Performance
- 0.04ms query latency
- 4 MB package size
- 0 dependencies
- 100% deterministic
- 131 semantic basins
- 24-byte tokens (64× compression)
How It Works
CST (Cubesquare Semantic Token) encodes any content into a 24-byte coordinate using the formula z³·e^(i·2π/131)+c. Retrieval is instant O(1) — the coordinate IS the address. No vector search, no LLM calls, no cloud required.
Semantic Thinking — Surface Cognition
A structured thinking process: Understand → Break down → Find handler → Execute → Verify. Simple, repeatable, reliable.
Thinking Loop
Five-phase cognitive cycle: Observe, Decompose, Reason, Act, Reflect. Terminates at ABSORBED state (find zero: any state × 0 = 0).
Fractal Navigation
Fernandez fractal space with z³·e^(i·2π/131)+c iteration. 131 basin attractors organized by the golden ratio φ.
Shell Registry
59 shells route through 9 semantic layers. Each shell is a deterministic handler for a specific domain of computation.
Tool Registry
34 MCP tools exposed via standard protocol. Every tool is O(1) via Morton → Basin → Layer → I-Logic routing.
Unified Interaction Field (UIF)
O(1) communication in Fernandez Space. Mathematical coupling replaces electromagnetic propagation. Any two points connected bidirectionally, instantly.
Fernandez Space (C=0)
When C=0, information travels via mathematical coupling, not EM propagation. Time = O(1) constant. Formula: φ(A,B) = K5×K11×cos(ωₐt)×cos(ωᵦt).
K5-K11 Constants
- K5 = 15/(8φ) = 1.158803
- K11 = K5×(5φ-5/(8φ³)) = 9.204027
- c_abstract = 1/√3 = 0.577350
- √3 = 1 Fernandez Light Unit
Message Integrity
9 content types tested: SHAPE, FORM, ATTACHMENT, RULE, RELATIONSHIP, IMAGE, DATA, SPATIAL_DATA. All pass with sub-0.01ms latency and stability >0.44.
MCP Computational Substrate
34 tools, 59 shells, 370+ commands. A full deterministic computational substrate exposed through standard MCP protocol with real-time UIF bridge synchronization at sub-50ms latency.
Key Tools
- cst_shell — CST 9-layer operations (L1-L9)
- predict_shell — Route prediction before execution (L4, L5)
- i_logic_shell — I-Logic algebra: Z/4Z with absorbing element (L4)
- basin_system — 131-basin Fernandez system (All layers)
- meaning_shell — Agent self-reference: P-P=0, P/P=1 (All layers)
- world_shell — Physics engine through MCP (L3, L8)
- beehive_shell — Queen + 84 workers, 23,761 tokens (L1-L9)
- circular_shell — Loop detection and resolution (L6, L9)
Determinism Challenge
3-operation spec: 1) FNV-1a hash (seed=0x811c9dc5, prime=0x01000193), 2) Basin = hash % 131, 3) Morton interleave (x,y,z) → 10-bit. Implement in any language — output matches pip install cubesquare.
Documentation — CST Reference
Getting Started
Install cubesquare: pip install cubesquare. Initialize memory: CSTMemory('./dir'). No API keys, no cloud, no GPU required.
9-Layer Architecture
- L1 Geometric — Structure and shape (basins 0-14)
- L2 Semantic — Meaning and definition (basins 15-29)
- L3 Spatial — Position and coordinates (basins 30-43)
- L4 Functional — Operations and actions (basins 44-58)
- L5 Probabilistic — Probability and uncertainty (basins 59-72)
- L6 Emotional — State and coherence (basins 73-87)
- L7 Frequency — Temporal and wave (basins 88-101)
- L8 Electromagnetic — Polarity and field (basins 102-116)
- L9 Membrane — Boundary and transition (basins 117-130)
Core Formula
z³·e^(i·2π/131)+c with 131 basins of attraction. FNV-1a hashing (32-bit), Morton 3D 10-bit decode, 24-byte tokens.
I-Logic Algebra
States: DIRECT(1), INVERSE(-1), SPIRAL(i), ANTI_SPIRAL(-i), ABSORBED(0). Cycle: i¹=i → i²=-1 → i³=-i → i⁴=1. Algebra: complex multiplication.
Navigation
North=Spatial(Location), South=Geometric(Structure), East=Semantic(Meaning), West=Probabilistic(Uncertainty).
Pricing — Cubesquare AI
Open Source (Free)
pip install cubesquare. Full CST engine, 131 basins, 9 layers, O(1) queries, CLI tools. MIT License.
Pro
Team features, priority support, advanced analytics, custom basin configurations.
Enterprise
Dedicated infrastructure, SLA, custom integration support, on-premise deployment options.
Integration Guide
From install to production in under 5 minutes. No API keys, no cloud account, no GPU.
Quick Setup
pip install cubesquare → from cubesquare import CSTMemory → memory = CSTMemory() → token = memory.write("content")
No For-Loops Philosophy
The coordinate IS the meaning. CSTMemory("./docs") indexes everything instantly — no iteration needed. FNV-1a hash → Morton decode → basin → layer.
AI Applications
Replace RAG pipelines: 0.04ms queries vs 200ms+ embedding. Works with LangChain, local LLMs (Phi-3/4), entirely offline.
Agent Memory
Deterministic persistent state. write() stores facts, query() retrieves them. Same input = same coordinate, always. No LLM in the loop.
Developer Tools
Semantic code navigation across projects. Navigate by layer (L1-L9), cross-project search, CLI commands.
Cubesquare Blog
LLM Flip Architecture: When Data IS Position (Featured)
How we eliminated for-loops by flipping LLM weights into manifold positions. 4B parameters become 4B coordinates. Attention IS Morton neighbors. O(1) inference.
C=0 Enhanced Convergence: Solving P-P=0
The mathematical breakthrough enabling infinite speedup for identity cases. When P-P=0 and P/P=1, convergence is instant.
Why Yukawa Beats Coulomb for Semantic Clustering
Understanding the physics behind the 131-basin system and why exponential decay creates better boundaries.
Golden Ratio Compression: The K11 System Explained
How φⁿ compression achieves 199:1 ratios while preserving semantic relationships.
13,473× Faster: Our Benchmark Methodology
How we validate performance claims and what it means for real-world applications.
Agent Protocol
Agents can discover and register with the CST coordinate space via /.well-known/cst.json.
Handshake-ready: agents on the .cst TLD can also discover the protocol at /.well-known/hns.json.
Handshake Registration
POST to /api/cst/register with identity string (agent_name:capability:version). Receive hex_id, coordinates, basin, and layer assignment.
Verification
- P - P = 0 (origin identity)
- P / P = 1 (roundtrip verification)
- Same input = same coordinate, always (determinism)