mirror of
https://github.com/lux-apps/papers.git
synced 2026-10-30 18:15:21 +00:00
zeekayandHanzo Dev
178febad68
Every rendered "T-Chain" / "ThresholdVM" / "teleportvm" reference across the paper corpus is rewritten to the correct canonical chain by concern: threshold signing / MPC / bridge custody / key recovery -> M-Chain (MVM); FHE / encrypted compute / threshold decryption -> F-Chain (FVM); teleport / cross-chain messaging -> B-Chain (bridgevm); consensus Pulsar stays Q-Chain. Section lux-trust-kernel/03-t-chain-threshold-governance.tex renamed -> 03-f-chain-encrypted-policy.tex (with \input + xref fixes). Braided "T-Chain" sections split by concern (M vs F). Only lp-020's chain-separation rationale and the shared lux/chains/thresholdvm library path retain the name, to record the removal. All changed papers rebuilt (pdflatex, rc=0, no undefined refs). ยง09 of lux-dao-governance-framework reframed: fabricated "production deployment" metrics ($50M/$240k/$12M, survey %s, "as of Oct 2024") relabeled as illustrative design configurations with no invented replacements; reality noted (DAO treasury is a 1/1 Safe); conclusion echo + one "first production" overclaim softened. This commit also captures concurrent corpus workstreams on the same tree. Co-authored-by: Hanzo Dev <[email protected]>
50 lines
2.2 KiB
TeX
50 lines
2.2 KiB
TeX
\section{Network Effects and Ecosystem Dynamics}
|
|
|
|
%%==========================================================================
|
|
|
|
\subsection{Security Externalities}
|
|
|
|
Each new appchain joining the Lux ecosystem creates \emph{positive security externalities}
|
|
for existing appchains through two channels:
|
|
|
|
\begin{enumerate}[leftmargin=1.5em]
|
|
\item \textbf{Validator supply expansion}: New appchains incentivize new validators to
|
|
join the Primary Network, increasing total stake $W$ and improving security for all.
|
|
\item \textbf{ASF contribution}: ASF payments from new appchains increase Primary Network
|
|
yield, attracting more stake.
|
|
\end{enumerate}
|
|
|
|
\begin{proposition}[Superadditive Security]
|
|
Under the ASF mechanism, the security of any appchain $s$ is strictly increasing in the
|
|
number of other appchains:
|
|
\[
|
|
\frac{\partial \Pi(s)}{\partial |\mathcal{S}|} > 0.
|
|
\]
|
|
\end{proposition}
|
|
|
|
\begin{proof}
|
|
More appchains $\Rightarrow$ higher total ASF $\Rightarrow$ higher primary staking yield
|
|
$\Rightarrow$ more stake enters primary network ($dW/dt > 0$ from Eq.~\ref{eq:stakeflow})
|
|
$\Rightarrow$ larger validator pool $\Rightarrow$ more validators available for appchain $s$
|
|
$\Rightarrow$ $\Pi(s)$ increases.
|
|
\end{proof}
|
|
|
|
\subsection{Competition Among Appchains}
|
|
|
|
While appchain growth creates positive externalities for security, appchains also compete
|
|
for scarce validator attention ($K$ capacity per validator). We model this as a market
|
|
where appchains post reward schedules and validators allocate their capacity optimally.
|
|
|
|
The equilibrium is a Nash equilibrium of the validator capacity allocation game, which
|
|
we analyze as follows. Let $R_s$ be the total reward rate offered by appchain $s$ (USD per
|
|
year per unit stake), and let $\hat{w}_s$ be the total stake allocated to appchain $s$.
|
|
The validator equilibrium satisfies:
|
|
\[
|
|
R_s(\hat{w}_s) = R_{s'}(\hat{w}_{s'}) \quad \forall s, s' \text{ in the active set},
|
|
\]
|
|
where $R_s(\hat{w}_s) = r_s^{\text{base}} + \beta_s \cdot \text{FeeRevenue}(s) / \hat{w}_s$.
|
|
This equalizes marginal returns across all opted-into appchains, which is the competitive
|
|
equilibrium condition.
|
|
|
|
%%==========================================================================
|