mirror of
https://github.com/lux-apps/papers.git
synced 2026-10-30 18:15:21 +00:00
zeekay
8be0e0591d
Replace generic STARK/FRI mentions with P3Q (luxfi/p3q) in production-context
sentences across the Lux Tier-2/3 catalogue: lux-bridge, lux-warp-v2,
lux-quasar-horizon, lux-cross-chain-security, lux-nist-mptc-submission,
lux-whitepaper, lux-achain-attestation. Add @misc{luxp3q} bibtex entries to
the three papers with bibliographies. Tier-1 papers (pq, lp-stricte2epq,
lp-073-pulsar, lp-020-quasar-consensus) untouched.
Academic-reference STARK mentions (related-work surveys, formula-table
category labels) are preserved. Builds remain green.
54 lines
2.0 KiB
TeX
54 lines
2.0 KiB
TeX
\section{Triple-Proof Finality Propagation}
|
|
|
|
|
|
\subsection{Intra-Chain Finality}
|
|
|
|
Each chain produces triple-proof epoch proofs independently:
|
|
\begin{itemize}[leftmargin=2em]
|
|
\item BLS aggregate over the epoch's blocks (classical speed).
|
|
\item P3Q-compressed (P3Q; \texttt{luxfi/p3q}) ML-DSA signatures (post-quantum identity).
|
|
\item Pulsar threshold signature (post-quantum privacy).
|
|
\end{itemize}
|
|
|
|
Total: 248 bytes per epoch per chain.
|
|
|
|
\subsection{Cross-Chain Finality Propagation}
|
|
|
|
When chain $C_i$ finalizes epoch $e$, it emits a Warp \texttt{FINALITY\_PROOF} message containing:
|
|
|
|
\begin{verbatim}
|
|
FinalityProof {
|
|
chainID: [32]byte // Chain that finalized
|
|
epoch: uint64 // Epoch number
|
|
stateRoot: [32]byte // State root at epoch boundary
|
|
epochProof: [248]byte // Triple-proof (BLS + STARK + Pulsar)
|
|
}
|
|
\end{verbatim}
|
|
|
|
The P-Chain collects finality proofs from all active chains and includes them in its own epoch proof. This creates a finality tree:
|
|
|
|
\begin{center}
|
|
\begin{tikzpicture}[
|
|
node distance=1.5cm,
|
|
every node/.style={draw, rounded corners, minimum width=2cm, minimum height=0.7cm, font=\small},
|
|
arrow/.style={-{Stealth}, thick}
|
|
]
|
|
\node (p) {P-Chain epoch $e$};
|
|
\node (c) [below left=1.2cm and 0.5cm of p] {C-Chain $e$};
|
|
\node (x) [below=1.2cm of p] {X-Chain $e$};
|
|
\node (d) [below right=1.2cm and 0.5cm of p] {D-Chain $e$};
|
|
\draw[arrow] (c) -- (p);
|
|
\draw[arrow] (x) -- (p);
|
|
\draw[arrow] (d) -- (p);
|
|
\end{tikzpicture}
|
|
\end{center}
|
|
|
|
\begin{theorem}[Cross-Chain Finality]
|
|
If a transaction $tx$ is included in epoch $e$ of any chain $C_i$, then $tx$ is finalized across all chains within epoch $e+1$.
|
|
\end{theorem}
|
|
|
|
\begin{proof}
|
|
Chain $C_i$ emits a finality proof for epoch $e$ via Warp message. The P-Chain includes this proof in its epoch $e$ or $e+1$ proof (depending on propagation timing). All chains observe P-Chain finality proofs. Since P-Chain epoch proofs are triple-proof final (no reorganization), the transaction's finality is transitively guaranteed.
|
|
\end{proof}
|
|
|