Architecture
GCM is not a replacement for transformers. It wraps the generation layer on both sides, handling context, routing, and post-generation verification. The generation layer stays exactly where it is.
Division of Labor
When you use any AI assistant, two distinct things are happening: something is understanding what you want and tracking where the conversation is, and something else is producing the words. These do not have to be the same system. GCM handles the first. The transformer handles the second.
Generating fluent text, images, code, and voice. Complex multi-step reasoning with explicit chain of thought. Open-ended creative tasks with no fixed structure. Full statistical breadth of a large training corpus.
Understanding intent geometrically at 85% agent routing accuracy. Maintaining context in 52 bytes with no growth and no reset. Running entirely on-device at 44,000 to 97,000 tokens per second. Inspectable routing decisions with an auditable geometric state. Post-generation verification of context, register, and truth alignment.
The Complete Loop
Generation without context verification produces responses that may serve the wrong context, drift in register, or conflate truthfulness with social approval. GCM catches all three geometrically, at generation time, without any additional system.
User input arrives. GCM reads intent, updates the 52-byte SSM state, computes the target semantic position, and routes to the right capability. The generation layer receives a precise geometric starting point rather than approximating context from a growing token sequence.
The generation layer produces output, whether a transformer LLM or a geometric generator for constrained text and code. The generation is informed by the precise context state from Step 1 rather than inferring context from token statistics.
The output is encoded back through the SSM. GCM compares it against the state at generation time. Three checks run: context mismatch detection, register verification, and the sycophancy check. Flagged responses can be corrected before delivery.
Post-Generation Verification
Because the SSM state is maintained continuously and is inspectable at any moment, the state at generation time can be compared against the output. This is native to the architecture, not an add-on.
After generation, the output is encoded back through the SSM and compared against the state at generation time. If they are far apart on key axes, the response served the wrong context. Detectable, flaggable, and correctable without any additional system.
If the conversation has been formal and high-constraint but the response lands casual and low-dominance, the geometry detects the mismatch. For clinical, legal, and educational applications, register errors cause real harm. Geometric verification catches them before delivery.
If the state at generation time shows low truth-axis and high social-approval-axis values, the system flags that the response may have been generated to please rather than inform. Derived directly from the moral/truth Gram cosine of 0.744 found in Paper 3. No transformer can offer this: the entanglement that causes sycophancy also makes it invisible from inside a statistical model.
Dual State Tracking
The current architecture tracks the user's input trajectory. But a complete conversation has two participants. A complete geometric architecture maintains both trajectories in parallel, in approximately 104 bytes of total active state regardless of conversation length.
The primary SSM state tracks every word the user has said, weighted by recency and per-axis decay. This records intent, register, context, and trajectory, available for inspection at any moment.
A parallel SSM state processes the AI's own output token by token. The AI now has a geometric record of its own line of thought: where it started, what trajectory it followed, and where it landed. The response is not lost after delivery. It becomes part of the conversation's geometric history.
At any moment, compute the cosine distance between the user state and the agent state. If geometrically close, the AI is tracking the user's context. If diverging, the AI is drifting. If moving in opposite directions, the AI is contradicting the user's trajectory. These are geometric measurements available in constant time.