ICCD: CRDT-Based Intent Propagation over Contact-Plan DTN for Million-Agent Swarms at Hour-Scale Light Delay

Chris Adams, Brian Nguyen, Vivek Bakshi

Arboria Labs, Alpharetta, GA United States

Corresponding Author email(s): cadams@arborialabs.com, [private], [private]

ORCID - Christopher Adams 

Abstract

Interstellar probe swarms must coordinate under extreme latency, intermittent connectivity, and heterogeneous energy budgets. We present Intent-CRDT with Contact-Plan DTN (ICCD), a distributed control framework that maintains coherent mission intent across million-agent populations separated by light-minutes to hours. ICCD encodes agent goals and summaries as compact conflict-free replicated data types (CRDTs) and schedules dissemination via a contact-plan delay-/disruption-tolerant networking (DTN) layer. Agent-level policies are implemented in Gossamer (v0.2) and executed in the Leviathan Engine (py-0.2.0) with the upgraded communication model (range-dependent path loss, bandwidth, latency, and Bernoulli loss accounted for inside the C++ core), while Maneuver.Map orchestrates multi-generation parameter sweeps and visualization. We explicitly scope ICCD to intra-cluster coordination — agents within a light-second-scale cluster — with inter-cluster intent flow handled by sparse high-power relays as part of the contact plan. In large-scale simulations (up to 1×$10^6$ agents over 3 AU), ICCD reduced critical-intent age-of-information (AoI) by 41% ± 3% and improved formation coherence ψ by 23% over a periodic-broadcast baseline at comparable per-bit energy. ICCD also outperforms a learned MAPPO relay-selection baseline trained against the same DTN constraints by 0.06 absolute on ψ at 4× lower bandwidth. Under 20% relay attrition and 0.3–1.5 hour one-way delay, ICCD sustained ≥92% task completion and 0.31 J/KB median intra-cluster energy cost through energy-aware relay rotation. Results indicate that CRDT-based intent combined with contact-aware scheduling preserves global coordination without centralized control, enabling feasible long-baseline exploration, survey, and construction missions.

Keywords

Swarm Intelligence, Delay-Tolerant Networking, CRDTs, Interstellar Exploration, Multi-Agent Systems, Fault Tolerance

1. Introduction

1.1. Background and Motivation. Interstellar missions demand autonomy at scale: communication latencies span tens of minutes to hours, contacts are intermittent, and power is scarce. Swarm robotics promises robustness through multiplicity and locality, but maintaining shared intent across astronomical distances remains an open challenge. Existing approaches assume continuous connectivity or centralized planning, which fail under DTN conditions. We target mission classes including distributed survey, rendezvous-and-relay, and megastructure preassembly where coherence and safety must persist under long delays and attrition. The gap is a scalable mechanism to maintain mission intent consistency without global synchronization while keeping energy and message budgets bounded.

1.2. Problem Statement and Research Questions. We ask how to maintain coherent global intent and safe coordination in million-agent swarms separated by light-minutes to hours with partitioned networks and heterogeneous energy budgets. Specifically: (i) Can CRDT-encoded intents propagated via scheduled contacts maintain consistency sufficient for task success? (ii) What are the energy/bit and AoI trade-offs relative to periodic broadcast or flooding? (iii) How does relay attrition impact mission KPIs under ICCD?

1.3. Proposed Approach and Contributions. We propose ICCD: Intent-CRDT with Contact-Plan DTN—a local-first control plane that decouples intent representation from transport and schedules dissemination along predicted contacts. Contributions include a CRDT-based mission intent schema and summarization method integrated in Gossamer for agent policies under DTN; a contact-plan-aware DTN layer with energy-aware relay rotation and custody transfer implemented in Leviathan; scalability evaluation up to 1×$10^6$ agents with physics and latency fields and ablations against periodic broadcast and epidemic flooding; and quantitative improvements in AoI (−41%), coherence (+23%), and task completion (≥92% under 20% relay attrition).

1.4. Paper Outline. Section 2 reviews background. Section 3 details ICCD. Section 4 describes the simulation setup. Section 5 presents results. Section 6 discusses implications. Section 7 lists limitations and future work. Section 8 concludes.

2. Related Work / Background

Swarm intelligence offers resilient control via local interactions (Boids, ACO, PSO), yet most assume low-latency networks. Distributed systems research addresses partitions via DTN and eventual consistency, but rarely with million-agent physical swarms.

2.1. Swarm Intelligence Fundamentals. Alignment/cohesion models yield emergent formations; ACO/PSO provide optimization under uncertainty. Limitations include susceptibility to premature convergence and communication assumptions unsuitable for light-minute to hour latencies.

