papers/lp-211-cross-shard-atomic/sections/01-introduction.tex

\section{Introduction}

This paper expands on LP-211
(\texttt{lps/LP-211-cross-shard-atomic.md}) with the five new wire
schemas, the atomicity proof sketch, the load-bearing composition
with LP-202's monotonic cert-tier upgrade, and the latency
projections at LAN/WAN $\times$ PQ-strict/PQ-heavy.

\subsection{What was wrong before}

LP-204 organizes state into Tier-2 chain-VMs running on a parent L1.
Each chain-VM has its own LP-208 mempool, LP-209 wave ordering, and
LP-210 Block-STM executor. Per-shard finality is independent: each
shard publishes its own QuasarCert per wave.

For a transaction group whose state touches multiple chain-VMs, this
shard-independence is a correctness problem. If shard $A$'s wave
commits but shard $B$'s wave aborts, the cross-shard transaction is
half-applied: $A$'s state has moved, $B$'s has not. The protocol
needs cross-shard atomicity.

\subsection{What this LP solves}

Cross-shard 2PC via a parent-L1 QuasarCert. A coordinator (one of
the parent L1's validators, selected deterministically per cross-shard
tx group) dispatches per-shard portions to shard executors, collects
prepare-acks (LP-210 Phase-4 staged-prepare), and when all shards
have prepared, submits a cross-shard commit transaction to the
parent L1. The parent L1's next wave (LP-209) includes that commit
tx; the wave's LP-217 cert is the cross-shard cert. Once the parent
L1's cert finalizes, every shard's prepared overlay is committed
atomically.

If any shard refuses to prepare, the coordinator submits a
cross-shard abort transaction instead; every prepared shard unwinds
its staged overlay via LP-202 \texttt{txn.Discard()}. ALL shards
commit OR NONE.

\subsection{Why Polaris cert, not a sidechain mechanism}

A naive cross-shard atomicity mechanism uses a sidechain or a relay
validator set. LP-211 instead uses the \emph{parent L1's existing
QuasarCert} as the atomic-commit anchor. The parent L1 already has a
validator set; LP-204's chain-VMs inherit the parent's security
automatically. The parent L1's cert at LP-217's chosen mode is the
strongest cryptographic statement available on the network -- using
it for cross-shard commit means cross-shard finality is exactly as
strong as the parent L1's finality at that mode.

No new validator set. No new bridge contract. No new dispute window.
The cert that the parent L1 already publishes per wave serves as
the cross-shard commit anchor. The shards prepare; the parent L1
commits; the cert covers the commit.

This is the canonical pattern from LP-204 ``Cross-VM atomic memory''
elevated to a wave-scale formal protocol.

\subsection{Latency and throughput dividends}

\paragraph{Latency.} Per-shard waves continue at the LP-209 cadence
($\sim$\SI{100}{\milli\second} LAN under the projected GPU-accelerated
cert; $\sim$\SI{711}{\milli\second} on the measured CPU-only cert
per the 2026-06-04 quasar-matrix-bench Spark $N{=}64$ PQ-strict
row, \texttt{/tmp/quasar-results-spark.txt}). The cross-shard cert
adds one parent-L1 wave plus the LP-217 cert mode timing
($\sim$\SI{5}{\milli\second} at PQ-strict projected GPU;
$\sim$\SI{595}{\milli\second} measured CPU). Total cross-shard
latency: $\sim$\SI{260}{\milli\second} (projected GPU) or
$\sim$\SI{1326}{\milli\second} (measured CPU) at LAN scale at
PQ-strict.

\paragraph{Throughput.} Each shard's waves run independently except
for the cross-shard txs, which by construction are a minority of the
workload (in securities-style traffic: $\sim 5\%$). The $95\%$
intra-shard waves commit at the LP-210 single-shard rate; the $5\%$
cross-shard waves pay the 2PC tax.