Merge branch 'gavofyork:main' into main

Author: ggwpez

biblio.bib

@@ -301,7 +301,7 @@ @article{hosseini2024bandersnatch
   author          = {Seyed Hosseini and Davide Galassi},
   year            = {2024},
   url = {https://github.com/davxy/bandersnatch-vrfs-spec/blob/main/specification.pdf},
-  note = {Fetched 4th April, 2024}
+  note = {Fetched 10th March, 2025}
 }
 
 @article{ethereum2024sigital,

text/accumulation.tex

@@ -143,8 +143,8 @@ \subsection{Execution}
       \mathbf{t} &= [\Delta_1(\mathbf{o}, \mathbf{w}, \mathbf{f}, s)_\mathbf{t} \mid s \orderedin \mathbf{s}] \\
       &(\mathbf{d}, \mathbf{i}, \mathbf{q}, (m, a, v, \mathbf{z})) = \mathbf{o} \\
       \mathbf{x}' &= (\Delta_1(\mathbf{o}, \mathbf{w}, \mathbf{f}, m)_\mathbf{o})_\mathbf{x} \\
-      \mathbf{i}' &= (\Delta_1(\mathbf{o}, \mathbf{w}, \mathbf{f}, a)_\mathbf{o})_\mathbf{i} \\
-      \mathbf{q}' &= (\Delta_1(\mathbf{o}, \mathbf{w}, \mathbf{f}, v)_\mathbf{o})_\mathbf{q} \\
+      \mathbf{i}' &= (\Delta_1(\mathbf{o}, \mathbf{w}, \mathbf{f}, v)_\mathbf{o})_\mathbf{i} \\
+      \mathbf{q}' &= (\Delta_1(\mathbf{o}, \mathbf{w}, \mathbf{f}, a)_\mathbf{o})_\mathbf{q} \\
       \mathbf{n} &= \bigcup_{s \in \mathbf{s}}(\{ (\Delta_1(\mathbf{o}, \mathbf{w}, \mathbf{f}, s)_\mathbf{o})_\mathbf{d} \setminus \keys{\mathbf{d} \setminus \{s\}} \}) \\
       \mathbf{m} &= \bigcup_{s \in \mathbf{s}}(\keys{\mathbf{d}} \setminus \keys{(\Delta_1(\mathbf{o}, \mathbf{w}, \mathbf{f}, s)_\mathbf{o})_\mathbf{d}})
     \end{aligned}

text/bandersnatch.tex

@@ -1,20 +1,20 @@
-\section{Bandersnatch Ring VRF}\label{sec:bandersnatch}
+\section{Bandersnatch VRF}\label{sec:bandersnatch}
 
 The Bandersnatch curve is defined by \cite{cryptoeprint:2021/1152}.
 
-The singly-contextualized Bandersnatch Schnorr-like signatures $\bandersig{k}{c}{m}$ are defined as a formulation under the \emph{ietf} \textsc{vrf} template specified by \cite{hosseini2024bandersnatch} (as IETF VRF) and further detailed by \cite{rfc9381}.
+The singly-contextualized Bandersnatch Schnorr-like signatures $\bandersig{k}{c}{m}$ are defined as a formulation under the \emph{IETF} \textsc{vrf} template specified by \cite{hosseini2024bandersnatch} (as IETF VRF) and further detailed by \cite{rfc9381}.
 
 \begin{align}
-  \bandersig{k \in \H_B}{c \in \H}{m \in \Y} \subset \Y_{96} &\equiv \{ x \mid x \in \Y_{96}, \text{verify}(k, c, m, \text{decode}(x_{\dots32}), \text{decode}(x_{32\dots})) = \top \}  \\
-  \banderout{s \in \bandersig{k}{c}{m}} \in \H &\equiv \text{hashed\_output}(\text{decode}(x_{\dots32}) \mid x \in \bandersig{k}{c}{m})
+  \bandersig{k \in \H_B}{c \in \H}{m \in \Y} \subset \Y_{96} &\equiv \{ x \mid x \in \Y_{96}, \text{verify}(k, c, m, x) = \top \}  \\
+  \banderout{s \in \bandersig{k}{c}{m}} \in \H &\equiv \text{output}(x \mid x \in \bandersig{k}{c}{m})_{\dots32}
 \end{align}
 