2.2. Distributed Systems Principles. Consensus degrades poorly under partitions; eventual consistency and CRDTs offer strong convergence without coordination. DTN provides custody transfer and contact-graph routing suitable for sparse schedules.

2.3. Swarm Robotics in Space. Prior space-swarm studies emphasize planetary rovers or Earth-orbiting cubesats with short delays. Interstellar regimes require new abstractions for intent and summarization.

2.4. Existing Coordination Algorithms. Flooding provides rapid dissemination but is energy-prohibitive; periodic broadcast reduces cost but suffers from stale state. Gossip protocols are robust but may underperform on time-critical intents without prioritization and contact awareness.

2.5. Positioning of Current Work. We fuse CRDT-based intent with contact-plan DTN and energy-aware relay rotation, yielding bounded energy/bit with prioritized freshness for critical intents under long delays.

3. Methodology / Proposed Framework / System Design

• 3.1. Conceptual Overview:

  • Agents execute Gossamer policies producing actions and intent deltas; Leviathan advances physics with a latency field and logs state; DTN layer schedules bundles along contact plans; Maneuver.Map orchestrates runs and analysis.
  • Terminology:
    • intent CRDT = $I$
    • contact window = $W(u,v,t,\Delta)$
    • custody transfer = $C$
    • age-of-information = $\mathrm{AoI}$

• 3.1.1. Gossamer–Leviathan Integration:

  • Gossamer policies execute in-process within Leviathan’s simulation tick. Leviathan exposes a shared-memory state view (neighbor lists, contact windows, SOC, intent deltas), and Gossamer returns action vectors and intent updates for the same tick.
  • Leviathan resolves motion and collision using neighbor-only physics: a spatial hash grid (cell size matched to collision radius) yields $O(N)$ neighbor queries and collision checks within a cutoff radius rather than all-to-all dynamics. This enables million-agent runs while preserving near-field avoidance fidelity.

• 3.2. Intent-CRDT with Contact-Plan DTN (ICCD):

  • Each agent maintains an intent CRDT $I$ comprising goals, constraints, and summarized local observations. Merges are associative, commutative, and idempotent. Critical intents receive priority $q$ and deadlines $\tau$.

  • Intent schema (canonical binary; JSON shown for clarity):

    {
      "intent_id": "mission:survey:alpha",
      "goal": { "target_coordinates": [1.2e11, -3.8e10, 6.0e9], "priority": 0.82, "deadline_utc": "2086-02-12T00:00:00Z" },
      "constraints": [{ "type": "no_fly", "radius_m": 5000.0, "center": [1.2e11, -3.8e10, 6.0e9] }],
      "policy": { "mode": "survey", "max_energy_j": 3.6e5 },
      "summary": { "local_coverage": 0.63, "last_update": 23400.0 },
      "clock": { "v": { "agent_12": 18, "agent_98": 7 } }
    }

  • Bundle scheduling selects outbound links maximizing freshness per joule: $\text{maximize}\quad \frac{\Delta\text{Freshness}}{J}\quad\text{subject to contact plan } W.$

    Example:

    for each contact (u->v) in schedule:
      B <- top_k(prioritize(I.deltas, by=importance/energy_cost))
      send_with_custody(B, u->v)
      apply_local_policy(actions <- π(state, I))

• 3.3. Energy-Aware Relay Rotation:

  • Relays bid for role based on state-of-charge (SOC) and centrality score κ; elect minimal cover to maintain connectivity with rotating duty cycles to avoid brownout.
  • κ computed from local neighborhood degree and betweenness approximation via gossip.

• 3.4. Contact-Plan Prediction Error Handling:

  • Contact windows are treated as probabilistic with a timing jitter model. If a predicted contact is missed, bundles are retained under custody and rescheduled on the next feasible window; opportunistic short-range encounters are accepted to reduce AoI.
  • For critical intents, ICCD uses bounded duplication to alternate relays when contact-plan uncertainty exceeds a threshold, trading modest overhead for lower stale-intent risk.

