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@@ -11,7 +11,7 @@ Blockchain $\mathbb{C_{loc}}$ is a series of epochs: it's a tree of chains,
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$C^1$, $C^2$, $\dots$, $C^n$, the chain ending in a single leader per slot single finalization.
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Crypsinous Blockchain is built on top of Zerocash sapling scheme, and Ouroboros Genesis blockchain.
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-Each participant $U_p$ stores it's own local view of the Blockchain $C_{loc}^{U_p}$.
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+Each participant $U_p$ stores its own local view of the Blockchain $C_{loc}^{U_p}$.
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$C_{loc}$ is a sequence of blocks $B_i$ (i>0), where each $B \in C_{loc}$
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$$ B = (tx_{lead},st)$$
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$$tx_{lead} = (LEAD, header, txs, stx_{proof})$$
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@@ -58,7 +58,7 @@ validation of proposed lead proof as follows:
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* verify block header hash
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* public inputs $\mu_y$, $\mu_{rho}$ are hash of current consensus $\eta$, and current slot
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* public inputs of target 2-term approximations $\sigma_1$, $\sigma_2$ are valid given total network stake and controller parameters
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-* the competing coin nullifier isn't published before to protect against double spening, before burning the coin.
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+* the competing coin nullifier isn't published before to protect against double spending, before burning the coin.
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* verify block transactions
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<!--
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@@ -100,7 +100,7 @@ $$sn_{c_i}=PRF_{root_{sk_{c_i}^{COIN}}}^{sn}(\rho_{c_i}), \forall_i \in \{1,2\}$
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## Epoch
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-An epoch is a vector of blocks. Some of the blocks might be empty if there is no winnig leader. tokens in stake are constant during the epoch.
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+An epoch is a vector of blocks. Some of the blocks might be empty if there is no winning leader. tokens in stake are constant during the epoch.
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## Leader selection
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@@ -133,9 +133,9 @@ family of functions.
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### automating f tuning
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-the stable consensus token supply is maintained by the help of discrete PID controller, that maintain stabilized occurance of single leader per slot.
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+the stable consensus token supply is maintained by the help of discrete PID controller, that maintain stabilized occurrence of single leader per slot.
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-#### control lottery f tunning paramter
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+#### control lottery f tunning parameter
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$$f[k] = f[k-1] + K_1e[k] + K_2e[k-1] + K_3e[k-2]$$
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@@ -233,7 +233,7 @@ be used by the protocol.
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| `rho_mu` | `pallas::Base` | random seed base from blockchain |
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| `rho` | `pallas::Base` | hash of random seed and `rho_mu` to constrain lottery |
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| `sigma1` | `pallas::Base` | first term in 2-terms target approximation. |
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-| `sigma2` | `pallas::Base` | second term in 2-terms target approximatino. |
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+| `sigma2` | `pallas::Base` | second term in 2-terms target approximation. |
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### Linear family functions
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@@ -333,7 +333,7 @@ assume there is a solution for the lead statement parameters and constants $S, f
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for the statement $y<T$, $$T=L\phi_{max}\phi(\alpha)=S\phi(\alpha)$$
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$$S=ord(G)\phi_{max}\phi(\alpha)$$
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such that S $in Z$
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-$\phi_{max}=\phi(\alpha_{max})$ where $\alpha_{max}$ is the maximum stake value being $2^{64}$, following from the previous proof that the family of function haveing independent aggregation property is the exponential function $f^\alpha$, and $f \in Z | f>1$, the smallest value satisfying f is $f=2$, then $$\phi_{max} = 2^{2^{64}}$$
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+$\phi_{max}=\phi(\alpha_{max})$ where $\alpha_{max}$ is the maximum stake value being $2^{64}$, following from the previous proof that the family of function having independent aggregation property is the exponential function $f^\alpha$, and $f \in Z | f>1$, the smallest value satisfying f is $f=2$, then $$\phi_{max} = 2^{2^{64}}$$
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note that since $ord(G)<<\phi_{max}$ thus $S<<1$, contradiction.
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@@ -355,11 +355,11 @@ R is the epoch length in terms of slots.
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### toward better decentralization in ouroboros
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-the randomization of the leader selection at each slot is hinged on the random $y$, $\mu_y$, $\rho_c$, those three values are dervied from $\eta$, and root of the secret keys, the root of the secret keys for each stakeholder can be sampled, and derived beforehand, but $\eta$ is a response to global random oracle query, so it's security is hinged on $\textit{centralized global random node}$.
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+the randomization of the leader selection at each slot is hinged on the random $y$, $\mu_y$, $\rho_c$, those three values are derived from $\eta$, and root of the secret keys, the root of the secret keys for each stakeholder can be sampled, and derived beforehand, but $\eta$ is a response to global random oracle query, so it's security is hinged on $\textit{centralized global random node}$.
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#### solution
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-to break this centeralization, a decentralized emulation of $G_{ro}$ functionality for calculation of: $\eta_i=PRF^{G_{ro}}_{\eta_{i-1}}(\psi)$
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+to break this centralization, a decentralized emulation of $G_{ro}$ functionality for calculation of: $\eta_i=PRF^{G_{ro}}_{\eta_{i-1}}(\psi)$
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$$\psi = hash(tx^{ep}_{0})$$
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$$\eta_0 = hash(\mathrm{"let\; there\; be\; dark!"})$$
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note that first transaction in the block, is the proof transaction.
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omahs