeister Type II reductions (ii-1e) act as an algebraic peephole optimizer that strips self-canceling state mutations and redundant lock pairs, while Reidemeister Type III moves (ii+1i=i+1ii+1) enable latency-hiding instruction reordering under strict semantic preservation. 1.2 High-Dimensional Lattice Vector Quantization (SH4Z) To fit multi-billion-parameter reasoning cascades within tight workstation VRAM and mobile unified memory budgets, ACT-Omega abandons scalar weight rounding in favor of Gain-Shape Lattice Vector Quantization. Drawing on optimal sphere-packing bounds in R8 and R24, our quantization engine projects contiguous 8-element and 24-element weight sub-vectors onto the 240-root E8 Gosset polytope (E8) and the Leech lattice (24) via fast Conway-Sloane coset decoding. By decoupling vector orientation (quantized to discrete lattice roots and 1.58-bit ternary states {-1,0,+1}) from radial magnitude (stored via dual-shell Quantization-Aware Training projection heads), the runtime achieves superior vector packing density per bit and executes matrix projections using multiplier-free integer addition and zero-skipping bitmasks. Weights are packaged in the SH4Z v3101 Tag-Length-Value (TLV) binary format—a deterministic, 64-byte-aligned container that maps directly into virtual memory (mmap) with zero heap allocation or deserialization parsing latency. 1.3 Cellular Sheaf Consensus and Control-Theoretic Fault Recovery (Vesper & UARM) To coordinate execution across memory boundaries and multi-model deliberation pipelines—specifically our Universal Agent Reasoning Model (UARM) cascade—the Vesper routing engine models distributed system state as a Cellular Sheaf F over a communication graph X=(V,E). Each computational node or model stage vV maintains a local state vector (stalk F(v)), while shared memory rings and IPC schemas are governed by linear restriction maps Fv e : F(v) → F(e). Using the sheaf coboundary operator and the Sheaf Laplacian (LF=T), the runtime continuously audits cross-boundary agreement at a deterministic 15.965 Hz real-time scheduling cadence (=62.636ms watchdog quantum): Global Linearizability (H1(X;F)=0): When the first sheaf cohomology vanishes, all local state shards satisfy their boundary contracts, guaranteeing a globally consistent, race-free execution state (a global section (X,F)). PID Dampening and Circuit-Breaker Quarantine (H1(X;F)0): When thread contention, queue backpressure (writhe imbalance Δφ > 0.40), or a Byzantine schema violation induces a non-zero cohomological obstruction, the runtime transitions through a deterministic 4-phase recovery cycle: Phase 1 (Cascade Core): Nominal lock-free execution. Phase 2 (RAS Dampening): A 30% proportional-derivative step contraction (0.70) that scales down logit temperature or queue ingestion rates to suppress oscillatory divergence. Phase 3 (Stomachion Circuit Breaker & Aegis Failover): If the obstruction persists, the faulting state shard is isolated behind zero-flux boundary conditions while healthy traffic is rerouted through disjoint far-commuting failover channels (5-1). Phase 4 (Topological Reboot): Corrupted memory rings are rolled back to the last verified immutable E8 lattice checkpoint (verified via unitary norm preservation Tr(Ures)=1.00000) and restitched into the global state graph. 1.4 Contributions The primary contributions of this work are fourfold: The BraidIR Execution Model: A formal mapping between Artin braid generators and lock-free Static Single Assignment (SSA) dependency scheduling, implemented natively across Rust and C++23 without garbage-collected runtime pauses. Sub-2-Bit Lattice Vector Quantization (SH4Z): An end-to-end quantization and zero-copy mmap serialization pipeline leveraging E8E_8E8​ and Leech lattice Voronoi codebooks alongside 1.58-bit ternary arithmetic. Sheaf-Verified Distributed Routing (Vesper): A real-time consistency verifier that uses cellular sheaf cohomology (H1H^1H1) and a 536-mode combinatorial task scheduler (Stomachion Router) to guarantee fault-isolated execution across multi-model cascades (UARM). Tri-Silicon Heterogeneous Validation: An empirical systems implementation uniting an x86_64 Windows workstation host (Intel Core i5-12450HX, NVIDIA RTX 3050) with ARM64 Android edge nodes (Google Tensor G5 and G3) via QUIC peer-to-peer streams and ADB loopback bridges. The remainder of this paper is organized as follows: Section 2 formalizes the algebraic structure of BraidIR and Reidemeister compiler passes; Section 3 derives the rate-distortion bounds and Conway-Sloane decoding algorithms of the E8E_8E8​/Leech SH4Z quantizer; Section 4 defines the Cellular Sheaf Laplacian and the 4-phase fault