 The singly-contextualized Bandersnatch Ring\textsc{vrf} proofs $\bandersnatch{r}{c}{m}$ are a zk-\textsc{snark}-enabled analogue utilizing the Pedersen \textsc{vrf}, also defined by \cite{hosseini2024bandersnatch} and further detailed by \cite{cryptoeprint:2023/002}.
 
 \begin{align}
-  \mathcal{O}(\seq{\H_B}) \in \Y_R &\equiv \text{KZG\_commitment}(\seq{\H_B})  \\
-  \bandersnatch{r \in \Y_R}{c \in \H}{m \in \Y} \subset \Y_{784} &\equiv \{ x \mid x \in \Y_{784}, \text{verify}(r, c, m, \text{decode}(x_{\dots32}), \text{decode}(x_{32\dots})) = \top \}  \\
-  \banderout{p \in \bandersnatch{r}{c}{m}} \in \H &\equiv \text{hashed\_output}(\text{decode}(x_{\dots32}) \mid x \in \bandersnatch{r}{c}{m})
+  \mathcal{O}(\seq{\H_B}) \in \Y_R &\equiv \text{commit}(\seq{\H_B})  \\
+  \bandersnatch{r \in \Y_R}{c \in \H}{m \in \Y} \subset \Y_{784} &\equiv \{ x \mid x \in \Y_{784}, \text{verify}(r, c, m, x) = \top \}  \\
+  \banderout{p \in \bandersnatch{r}{c}{m}} \in \H &\equiv \text{output}(x \mid x \in \bandersnatch{r}{c}{m})_{\dots32}
 \end{align}
 
-Note that in the case a key $\H_B$ has no corresponding Bandersnatch point when constructing the ring, then the Bandersnatch \emph{padding point} as stated by \cite{hosseini2024bandersnatch} should be substituted.
+Note that in the case a key $\H_B$ has no corresponding Bandersnatch point when constructing the ring, then the Bandersnatch \emph{padding point} as stated by \cite{hosseini2024bandersnatch} should be substituted.

text/overview.tex

@@ -55,16 +55,16 @@ \subsubsection{State Transition Dependency Graph}
   \psi' &\prec (\xtdisputes, \psi) \\
   \rho^\dagger &\prec (\xtdisputes, \rho) \label{eq:rhodagger} \\
   \rho^\ddagger &\prec (\xtassurances, \rho^\dagger) \label{eq:rhoddagger} \\
-  \rho' &\prec (\xtguarantees, \rho^\ddagger, \kappa, \tau') \\
+  \rho' &\prec (\xtguarantees, \rho^\ddagger, \kappa, \tau') \label{eq:rhoprime} \\
   \mathbf{W}^* &\prec (\xtassurances, \rho') \\
-  (\ready', \accumulated', \accountspostxfer, \chi', \iota', \varphi', \beefycommitmap) &\prec (\mathbf{W}^*, \ready, \accumulated, \accountspre, \chi, \iota, \varphi, \tau, \tau') \\
-  \beta' &\prec (\mathbf{H}, \xtguarantees, \beta^\dagger, \beefycommitmap) \\
+  (\ready', \accumulated', \accountspostxfer, \chi', \iota', \varphi', \beefycommitmap) &\prec (\mathbf{W}^*, \ready, \accumulated, \accountspre, \chi, \iota, \varphi, \tau, \tau') \label{eq:accountspostxfer} \\
+  \beta' &\prec (\mathbf{H}, \xtguarantees, \beta^\dagger, \beefycommitmap) \label{eq:betaprime} \\
   \accountspostpreimage &\prec (\xtpreimages, \accountspostxfer, \tau') \label{eq:accountspostpreimage} \\
   \alpha' &\prec (\mathbf{H}, \xtguarantees, \varphi', \alpha) \\
   \pi' &\prec (\xtguarantees, \xtpreimages, \xtassurances, \xttickets, \tau, \kappa', \pi, \mathbf{H})\!\!\!\!\!\!\!\!
 \end{align}
 
