@Walrus 🦭/acc builds its entire reliability model on the idea that data does not need to be perfectly delivered at the moment it is written in order to be permanently safe. The lemmas shown in the diagram formalize this idea with mathematical guarantees, but their real importance lies in what they enable at the system level. They explain why Walrus can tolerate failures, delays, and partial delivery while still converging toward a complete and correct storage state over time. Instead of treating missing pieces as fatal errors, Walrus treats them as recoverable conditions governed by clear reconstruction thresholds.
The first lemma describes primary sliver reconstruction, which is the backbone of Walrus’s main data distribution. Each primary sliver is constructed using erasure coding with a reconstruction threshold of 2f + 1. This means that even if many symbols are missing or some nodes behave adversarially, any party that can collect 2f + 1 valid symbols from a primary sliver can reconstruct the entire sliver. In practice, this ensures that a storage node does not need to receive its full primary sliver during the write phase. As long as enough encoded symbols exist somewhere in the network, the sliver is never permanently lost.
This property is critical in asynchronous networks where timing cannot be assumed. Nodes may be offline, messages may be delayed, and writes may overlap with failures. Walrus does not block progress waiting for perfect delivery. Instead, it relies on the guarantee that missing primary slivers can always be rebuilt later once sufficient symbols are obtained. The system therefore prioritizes forward progress and availability proofs over immediate completeness, knowing that reconstruction remains possible.
The second lemma introduces secondary sliver reconstruction, which complements the first and completes Walrus’s two-dimensional design. Secondary slivers are encoded with a lower reconstruction threshold of f + 1, meaning fewer symbols are needed to recover them. This asymmetry is intentional. Secondary slivers act as recovery helpers for primary slivers. If a node missed its primary sliver entirely, it can use secondary slivers obtained from other nodes to reconstruct the missing primary data.
Together, these two lemmas explain why Walrus can guarantee eventual completeness for every honest node. Primary slivers ensure strong durability and correctness, while secondary slivers provide efficient recovery paths. The interaction between the two dimensions allows data to flow back into missing parts of the system without global rebuilds or full re-uploads. Recovery becomes local, proportional, and continuous rather than disruptive.
What makes this design especially powerful is that it decouples safety from synchrony. Many systems assume that data must be delivered correctly at write time to be safe. #walrus proves that this assumption is unnecessary. Safety comes from reconstruction guarantees, not delivery guarantees. As long as enough symbols exist in the network, data can always be recovered, verified, and redistributed.
In practical terms, these lemmas are what allow Walrus to scale. Nodes can join late, crash temporarily, or be replaced during reconfiguration without threatening stored data. Read load can be balanced because nodes eventually converge to holding their required slivers. Reconfiguration does not stall epochs because missing data can be reconstructed instead of transferred directly from unavailable nodes.
These reconstruction lemmas are not just theoretical results. They are the foundation of Walrus philosophy: decentralized storage should be resilient by design, not fragile by assumption. By mathematically guaranteeing recovery from partial data, Walrus transforms uncertainty into a controlled and predictable process, making long-term decentralized storage feasible at scale.
