Cryptographic Notarization Across Independent Ledgers: Cross-Chain Anchoring Protocols — Hash Chain, Cryptography, Audit, Sovereign AI, and Post-Cloud Architecture (Aioss-Format)

Abstract

Organizations operating multiple AI systems generate independent cryptographic ledgers that may need mutual verification, cross-referencing, or consolidated audit for enterprise-wide compliance reporting. Cross-chain notarization provides cryptographic evidence that a ledger's state is acknowledged by another independent ledger, enabling distributed audit verification without central coordination. This paper presents the design and analysis of the AIOSS cross-chain notarization protocol, which anchors the hash chain head of one ledger into another by inserting a notarization entry containing the cross-chain proof. We define three notarization modes: unilateral (ledger A notarizes ledger B's state), bilateral (mutual notarization between A and B), and supervised (third-party notarizer with independent proof). The notarization proof comprises a Merkle inclusion proof of the source ledger's state proof within a notarization ledger entry, enabling verification by any party holding both ledger files. We analyze the security of cross-chain anchoring under the common prefix assumption, proving that notarization preserves the integrity of both ledgers. Performance benchmarks demonstrate that notarization completes in under 200 milliseconds for ledgers of up to 1 million entries. We further evaluate the notarization merge operation, which produces a unified ledger from multiple notarized ledgers with cross-reference integrity. The protocol supports regulatory requirements for multi-system audit consolidation under SOC2 reporting and GDPR Article 30 record-of-processing activities. --- Part of The Anticloud research corpus by Lois-Kleinner Alpasan (ORCID: 0009-0009-2233-6107). This work explores hash chain, cryptography in the context of sovereign AI infrastructure, post-cloud computing architectures, and transparent, blackbox-free systems.