X^∞ as a Recursive Infrastructure: Responsibility-Driven Replacement of Classical ITSM

This working paper introduces X^∞ (X to Infinity) as a mathematically auditable, responsibility-centric alternative to traditional IT service management (ITSM) frameworks such as ITIL 4. Grounded in Cap logic and systemic feedback mechanisms, X^∞ replaces static roles and opaque processes with dynamic authority units (Cap), recursive delegation, and intelligent need expression via CapPetitions. The model enables verifiable, zero-trust operations through constructs like CapNFT, CapGate, CapLedger, and ∆Cap, while fostering emergent alignment across complex infrastructures. The paper offers a full mapping of all 34 ITIL 4 practices—spanning general, service, and technical management—and demonstrates how each is transformed under the X^∞ paradigm. It formalizes a prioritization logic (P = N·w_E) that amplifies structurally relevant needs, particularly from underrepresented actors, and implements this in a prototype system capable of automatic delegation, feedback propagation, and incident attribution. A detailed case study highlights the operational superiority of X^∞ compared to classical frameworks, achieving faster incident resolution and proactive systemic improvement. This publication invites collaboration towards a silent revolution in IT governance and post-organizational infrastructure design.