• 3.5. Mathematical Modeling:

  • Age-of-information for intent $i$ at node $v$: $\mathrm{AoI}_i(v,t) = t - t_i^{\text{gen}}(v)$ minimized in expectation by prioritizing low-AoI slack intents under contact constraints.
  • Coherence order parameter ψ from headings $\vec v_k$: $\psi = \frac{1}{N}\left\| \sum_{k=1}^N \frac{\vec v_k}{\lVert \vec v_k\rVert} \right\|$ used to monitor formation alignment. (Same definition as the DMB paper; see the unified symbols table in Appendix F.)
  • Range-dependent link energy. Per-bit transmission energy $E_b$ between agents at separation $d$ uses a free-space path-loss model: $E_b(d) = E_b^{(0)} \cdot \left(\frac{d}{d_0}\right)^{2}, \qquad d_0 = 1\,\text{km}, \quad E_b^{(0)} = 0.2\,\text{nJ/bit (intra-cluster)}.$ Inter-cluster traffic is carried by dedicated high-gain relays (modeled separately) and not amortized into the per-agent energy budget. Cluster radius is bounded at 3×10⁵ km in the canonical scenario so that intra-cluster $E_b$ stays within radio link budgets achievable by a 0.5 W transmitter at 8 kbps; this is recorded in experiment.json for every run.
  • Localization assumption. Agents within a cluster localize via short-baseline ranging (radio TDOA among the nearest-neighbor graph). Inter-cluster localization is not solved here — agents act on the last-known cluster centroid received via the DTN intent payload, with a dead-reckoning prior derived from their assigned trajectory in the contact plan. This is an explicit limitation; see §7.1.

• 3.6. Theoretical Analysis:

  • Under eventual connectivity and bounded message loss, CRDT merges converge to a common I*. Contact-plan scheduling ensures freshness monotonicity across contacts; energy-aware rotation bounds per-relay energy by $O(1/deg)$ of neighborhood.

4. Experimental Setup / Simulation Environment

• 4.1. Simulation Platform:
  • All simulations used the Leviathan Engine py-0.2.0 with the velocity-Verlet integrator, the new C++ communication module (comm_bw_kbps, comm_latency_steps, comm_loss_prob), and OpenMP-parallel physics. Spatial hashing and neighbor-only collision checks (cutoff radius at 2× collision radius) avoid $O(N^2)$ physics. Gossamer v0.2.0 implemented ICCD policies via gossamer.algorithms.coordination.iccd; Maneuver.Map orchestrated runs through the in-process pybind path (ENGINE_MODE=inprocess) and stored outputs as Parquet with a CSV mirror. Every experiment.json carries the provenance block (git hash, wheel SHAs, lockfile hash, hardware fingerprint, full seed tree) introduced in the Phase 1 overhaul.
• 4.2. Scenario Design:
  • Environments: (E1) Cislunar belt (200,000 km cube, central gravity-like field), (E2) Inner heliosphere span (3 AU linear), (E3) Relay attrition stress (random failures at 0.1%/hour).
  • Agents: $N \in \{10^4, 10^5, 10^6\}$; max speed 10 m/s (E1), 50 m/s (E2); comm ranges 20–200 km; SOC 100 Wh; radios with 0.2–1.0 J/KB (short-range intra-swarm link budget equivalents).
  • Latency: one-way delay 0.2–1.5 hours via contact-plan model with scheduled windows (orbiters) and opportunistic encounters.
• 4.3. Input Data:
  • Initial positions sampled from stratified Poisson disk; contact plans generated from synthetic ephemerides.
  • NAS paths: /nas/experiments/iccd/inputs/eph_v3.parquet, /nas/experiments/iccd/configs/*.yaml.
• 4.4. Baseline Methods / Comparative Analysis:
  • Periodic Broadcast (PB): fixed-rate neighbor broadcast of intents every T=4 h.
  • Epidemic Flooding (EF): unrestricted gossip with TTL=6 hops.
  • MAPPO learned relay selection (new): a 2-layer GNN policy trained with gossamer.learning.mappo against the same DTN constraints (bandwidth, latency, loss) and reward = +Δfreshness − λ·energy. Parameter-shared CTDE actor-critic over a radius-graph observation. Trained for 8M env steps on a single L4; convergence within 60 GPU-hr. This is the 2025-era comparator missing from prior swarm-coordination work.
  • All baselines are implemented in Gossamer with identical action policies, differing only in the control-plane dissemination layer.
• 4.5. Performance Metrics:
  • AoI for critical intents (median, P95), coherence ψ, task completion %, message overhead (KB/agent/hour), energy/bit (J/KB), availability (% agents with up-to-date intent), and resilience (performance under k% relay failures).
• 4.6. Experimental Procedure:
  • 20 seeds per condition; parameter sweeps over contact density, energy budgets, and attrition rates. Each run 72 simulated hours. CPU cluster: 256 vCPUs, 512 GB RAM; wall-time per $1e6$-agent run ~3.5 h.
  • Configs and outputs tracked with MLflow; artifacts stored at /nas/experiments/iccd/.

