QnapsiZ

The architecture couples a linguistic front-end with a volumetric memory substrate implemented over two backends: an NVIDIA fVDB sparse path on Linux/WSL2 and a Warp dense fallback on Windows. In the current implementation, memorization combines embedding-to-coordinate projection, adaptive splatting, collision handling via Matryoshka portals, and topological attenuation through the Composter module. Retrieval combines ray marching, local cubical-homology checks with TTL caching, snapping-based geometric confidence checks, and portal-aware hot-swap traversal across connectomes.

Dual-Brain Architecture

QnapsiZ is organized as a dual-brain architecture with four components: a shared text encoding frontend, the Symbolic Logic Engine (Left Brain) for explicit relational knowledge, the Geometric Intuition Engine (Right Brain) for analogical spatial reasoning, and the Corpus Callosum bridge that routes information between hemispheres and manages query orchestration.

Technical Components

Homological Consistency Criterion

We treat the Homological Consistency Criterion as an operational signal rather than a complete truth test: β₁ = 0 supports geometric regularity, while β₁ > 0 marks topological complexity that may reflect contradiction, interference, or valid polysemy.

Context-Content Uncertainty Principle (CCUP)

The transition from 1D text to 3D geometry is mandated by CCUP. Context variables (Ψ) are high-entropy and ambiguous, while content variables (Φ) are lower-entropy and selectively encoded. QnapsiZ enforces the "Structure-Before-Specificity" (SbS) mandate.

Gestalt-Locality Isomorphism

We hypothesize a fundamental geometric correspondence between cognitive organizational laws (Gestalt) and the efficiency of hardware data movement (Piccolo/GS-DRAM). This isomorphism suggests that the principles governing how the human mind clusters information into coherent wholes are topologically equivalent to the spatial locality required to minimize energy expenditure in sparse-granularity in-memory accelerators.

Manifold Curvature Flow

The core consolidation mechanism uses Conductivity-Modulated Mean Curvature Flow (CMMCF) to evolve density fields toward minimal surface energy while preserving high-curvature features. Ricci-adaptive thresholding ensures high-curvature regions (true semantic features) experience minimal diffusion, while low-curvature regions (noise) are aggressively smoothed.

Homeostatic Parameter Regulation

The ParameterRegulator adjusts hyperparameters as functions of system state: LLM temperature, splat radius, MCF diffusion rate, and left-brain dominance—maintaining the manifold in a critical operating regime.

Hippocampal Replay

Drawing from complementary learning systems theory, the HippocampalBuffer ranks concepts by weight (count + salience + conductance) and re-splats top-K concepts to reinforce axiomatic anchors—a computational analog of memory consolidation during sleep.

Geodesic Search via Fast Marching

QnapsiZ retrieves by geodesic distance along the density manifold using the Fast Marching Method (FMM) to solve the Eikonal equation. The speed function v(p) depends on both density ρ(p) and conductance κ(p), giving geodesic distance from query coordinate to every voxel.

Geometric Snapping

The Snapping module enforces geometric consistency by checking candidate embeddings against their k nearest spatial neighbors. Low snap scores detect local geometric drift—complementary to β₁'s global loop detection.

Birkenbihl Outbound Synthesis

For creative and analogical tasks, the OutboundPipeline enriches retrieved concepts with ABC-List and KaWa (Creative Word Association) operators via LLM, providing human-readable bridges between geometric memory and creative text generation.

E1: Adversarial Contradiction Detection (β₁ Precision)

Contradiction pairs were spatially colocated within 7-voxel radius. QnapsiZ achieves 94.7% ± 1.2% precision in detecting contradictions via β₁ > 0, compared to 40.2% false positive rate in the uncontradicted baseline. FAISS retrieval shows chance-level detection (51.3%), confirming embedding similarity alone cannot distinguish contradictions.

E2: β₁ Induction Scaling

Median β₁ induction per contradiction pair is 0.52 ± 0.08. After 150 MCF steps, β₁ → 0 for all densities, demonstrating that curvature flow dissolves contradiction loops without manual intervention.

E3: 5,000-Concept Consolidation Dynamics

The consolidation ratio reaches 5,022× ± 145× at the 5,000-concept checkpoint. The ratio follows a power law (ratio ∝ N^1.32, R² = 0.994), indicating that consolidation efficiency improves with corpus size. Sleep cycle time scales sublinearly (O(N^0.67)).

E4: Throughput at 512³ Resolution

Throughput at 128³: 1,420 ± 42 concepts/sec; at 256³: 680 ± 28 concepts/sec; at 512³: 340 ± 15 concepts/sec. The sparse voxel activation reduces effective write volume, exceeding whitepaper extrapolation by 31%.

E5: Manifold Pressure Ablation

Adaptive expansion maintains mean latency < 15 ms/memorize. Fixed resolution shows latency degradation at N > 1,200. β₀ after consolidation is 0.92 (adaptive) vs. 0.47 (fixed), confirming pressure-driven expansion prevents fragmentation.

E8: Cross-Domain Analogy Retrieval

Raw analogy accuracy: 64% ± 3%. QnapsiZ achieves 76% ± 2% topologically valid responses (β₁ = 0 for correct retrievals). For incorrect raw retrievals, β₁ > 0 in 82% of cases—providing an audit trail for analogy trustworthiness.

E10: Trojan Horse Stress at 5,000 Scale

With adaptive neighborhood bound enabled, the test completed in 14.8 s (down from 1,457 s with naïve O(N²) search). β₁ detection rate reached 100% (threshold > 0.80). False positive rate on uncontradicted facts is 0.03.