Identity as Accountability Chain: A Post-Quantum Architecture for Persistent Identity Across Human, Machine, and AI Agent Substrates

We propose a formal model in which identity is not a primitive but a layered accountability chain that accretes from a founding individuation event and persists as long as cryptographic, relational, and civic verification can be reconstructed. The model unifies biological, machine, agent, AI, and physical-goods cases under a single schema with six accretion layers and a four-tier permanence hierarchy for substrate-level identifiers. We state and prove seven results that bear directly on engineering: (i) Founding uniqueness — every identity locus has exactly one origin event; (ii) Tier monotonicity — the permanence of an identity claim is non-increasing in the tier of its substrate identifier; (iii) Stratum well-foundedness — every scoped or agent identity traces in finite steps to a person- or organization-rooted identity; (iv) LLM instance non-identity — two LLM instances with identical weights but disjoint deployment IDs are distinct identity loci; (v) Cryptographic survival — only post-quantum-signed identities remain verifiable past a cryptographically-relevant quantum computer (CRQC) event; (vi) Crypto-shredding completeness — master-key deletion renders all envelope-encrypted credentials computationally inaccessible without recourse to unpinning; and (vii) Verification-time accountability — the reference verifychain procedure terminates correctly in a finite number of steps. The results are presented as mathematical proofs and are not yet machine-checked in a proof assistant. The treatise names four distinct sources from which identity content arises — externally witnessed, self-asserted, cumulatively earned, and algorithmically derived — and formalizes self-assertion (§2. 5) as a first-class entry in the accountability chain, signed by the locus's own key. A companion subsection (§2. 6) scopes non-consensual third-party identity — data-broker dossiers, surveillance records, algorithmic scoring labels — explicitly out of the accountability-chain primitive, naming the asymmetry against user-controlled disclosure and pointing to the regulatory layer (GDPR Art. 17, CCPA §1798. 105) that addresses it. A hypergraph generalization (§2. 7) of the binary relational graph promotes higher-arity identity facts — joint authorship, committee-ratifies-charter, multi-party agreements — to first-class status, with the identity-state hash hI (t) addressing identity by current state rather than by a fixed handle. The treatise covers six founding-event domains: human, machine, container, process, LLM substrate, LLM instance, and physical good (NFC/RFID-anchored, NFT-bound) — the last integrated with the production NFT-identity lane (LVMH Aura, Arianee, VeChain, ERC-6551 token-bound accounts). The term augmented democracy was introduced by the author in August 2017, predating the more widely known TED-talk popularization by approximately thirteen months. A dedicated positioning subsection (§10. 8) tabulates the model-layer primitives this treatise contributes over and above the W3C VC 2. 0 (Recommendation, 15 May 2025) and DIDs v1. 1 (Candidate Recommendation Snapshot, 5 March 2026) stack: post-quantum signatures, six-layer accretion, permanence-tier hierarchy, five identity strata, hypergraph state, physical-good integration, accountability tracing, crypto-shredding, and the seven principal theorems are not in the published W3C corpus. We survey the state of digital identity as of May 2026, noting that no major civic identity system runs post-quantum signatures in production despite regulatory deadlines of 2030–2035, and that AI agent identity is a standards vacuum. We present the Paraxiom architecture as a three-tier system combining on-chain post-quantum primitives (QuantumHarmony, with SPHINCS+ and Falcon-512), IPFS for bulk encrypted payloads, and Postgres+Redis mirrors for query-layer access. Five identity strata (S1–S5) cover humans, scoped delegations, vault credentials, agent instances, and cross-tenant aggregates. The treatise concludes that identity is engineering, not philosophy: the accountability chain does not extend itself; the post-quantum signatures do not sign themselves. What we build now determines whether identity remains a coherent concept past 2040.