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Legible Consensus: Topology-Aware Quorum Geometry for Asymmetric Networks

Tony Mason

Abstract

Quorum design over asymmetric topologies conflates two independent concerns: inter-tier obligation (which tiers must participate for cross-tier safety) and intra-tier replication (how each tier survives local failures). Flat quorums treat all nodes as interchangeable; when consensus fails, the structure does not reveal whether a tier was unreachable or a tier lost too many replicas. We show that mapping a crumbling-wall quorum construction to a physically tiered network separates these concerns and makes the protocol's failure modes legible: an operator can determine which tiers retain global consensus capability from the wall structure and connectivity state alone, without runtime probing. Using a 10-node Earth/LEO/Moon/Mars topology as a magnifying glass, we confirm that three of four tiers retain global liveness during Mars conjunction blackout; only the disconnected tier loses it. Consensus latency at each tier equals the speed-of-light round-trip to Earth: 183~ms (Earth), 131~ms (LEO), 5.1~s (Moon). The wall also imposes a leadership cost gradient on Multi-Paxos elections that symmetric grid quorums cannot express. A comparison between sparse and full-coverage topologies separates wall obligations from network reachability as independent liveness constraints. All results are design-level; quorum intersection is verified exhaustively in TLA+.

Legible Consensus: Topology-Aware Quorum Geometry for Asymmetric Networks

Abstract

Quorum design over asymmetric topologies conflates two independent concerns: inter-tier obligation (which tiers must participate for cross-tier safety) and intra-tier replication (how each tier survives local failures). Flat quorums treat all nodes as interchangeable; when consensus fails, the structure does not reveal whether a tier was unreachable or a tier lost too many replicas. We show that mapping a crumbling-wall quorum construction to a physically tiered network separates these concerns and makes the protocol's failure modes legible: an operator can determine which tiers retain global consensus capability from the wall structure and connectivity state alone, without runtime probing. Using a 10-node Earth/LEO/Moon/Mars topology as a magnifying glass, we confirm that three of four tiers retain global liveness during Mars conjunction blackout; only the disconnected tier loses it. Consensus latency at each tier equals the speed-of-light round-trip to Earth: 183~ms (Earth), 131~ms (LEO), 5.1~s (Moon). The wall also imposes a leadership cost gradient on Multi-Paxos elections that symmetric grid quorums cannot express. A comparison between sparse and full-coverage topologies separates wall obligations from network reachability as independent liveness constraints. All results are design-level; quorum intersection is verified exhaustively in TLA+.

Paper Structure

This paper contains 27 sections, 6 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Flexible Paxos
  4. Crumbling-Wall Quorum Systems
  5. Composing the Two Ideas
  6. Construction
  7. System Model
  8. Per-Tier Phase 1 Families
  9. Phase 2 Family
  10. Safety: Quorum Intersection
  11. Liveness: Reading the Wall
  12. What "Global" Means
  13. Related Work
  14. Experimental Design
  15. Topology
  16. ...and 12 more sections

Figures (3)

  • Figure 1: The crumbling-wall construction over the 5/1/1/3 topology. Each tier's Phase 1 quorum reads downward through the wall (dashed arrows). Phase 2 uses only the Earth row (shaded). The wall narrows from bottom to top: wider rows offer more quorum choices.
  • Figure 2: Liveness under Mars conjunction blackout. The partition (dashed line) disconnects $T_3$. Earth, LEO, and Moon can still read downward to form Phase 1 quorums (green arrows). Mars cannot reach any inner tier (red $\times$). The wall crumbles from the top.
  • Figure 3: Phase 1 quorum count by initiating tier (strict $\mathcal{Q}_2$, from exhaustive TLA+ enumeration). Leadership flexibility increases monotonically from top to bottom of the wall.