-The only synchronous entanglements are visible through the intermediate components superscripted with a dagger and defined in equations \ref{eq:betadagger}, \ref{eq:accountspostpreimage} and \ref{eq:rhoddagger}. The latter two mark a merge and join in the dependency graph and, concretely, imply that the availability extrinsic may be fully processed and accumulation of work happen before the preimage lookup extrinsic is folded into state.
+The only synchronous entanglements are visible through the intermediate components superscripted with a dagger and defined in equations \ref{eq:betadagger}, \ref{eq:rhodagger}, \ref{eq:rhoddagger}, \ref{eq:rhoprime}, \ref{eq:accountspostxfer}, \ref{eq:betaprime} and \ref{eq:accountspostpreimage}. The latter two mark a merge and join in the dependency graph and, concretely, imply that the availability extrinsic may be fully processed and accumulation of work happen before the preimage lookup extrinsic is folded into state.
 
 \subsection{Which History?}
 

text/pvm.tex

@@ -835,8 +835,8 @@ \subsection{Argument Invocation Definition}
   \end{aligned}\right.\\
   \where R&\colon (\varepsilon, \imath', \gascounter', \registers', \mem', \mathbf{x}') \mapsto \begin{cases}
     (\gascounter', \oog, \mathbf{x}') &\when \varepsilon = \oog \\
-    (\gascounter', \memory'_{\registers'_{7}\dots+\registers'_{8}}, \mathbf{x}') &\when \varepsilon = \halt \wedge \mathbb{Z}_{\registers'_{7}\dots+\registers'_{8}} \subset \mathbb{V}_{\mem'} \\
-    (\gascounter', [], \mathbf{x}') &\when \varepsilon = \halt \wedge \mathbb{Z}_{\registers'_{7}\dots+\registers'_{8}} \not\subset \mathbb{V}_{\mem'} \\
+    (\gascounter', \memory'_{\registers'_{7}\dots+\registers'_{8}}, \mathbf{x}') &\when \varepsilon = \halt \wedge \mathbb{N}_{\registers'_{7}\dots+\registers'_{8}} \subset \mathbb{V}_{\mem'} \\
+    (\gascounter', [], \mathbf{x}') &\when \varepsilon = \halt \wedge \mathbb{N}_{\registers'_{7}\dots+\registers'_{8}} \not\subset \mathbb{V}_{\mem'} \\
     (\gascounter', \panic, \mathbf{x}') &\otherwise \\
   \end{cases}
 \end{align}

text/pvm_invocations.tex

@@ -621,7 +621,7 @@ \subsection{Accumulate Functions}\label{sec:accumulatefunctions}
   \end{aligned}$\\
   \cmidrule(lr){1-1}\cmidrule(lr){2-2}
   \makecell*[l]{
-  $\Omega_\Aries(\gascounter, \registers, \memory, (\mathbf{x}, \mathbf{y}))$ \\
+  $\Omega_\Taurus(\gascounter, \registers, \memory, (\mathbf{x}, \mathbf{y}))$ \\
   \texttt{yield} = 16 \\
   $g = 10$} &
   $\begin{aligned}

text/reporting_assurance.tex

@@ -120,7 +120,7 @@ \subsubsection{The Assurances Extrinsic}
 
 The signature must be one whose public key is that of the validator assuring and whose message is the serialization of the parent hash $\mathbf{H}_p$ and the aforementioned bitstring:
 \begin{align}
-  &\forall a \in \xtassurances : a_s \in \sig{\kappa'[a_v]_e}{\mathsf{X}_A\frown \mathcal{H}(\se(\mathbf{H}_p, a_f))} \\
+  &\forall a \in \xtassurances : a_s \in \sig{\kappa[a_v]_e}{\mathsf{X}_A\frown \mathcal{H}(\se(\mathbf{H}_p, a_f))} \\
   &\mathsf{X}_A \equiv \token{\$jam\_available}
 \end{align}