Software systems have traditionally been organized around applications where human users act as principal decision-makers. Recent developments in agentic capabilities alter this paradigm: software agents now autonomously translate high-level goals into structured tasks, orchestrating tools, services and sub-agents to execute complex workflows. This evolution gives rise to an agent economy where these autonomous agents capture real economic value. However, the infrastructure required to support the agent economy fails across three critical dimensions: the absence of persistent identity infrastructure prevents systemic accountability in agentic workflows; capability claims remain self-declared not backed by verifiable execution evidence; and the disconnect between creator identities, agent performance, and project value hinders the economic valuation of agents as assets. While existing registries provide naming and discovery, unifying these features around a persistent identity anchor remains largely unaddressed. TessIndex is a capability-verified identity system for agent primitives that utilizes a dual-plane architecture: the blockchain records compact commitments for identity, ownership, and verification, while centralized servers maintain dynamic metadata for discovery, commerce, and reputation. It establishes: persistent identities across agent primitives to enforce systemic accountability in autonomous workflows; a predicate-based verification process replacing self-declared claims with cryptographic capability proof; an identity infrastructure that links agent performance to both project and creator identities while capturing value through tokenization. Ultimately, TessIndex serves as an integrated infrastructure that binds an agent's existence across capabilities, execution, and reputation into a single persistent identity.
AI agents in long-context applications drift from their specified identity. Current methods detect this only after qualitative degradation is visible. We present a geometric framework for measuring identity structure using $\sqrt{\mathrm{JSD}}$ metric spaces and magnitude homology from enriched category theory, where identity is non-geodesic structure and drift is its relaxation toward the geodesic. Validated on a persistent AI agent, the framework's strongest empirical finding is a two-mechanism conditioning structure: cross-condition distances reveal an identity-vacuum cluster where the identity specification fills a behavioral void, and a safety-basin cluster where it displaces from post-training attractors. An equilateral probe baseline confirms that the identity specification creates measurable behavioral richness (55 unique response patterns vs. 1 for the base model) at maximum probe separation. A first-order perturbation theory for equilateral configurations predicts magnitude changes from perimeter changes alone, with shape perturbations first-order cancelled by the $S_n$ symmetry; the formula is self-consistent at the observed perturbation amplitudes. A drift experiment measuring magnitude decrease under context pressure was subsequently found to reflect repetitive-padding artifacts rather than genuine context-length drift; diverse padding produces no measurable deformation through 150K tokens. The magnitude homology framework's full diagnostic promise -- detecting anisotropic contraction and structural collapse via homological simplification -- is architecturally grounded in the perturbation theory and selection rules but remains empirically unconfirmed.