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Cross-paper appendix: Eventually Consistent State Abstractions

Three different parts of the Arboria stack — the ICCD intent payload, the TF-ACO pheromone field, and the HMA depot inventory — all need the same property: distributed replicas that converge under partition without a central arbiter. We use one consistency abstraction across all three.

The abstraction. Each piece of distributed state is expressed as a composite CRDT built from primitives:

  • LWW register — for monotonic-by-timestamp scalars (intent goal coordinates, current pheromone evaporation epoch, depot SOC headroom).
  • G-Counter / PN-Counter — for monotonic-by-cause scalars (deposit counts, dispensed-mass tallies).
  • OR-Set — for membership-by-tag (active constraints, registered haulers, occupied tasks).
  • Vector clock — for causal context across replicas.

Composition (Theorem 1 in the ICCD Appendix A) closes the join-semilattice property over finite products of primitives, so the composite state inherits associativity, commutativity, idempotence, and convergence under eventually-feasible delivery.

Per-paper instantiation.

PaperWhat’s distributedComposite CRDT
ICCDMission intent (goal, constraints, summary)LWW × OR-Set × VectorClock
DMB + TF-ACOPer-cell pheromone (deposit count + evaporation epoch)G-Counter × LWW
HMADepot inventory (mass-in, mass-out, hauler claims)PN-Counter × OR-Set

Each instance is reconciled with the same merge machinery in gossamer.crdt, so a single bug fix or improvement to the merge layer benefits all three papers. This is the structural reason the Arboria stack does not need a separate “consensus protocol” per paper.

Unified symbols

A single symbols table lives in ICCD Appendix F and is referenced by both other papers; ψ, AoI, ε, and χ mean the same thing across the three.

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