CCMA: Conversational Context Management Algorithm

Architecting Cognitive Persistence: Integrating CCMA with 768-Dimensional Hyperbolic Manifolds for Centroid-Preserving Memory

Patent Pending - U.S. Provisional Application No. 64/006,354 (Filed: March 15, 2026)

This repository contains the white paper and architectural specifications for the Conversational Context Management Algorithm (CCMA). CCMA is a deterministic framework designed to solve the $\mathcal{O}(n^2)$ attention bottleneck and catastrophic forgetting in long-horizon edge LLM interactions by bridging localized context caches with deeply hierarchical, hyperbolic lifelong memory.

🧠 Architectural Philosophy (The Universal Coding Manifesto)

CCMA adheres strictly to a Functional Core / Imperative Shell architecture, enforcing a zero-trust environment:

• Functional Core (Deterministic): Silicon-enforced mathematical gating, semantic-temporal decay calculations, hyperbolic metric tracking, and Trust No One (TNO) circuit breakers are implemented as pure, immutable functions.

• Imperative Shell (Probabilistic): Manages volatile generative state (the LLM/TPU), relying purely on the geometrically stable vectors fed to it by the Core. The LLM physically cannot hallucinate its own geometric memory coordinates.

🚀 Key Innovations

• The Poincaré Ball Paradigm: Transitions lifelong memory from flat Euclidean space to a 768-dimensional hyperbolic manifold, allowing exponential graph embedding without structural distortion.

• Colliding Weights & Centroid Collapse Mitigation: A deterministic hardware trigger that detects semantic crowding ($\Phi_{\text{total}} > \tau_{\text{collapse}}$) and executes Tangent Space Max-Pooling to mathematically preserve distinct semantic peaks.

• Biological Sleep Cycle Memory Consolidation: Mathematically maps Wake (Euclidean L1), NREM (Cartesian pooling), and REM (Generative Replay/Hyperbolic Projection) phases for asynchronous memory stabilization.

• Topological Isomorphism (Gabriel's Horn): Resolves the finite compute / infinite memory paradox by treating localized VRAM (Context Window) as the finite volume and the Hyperbolic Archival tier as the infinite surface area.

• TNO Circuit Breaker: Neutralizes Adversarial REM-Forcing (Compute Exhaustion DoS attacks) by evaluating payloads using Topological Entropy Scoring ($H_{\text{topo}}$) before authorizing hardware interrupts.

🛠 Silicon-Level Isomorphism (Hardware Spec)

The framework theorizes an integrated FPGA/TPU Hybrid System-on-Chip:

1. FPGA (The Core): Maintains geometric state monitoring, continuously calculating inverse hyperbolic cosines and collision densities in bounded clock cycles.

2. TPU (The Shell): Handles generative inference and natural language processing, maintained in a low-power "Dark Silicon" state until invoked by the FPGA's validated memory payloads.

📄 Abstract

The deployment of long-horizon conversational agents in resource-constrained computing environments is bottlenecked by the quadratic scaling of transformer self-attention and the catastrophic forgetting inherent to standard First-In-First-Out (FIFO) caches. This paper integrates the Conversational Context Management Algorithm (CCMA) with a 768-dimensional Poincaré ball model of hyperbolic geometry to establish a structurally flawless bridge between high-speed localized caches and deeply hierarchical lifelong memory. Operating on a strict Functional Core / Imperative Shell architecture, we define a Semantic-Temporal Modulator to correct Ebbinghaus decay, and mathematically formalize the threat of "Centroid Collapse" in standard Euclidean vector aggregation. By synthesizing a deterministic "Colliding Weights" trigger, Tangent Space Max-Pooling sequences, Riemannian Repulsion, and TNO Circuit Breakers executed on FPGA/TPU hybrid silicon, this framework ensures that high-entropy semantic peaks are preserved in perpetuity.

📦 PDF Availability

The full academic whitepaper PDF is produced automatically via GitHub Actions:

• Workflow Artifact: Generated on each successful compile run of the .tex source.

• GitHub Pages: Publishes a stable latest.pdf on the default trunk branch.

• GitHub Releases: Tagged SemVer releases (e.g., v1.2.0) include the PDF as a downloadable release asset.

🔗 Repository Structure

• CCMA_Hyperbolic_Memory.tex: Source manuscript (LuaLaTeX).

• .github/workflows/render-tex-to-pdf.yml: Automated PDF build and publication workflow.

• README.md: Project overview and publication details.

• LICENSE: Apache License 2.0.

Author: Dane Robert Jones

Software Engineering Student, Western Governors University

Technical SME, Essintial

danerjones@gmail.com | ORCID 0009-0003-8014-7298