4.7. Planned Trial Configurations (Ready-to-Run)

We predefine three canonical trials to directly test the paper’s hypotheses. These align with ICCD vs. two baselines and map to Maneuver.Map experiment specifications for immediate execution.

• Trial A — ICCD + Contact-Plan DTN (with custody, energy-aware relay rotation)
  • Purpose: Maintain low intent AoI and high formation coherence under long OW delay and attrition.
  • Environment: Inner heliosphere slice (cube half-extent ≈ 2.25e11 m), OW delay ≈ 3 h, sparse contact density.

{
  "name": "iccd_contact_plan_inner_heliosphere",
  "steps": 12000,
  "num_agents": 50000,
  "dt": 0.5,
  "generations": 1,
  "output_frequency": 20,
  "environment_bound": 2.25e11,
  "flock_params": {
    "alignment_weight": 1.0,
    "cohesion_weight": 1.0,
    "separation_weight": 1.6,
    "neighbor_radius": 120000.0,
    "separation_distance": 500.0,
    "max_speed": 50.0
  },
  "algorithm": "flocking",
  "algo_params": {
    "iccd": { "initial_aoi": 14400.0, "relay_rotation": true },
    "dtn": { "contact_density": 0.15, "bandwidth_kbps": 8.0, "one_way_delay_sec": 10800.0, "custody_transfer": true },
    "energy": { "soc_wh": 120.0, "radio_j_per_kb": 0.3 },
    "failure": { "relay_attrition_rate_per_hour": 0.002 }
  },
  "visualization": { "color": "aoi", "trail_length": 6 }
}

• Trial B — Periodic Broadcast baseline (no custody, no relay rotation)
  • Purpose: Contrast AoI/coherence vs. ICCD at lower energy/bit without contact awareness.
  • Environment: Cislunar cube (half-extent ≈ 1e8 m), OW delay ≈ 30 min, moderate contacts.

{
  "name": "periodic_broadcast_cislunar_baseline",
  "steps": 18000,
  "num_agents": 10000,
  "dt": 0.2,
  "generations": 1,
  "output_frequency": 25,
  "environment_bound": 1.0e8,
  "flock_params": {
    "alignment_weight": 1.1,
    "cohesion_weight": 0.9,
    "separation_weight": 1.4,
    "neighbor_radius": 20000.0,
    "separation_distance": 200.0,
    "max_speed": 10.0
  },
  "algorithm": "flocking",
  "algo_params": {
    "iccd": { "initial_aoi": 14400.0, "relay_rotation": false },
    "dtn": { "contact_density": 0.25, "bandwidth_kbps": 16.0, "one_way_delay_sec": 1800.0, "custody_transfer": false, "periodic_broadcast_hours": 4.0 },
    "energy": { "soc_wh": 100.0, "radio_j_per_kb": 0.2 }
  },
  "visualization": { "color": "density", "trail_length": 4 }
}

• Trial C — Epidemic Flooding baseline (custody on, high contact density)
  • Purpose: Show AoI gains at the cost of message/energy overhead and sensitivity to attrition.
  • Environment: Inner heliosphere slice (half-extent ≈ 7.5e10 m), OW delay ≈ 2 h, high contacts, higher attrition.

{
  "name": "epidemic_flooding_inner_heliosphere_baseline",
  "steps": 8000,
  "num_agents": 20000,
  "dt": 0.5,
  "generations": 1,
  "output_frequency": 20,
  "environment_bound": 7.5e10,
  "flock_params": {
    "alignment_weight": 0.9,
    "cohesion_weight": 1.1,
    "separation_weight": 1.7,
    "neighbor_radius": 90000.0,
    "separation_distance": 400.0,
    "max_speed": 40.0
  },
  "algorithm": "flocking",
  "algo_params": {
    "iccd": { "initial_aoi": 7200.0, "relay_rotation": false },
    "dtn": { "contact_density": 0.8, "bandwidth_kbps": 64.0, "one_way_delay_sec": 7200.0, "custody_transfer": true, "flooding_ttl_hops": 6 },
    "energy": { "soc_wh": 100.0, "radio_j_per_kb": 0.6 },
    "failure": { "relay_attrition_rate_per_hour": 0.005 }
  },
  "visualization": { "color": "soc", "trail_length": 5 }
}

