The Cascade Log: Reference-Stable Windowing over Tiered Append Sequences

2026-06-03

AI Summary

This work addresses reference instability in tiered append-only sequences—manifesting as dangling, stale, corrupted references, and snapshot skew—caused by migrating hot data to cold tiers. To resolve this, the authors propose the Cascade Log structure, which formally defines cross-tier reference anomalies for the first time and introduces a persistent merge-interval mapping as the authoritative version source. By integrating immutable root snapshots, block-level folding, and B-tree-like update strategies, Cascade Log achieves both reference stability and snapshot consistency under append-heavy workloads. The resulting index structure exhibits Θ(A) space complexity, supports point and range queries in O(log A) and O(log A + k) time respectively, and attains theoretically optimal update overhead. Experimental results demonstrate that the approach effectively eliminates reference anomalies at scale, even with millions of records.

Abstract

A long-running append-mostly sequence, such as an edit log, event store, or versioned working set, is usually tiered into a bounded hot stratum and colder folded summaries. This saves memory but breaks stable references: a handle minted while a record is hot may later be resolved after the record has moved into a digest, after it has been superseded, or while a fold is in flight. We define the resulting cross-tier anomalies--dangling, stale, corrupt, and snapshot-skewed resolution--and present the Cascade Log, a reference-stable tiered append structure. The structure keeps a single persistent coalescing interval map over handles as the sole authority on each live version; folding a contiguous run replaces many singleton entries by one digest-backed interval node, and immutable roots provide snapshot tokens. Its cost is characterized by the fragmentation $A$, the number of index pieces, namely live handles plus maximal same-digest runs. The index uses $Θ(A)$ space, resolves a point in $O(\log A)$, reports a $k$-handle range in $O(\log A+k)$, and performs $a$ appends and $s$ supersedes in $O((a/B+s)\log A)$ update work for fold block size $B$. Matching lower bounds show that $Ω(A)$ space and $Ω(\log A+k)$ ordered range cost are unavoidable, and an adversary can force $A=Θ(s)$. Thus the index is sublinear on append-dominated histories and grows linearly only under fragmenting edits. A reference implementation and reproducible experiments to $10^6$ records validate the anomaly-freedom and the fragmentation bounds.

Problem

• reference stability
• tiered storage
• append-only logs
• cross-tier anomalies
• versioned data

Innovation

• reference stability
• tiered append sequences
• coalescing interval map
• fragmentation
• snapshot consistency