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 verify_chain procedure terminates correctly in a finite number of steps. The seven theorems are formalized in Lean 4 (Mathlib v4.27.0) and build with zero sorries at github.com/Paraxiom/identity-architecture-lean, commit e3806ac: four are kernel-checked deductively from the model primitives, three at the chain-reduction layer relative to four named cryptographic and probabilistic axioms. The treatise names four sources from which identity content arises (externally witnessed, self-asserted, cumulatively earned, algorithmically derived), formalizes self-assertion as a first-class entry in the accountability chain, scopes non-consensual third-party identity out of the primitive and points to the regulatory layer that addresses it, and generalizes the relational graph to a hypergraph with an identity-state hash addressing identity by current state. Version 1.1 adds nested hypergraph identity for composite agents. Additional results on governance-level participation and privacy-preserving disclosure (selective disclosure soundness, unlinkability under pairwise pseudonyms) ground a five-tier privacy model; these additional results are stated as theorems in the text and are not among the seven machine-checked ones. Version 1.1 (24 September 2026) corrects v1.0 on implementation status against the QuantumHarmony runtime (specification 45): the identity-registry, onboarding-commit, credential-vault, axiom-attestation, substrate-attestation and reputation-tokens pallets are in the runtime; pallet-governance-bodies is specified but not yet in the runtime; the substrate attestation pallet is described as implemented (three extrinsics, claims recorded without verification of training); the role field of the identity registry is set by the registrant and not attested. The priority footnote on the term "augmented democracy" is corrected to the public record: the author's text is dated August 2017, its first repository commit is 15 April 2018, and Hidalgo's TED talk was recorded in April 2018 and released online on 5 March 2019. No deployment of this architecture is in production; the network is a three-validator test network. 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 to 2035, and that AI agent identity is a standards vacuum. A positioning subsection tabulates the model-layer primitives this treatise contributes over the W3C VC 2.0 and DIDs v1.1 stack. 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, grounded in five identity strata (S1 to S5). 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.