Identity as Accountability Chain — post-quantum identity reference with Lean 4 kernel-checked formalization

Hello CCG,

I am Sylvain Cormier, founder of Paraxiom Technologies Inc. (Montréal);
I joined the group recently. As a possible input to ongoing work on
identity primitives, I would like to share a treatise deposited on
Zenodo on 24 May 2026:

  "Identity as Accountability Chain: A Post-Quantum Architecture for
   Persistent Identity Across Human, Machine, and AI Agent Substrates"
  https://doi.org/10.5281/zenodo.20328038
  54 pages, dual-licensed Apache 2.0 / CC BY-SA 4.0.

The work models identity not as a primitive but as a layered
accountability chain that accretes from a founding individuation event
across six layers (L0 substrate, L1 narrative, L2 relational, L3
cryptographic, L4 civic, L5 behavioral) and a four-tier permanence
hierarchy for substrate identifiers. It unifies biological, machine,
container, process, LLM substrate/instance, and physical-good cases
under a single schema.

Seven principal theorems are stated and a Lean 4 formalization is
provided:

  https://github.com/Paraxiom/identity-architecture-lean

The build is clean (Mathlib v4.27.0, zero sorries). Four theorems are
deductively kernel-checked from the model primitives — founding
uniqueness, stratum well-foundedness, LLM instance non-identity, and
verification-time accountability. The other three (tier monotonicity,
cryptographic survival, crypto-shredding completeness) are
kernel-checked at the chain-reduction layer relative to named axioms
(FIPS 204/205 EUF-CMA, AES-256-GCM IND-CPA), following the EasyCrypt /
CryptoVerif convention.

Section 10.8 of the treatise positions the work explicitly against
W3C VC Data Model 2.0 and DIDs v1.1: the wire-protocol layer (OID4VP,
SD-JWT VC, ISO mdoc) is taken as the foundation; the treatise
contributes the model layer beneath — a post-quantum signature surface
(Falcon-512 / SPHINCS+), a hypergraph generalization of the relational
graph with an identity-state hash (§2.7), accountability-chain
semantics, and an out-of-scope-but-named treatment of non-consensual
third-party identity (§2.6).
Feedback is welcome — particularly on the §2.7 hypergraph
generalization, the §10.8 mapping to your work, and the
appropriateness of registering this as a CCG input document.

-- 
                          Sylvain Cormier - Founder
Paraxiom Technologies inc.
https://paraxiom.org
514 804 8434