papers/lux-capsule-architecture/sections/02-the-capsule-model.tex

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%% LP-134 canonical naming (2025-12-15):
%% Per LP-134 (Lux Chain Topology), T-Chain has been split into:
%%   M-Chain — MPC ceremonies for bridge custody of EXTERNAL wallets
%%             (CGGMP21, FROST, Pulsar-general)
%%   F-Chain — FHE compute + TFHE bootstrap-key generation (encrypted EVM)
%% T-Chain is REMOVED entirely; teleport is B-Chain (bridgevm, LP-6000). No teleportvm.
%% Where this paper says "M-Chain MPC" / "M-Chain threshold governance" /
%% "M-Chain TFHE" / "M-Chain custody", read as M-Chain (MPC) or F-Chain (FHE).
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\section{The Capsule Model}
\label{sec:model}
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\begin{definition}[Capsule]\label{def:capsule}
A \textbf{Capsule} is a seven-tuple
\[
  \mathcal{C} = (V, \mathcal{I}, \Gamma, \Sigma, \Pi, \mathcal{A}, \mathcal{P})
\]
where:
\begin{itemize}[nosep]
  \item $V$ is the \textbf{vault}: an encrypted SQLite database with a CRDT-based
        write-ahead log.
  \item $\mathcal{I}$ is the \textbf{identity}: a DID document anchored on I-Chain,
        binding the capsule to one or more public keys.
  \item $\Gamma$ is the \textbf{capability set}: a lattice of UCAN-style
        capability tokens governing read, write, sync, delegate, and revoke
        operations.
  \item $\Sigma$ is the \textbf{sync topology}: the set of peers, relays,
        and chain anchors through which the vault replicates.
  \item $\Pi$ is the \textbf{compute policy}: a specification of where computation
        may execute---local, provider-hosted, or confidential (FHE/TEE).
  \item $\mathcal{A}$ is the \textbf{audit chain}: an append-only sequence of
        anchored receipts on Lux recording policy changes, capability grants,
        and sync checkpoints.
  \item $\mathcal{P}$ is the \textbf{key policy}: the set of threshold, rotation,
        and recovery rules governing the capsule's cryptographic material,
        enforced on K-Chain.
\end{itemize}
\end{definition}

\begin{definition}[Principal]\label{def:principal}
A \textbf{principal} is any entity that owns a capsule: a human user, an
organization, an AI agent, a device, or a shared workspace. Each principal
has exactly one root capsule. Derived capsules (e.g., per-app or per-workspace
vaults) inherit capabilities from the root through delegation chains in $\Gamma$.
\end{definition}

\begin{definition}[Vault]\label{def:vault}
The vault $V = (\mathsf{DB}, \mathsf{WAL}, k_{\mathsf{enc}})$ consists of:
\begin{itemize}[nosep]
  \item $\mathsf{DB}$: a SQLite database encrypted with SQLCipher using AES-256-CBC
        with HMAC-SHA512 page authentication.
  \item $\mathsf{WAL}$: a CRDT-based write-ahead log where each entry is a
        $(\mathsf{hlc}, \mathsf{op}, \mathsf{sig})$ triple---hybrid logical clock
        timestamp, operation, and signature from the writing principal.
  \item $k_{\mathsf{enc}}$: the vault encryption key, derived from the principal's
        root key material via HKDF-SHA256, optionally wrapped under ML-KEM for
        post-quantum protection.
\end{itemize}
\end{definition}

\subsection{Ownership Invariants}

The Capsule model enforces four invariants that distinguish it from both
traditional cloud architectures and fully on-chain systems.

\begin{invariant}[Key Sovereignty]\label{inv:keys}
The vault encryption key $k_{\mathsf{enc}}$ is never transmitted in plaintext
to any party other than the owning principal. Providers receive only ciphertext.
Recovery requires threshold reconstruction on M-Chain, not provider cooperation.
\end{invariant}

\begin{invariant}[Data Locality]\label{inv:locality}
The authoritative copy of the vault state is the local replica. Remote replicas
(provider-hosted, peer-hosted) hold only encrypted snapshots and CRDT operation
logs. A principal can reconstruct the full vault from any replica plus the
encryption key.
\end{invariant}

\begin{invariant}[Provider Replaceability]\label{inv:provider}
No provider holds state that the principal cannot obtain elsewhere. Sync
topology $\Sigma$ can be reconfigured to exclude any provider at any time
without data loss. The protocol guarantees that switching providers requires
only re-pointing the sync target---no data migration, no key re-wrapping
(unless the principal chooses to rotate).
\end{invariant}

\begin{invariant}[Audit Completeness]\label{inv:audit}
Every policy change, capability grant, capability revocation, and key rotation
produces a receipt anchored in $\mathcal{A}$. The audit chain is append-only
and anchored to Lux. A third party can verify the complete history of a
capsule's trust configuration without access to the vault contents.
\end{invariant}

\begin{theorem}[Capsule Sovereignty]\label{thm:sovereignty}
Under Invariants~\ref{inv:keys}--\ref{inv:audit}, a capsule $\mathcal{C}$ is
\textbf{sovereign}: the owning principal can, at any time, (a) decrypt and read
all vault contents, (b) revoke all delegated capabilities, (c) migrate to a
new provider set, and (d) verify the complete trust history---without cooperation
from any provider or peer.
\end{theorem}

\begin{proof}
By Invariant~\ref{inv:keys}, the principal holds $k_{\mathsf{enc}}$ (or can
reconstruct it via M-Chain threshold recovery without provider participation),
so (a) holds. By Invariant~\ref{inv:locality}, at least one encrypted replica
is locally held, so the principal has data availability independent of providers.
Capability revocation (b) is a K-Chain transaction signed by the principal's root
key---no provider co-signature is required because $\Gamma$ is a unilateral
delegation lattice. Migration (c) follows from Invariant~\ref{inv:provider}:
the principal re-points $\Sigma$ and the new provider receives the encrypted
snapshot. Trust history verification (d) follows from Invariant~\ref{inv:audit}:
$\mathcal{A}$ is on Lux, readable by any party.
\end{proof}

\subsection{Capsule Lifecycle}

A capsule transitions through four phases:

\begin{enumerate}[nosep]
  \item \textbf{Genesis}: The principal generates root key material, derives
        $k_{\mathsf{enc}}$, creates the initial encrypted vault, registers the
        DID on I-Chain, and publishes the initial key policy to K-Chain.
  \item \textbf{Active}: The vault accepts local writes, syncs via $\Sigma$,
        and anchors checkpoints to $\mathcal{A}$. Capabilities in $\Gamma$
        may be delegated and revoked.
  \item \textbf{Recovery}: If the principal loses access to $k_{\mathsf{enc}}$,
        threshold reconstruction on M-Chain produces a new key share set.
        The vault is re-encrypted under the new key. The recovery event is
        recorded in $\mathcal{A}$.
  \item \textbf{Termination}: The principal publishes a revocation of all
        capabilities and a tombstone DID document. Provider replicas are
        garbage-collected. The audit chain remains on Lux permanently.
\end{enumerate}

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