GTX Rebirth and Symbolic Context Operations: A Unified Framework

Introduction

This document presents a full integration of the GTX Rebirth initiative with Lie algebraic transformations and the symbolic context operation pipeline. It reimagines the role of legacy GPUs—such as NVIDIA GTX 1070 and 1080—not as obsolete hardware, but as symbolic processing agents. In the Gyrator framework, these GPUs become context workers: saving, transforming, and reconstructing the memory states that underpin large language models. This paper expands upon Pillar 5 (Sovereign Scaffolding) and introduces structured operations for symbolic context transduction, delta compression, and memory geometry.

Deployment Order

1. Stage 1 – CPU + GTX 1070: The CPU hosts the model; inference occurs locally. GTX 1070 performs all context operations: KV snapshotting, delta computation, symbolic folding. No RTX involved yet.
2. Stage 2 – CPU + 1070 + 3090: Later, inference shifts to RTX 3090. GTX continues handling symbolic ops. CPU remains the orchestrator.

System Roles

• CPU: Performs inference (Stage 1), manages orchestration, schedules symbolic operations, and routes memory flow.
• GTX 1070 / 1080: Context assistant—handles save/load, delta, symbolic mapping, and Lie transforms independently from inference.
• RTX 3090 (Stage 2): High-speed inference GPU. Focuses only on decoding; offloads context to GTX and CPU.

Primary Context Operations

1. Store: Capture a snapshot of the past_key_values for a given turn. Stored as `.npy` or memory-native CuPy object.
2. Save: Write the snapshot to disk under timestamped folder structure (`m7d5x17x24x52`). GTX performs memory-to-disk transfers.
3. Load: Load a context snapshot back into memory. GTX verifies available VRAM before allocation. Loaded context can be injected or compared.
4. Memory: Reconstruct context through `exp(ξ)` from symbolic algebra. GTX handles exponential mapping using stored Lie algebra differentials.
5. Delta: Compare two snapshots. Compute `ξ = log(KV₂ ⋅ KV₁⁻¹)` representing contextual change as a vector in Lie algebra. GTX performs this differential mapping.

Lie Group Formulation

Each full KV snapshot across layers defines a matrix-like object `g` in Lie group G. The product of two such snapshots yields a new state; the log of their difference maps into a vector `ξ` in Lie algebra 𝔤.

• KV₁ → `g₁` ∈ G
• KV₂ → `g₂` ∈ G
• ξ = log(g₂ ⋅ g₁⁻¹)` → vector in 𝔤

This `ξ` defines the semantic or symbolic transition between two memory states. The reverse is `exp(ξ)`, reconstructing `g₂` from `g₁` and its symbolic delta.

Context Manifold Geometry

Contextual evolution is no longer linear. The manifold view implies curved semantic flow across time:

• KV(t) = exp(tξ) ⋅ g₀: Interpolated path through context
• Turn interpolation: Synthesize in-between states from turn `i` to `j`
• Temporal downsampling: Reduce stored KV to essential flows via vector field curvature

Symbolic Compute on GTX

GTX GPUs enable symbolic operations without triggering full model decoding:

• Save/Load from VRAM using CuPy
• Lie delta computation (matrix log)
• KV difference over selected layers only
• Symbolic projection onto reduced basis
• Context fold/unfold as symbolic sequence

These tasks are not bandwidth-intensive, and leverage ~8 GB VRAM for intermediate turns, not live chat decoding.

Micro-Inference Possibilities

Under selective conditions, GTX can perform inference-like operations:

• 1-token forward pass (rehydration probe)
• QKV attention layers only, no MLP
• Evaluating symbolic attention significance

This extends symbolic operations into semantic estimation and gated evaluation without full throughput bottlenecks.

Storage and Snapshot Layout

Snapshots follow strict timestamp-based directory convention under `/media/krusty/gm/gm194/context/`:

• m7d5x17x24x52 → Month 7, Day 5, Hour 17, Minute 24, Second 52
• Each folder contains multiple `.npy` files (per-layer or composite)
• last.txt: Latest snapshot path

Pipeline Coordination

Pipeline is divided by responsibility:

• CPU: Stage 1 inference and routing controller
• GTX 1070: Symbolic context handler, Lie delta operations, low-latency NV storage interface
• RTX 3090 (Stage 2): Dedicated decoder, fully offloads context logic to GTX

This enables real-time response while GTX asynchronously folds, restores, and stores symbolic memory.

Pillar 5 Synthesis

This framework realizes Pillar 5 of the Gyrator architecture: Sovereign Scaffolding. It enables:

• State re-entry through symbolic transforms
• KV resurrection without prompt replay
• Memory sovereignty — GPT models gain local recall via manifold-based scaffolding

Conclusion

GTX Rebirth begins with a CPU and a 1070—and from there, creates a scalable memory subsystem for transformers. Through Lie algebraic context modeling and real memory transport, we move closer to models that can reason about memory as space, not just history. By embedding symbolic transformation into dedicated hardware, we reclaim past devices and elevate them into agents of context logic under the Gyrator vision.