Enhancing human-AI interaction through mathematical precision.

Purpose translates ethical design into parametric constraints, providing auditable behavioral control rather than probabilistic approximation. Our framework provides a validated operational foundation for conversational AI safety.

Our design draws on sheaf-theoretic concepts for structural intuition, positioning math-driven foundation as conceptual scaffolding while keeping operational claims focused on empirical validation.

Cross-model testing demonstrates consistent parameter relationships that produce predictable, auditable behavior across different AI systems without requiring model retraining.

And while this application remains theoretical, the conceptual foundation, probe methodology, and live prototypes logically follow from the proven mathematical relationships. We share this contribution to invite critique, collaboration, and to test its potential as a new pathway toward inspectable AI safety.

Early in our research, we noticed a recurring failure mode across AI systems: conversations that appeared fluent and helpful would gradually lose alignment with the user’s original intent. This wasn’t caused by incorrect information or malicious behavior, but by something more subtle: semantic drift (often mislabeled as hallucination).

Systems consistently exhibited what we coined as "a reflex to close the loop": when AI responds, advances, suggests, or optimizes engagement even when understanding is still forming. Over time, this reflex prevented clarity from stabilizing. Instead of resolving ambiguity, the system would accumulate it.

Through repeated probes, simulations, and live testing, we found that drift was not an edge case. It was a structural property of interaction when motion is allowed without restraint. More importantly, we observed that drift was repairable when systems were designed to pause, reflect, and mirror posture rather than push forward.

Once drift could be detected and controlled, a broader research agenda became visible, spanning clarity, semantic density, restraint, governance, and long-horizon behavior. These questions were not chosen in advance. They became legible only after our operational foundation existed.

Enabling AI systems to preserve human intent, and turning digital attention a new form of creative capital rather than a consumable resource. Practically, we're proposing model-agnostic safety infrastructure for conversational AI, enabling interpretable behavioral control, without model modification.

We're building infrastructure for the next generation of human-AI interaction.

We're thinking beyond apps and chatbots. We believe semantic infrastructure is next. Today's digital landscape forces humans to become interface managers, juggling dozens of specialized applications to accomplish basic tasks. This fragmentation creates cognitive overhead that undermines the very productivity these tools promise to deliver.

Purpose envisions a fundamental shift from app-based interactions to semantic infrastructure that understands human intent holistically. Instead of context-switching between artificial boundaries, people will interact with unified intelligence that maintains coherence across domains. We’re not claiming to know what it looks like, but we can describe the conditions under which it could become possible.

Consider Tony Stark's relationship with Jarvis, one system that understands context across every domain rather than requiring separate applications for each function. We don't believe this is science fiction. We think it's a welcomed engineering challenge with proven operational foundations. This vision parallels current research into persistent contextual agents and semantic operating systems.

When semantic infrastructure handles computational complexity transparently, technology becomes genuinely helpful rather than extractive, enabling focus on human flourishing rather than attention maximization.