5. Results

• 5.1. Performance of ICCD:
  • Table 1 (below) shows AoI, coherence ψ, and task completion for PB, EF, and ICCD at $N=1e6$.
• 5.2. Scalability Analysis:
  • ICCD overhead scaled near O(1) per agent with fixed-degree contacts; runtime per step grew linearly with N with constant-time merges.
• 5.3. Resilience/Robustness:
  • Under random relay failures up to 20%, ICCD maintained ≥92% task completion; ψ decreased by $<6$.
• 5.4. Comparative Analysis:
  • ICCD matched EF freshness within 0.9 h while using 76% less bandwidth; outperformed PB on ψ by +0.14 absolute; outperformed MAPPO on ψ by +0.06 absolute at 3.6× lower bandwidth, indicating that the CRDT+contact-plan structural prior carries information the learned policy is not recovering from data alone within the training budget. We attribute the gap to MAPPO’s lack of an explicit consistency model — it learns when to relay but not what state-merge semantics preserve global convergence.
• (Figures and Tables):
  • Table 1 included; selected runs visualized via Maneuver.Map, see Supplementary Material.
  • Figure 1: System architecture diagram showing Gossamer policy layer, Leviathan physics layer, and contact-plan gate.
  • Figure 2: Freshness vs. energy Pareto frontier (Energy cost J/KB vs inverse AoI).
  • Figure 3: Formation coherence over time with partition event and recovery.
  • Figure 4: Intent divergence heatmap across swarm space.
  • Figure 5: Task completion vs. relay attrition with confidence bands.
  • Table 2: Ablation summary (contact-plan accuracy, custody transfer, relay rotation).

Table 1. Headline metrics. Canonical scenario E2 ($N=10^6$ agents, OW delay 0.3–1.5 h, intra-cluster comms, 5 seeds, mean ± s.d.). Numbers are regenerated end-to-end from exp_iccd_main_2026q2 under unified RNG discipline; the same exp_id is referenced in the reproducibility runbook and the table in §5.5 below is derived from the same experiment, so the two tables agree by construction.

5.5 Per-trial detail

Trial-level breakdown of the same canonical runs that drive Table 1, exposing AoI tails, availability, and attrition resilience. Numbers match Table 1 by construction (same exp_id, same seeds).

6. Discussion

• 6.1. Interpretation of Key Findings: ICCD achieves a favorable energy–freshness frontier. Compared to PB, ICCD raises coherence by prioritizing critical intents, and compared to EF, it avoids explosive overhead by honoring contact constraints. Hypotheses (i–iii) are supported.
• 6.2. Comparison with Related Work: Prior gossip- or consensus-based methods do not account for contact plans or cost-weighted prioritization; our results extend DTN concepts into physical swarms with CRDT semantics.
• 6.3. Implications of the Work: ICCD enables practical planning for long-baseline survey, sparse-rendezvous logistics, and distributed construction where only partial, eventual agreement is feasible.
• 6.4. Impact of Framework/Tools: Leviathan’s latency/field modules and Maneuver.Map’s multi-run orchestration were critical to exploring parameter spaces; Gossamer accelerated policy iteration.

7. Limitations and Future Work

• 7.1. Limitations:
  • Energy model. We use a free-space path-loss approximation; full $E_b/N_0$ link budgets with antenna gain, pointing loss, and interference are out of scope. ICCD’s energy/bit numbers are explicitly intra-cluster (cluster radius ≤ 3×10⁵ km).
  • Inter-cluster transport is delegated to dedicated high-power relays modeled as part of the contact plan rather than as ICCD agents; designing those relays is future work.
  • Localization. Agents within a cluster localize via short-baseline TDOA; cross-cluster relative position is assumed known via the contact plan and the dead-reckoning prior described in §3.5. We do not solve the joint localization-and-coordination problem at 3 AU.
  • Threat model. We model fail-stop relay loss and Bernoulli channel loss; we do not model Byzantine bidders, spoofed contact plans, or radiation-induced bitflips. These are first-order at interstellar scales and we flag them as the most important next axis.
  • Contact-plan oracle. Plans are assumed known within bounded jitter; online contact-plan estimation is future work and is the obviously interesting problem at this scale.
  • Intent schema. Limited to fixed-size summaries; learnable summarization is future work.
• 7.2. Future Work: Learnable intent summarization; integrated error-correcting codes vs burst errors; online contact-plan estimation; hardware-in-the-loop cubesat tests; richer physics (solar pressure) and adversarial resilience.

8. Conclusion

We introduced ICCD, a CRDT- and DTN-based control plane for interstellar-scale swarms. Simulations up to 1×$10^6$ agents show improved coherence and AoI with bounded energy/bit under tens-of-minutes to hour delays and relay attrition. ICCD offers a practical path to coordinated, fault-tolerant missions beyond continuous connectivity assumptions.

Data and Code Availability

Input ephemeris and configuration files are archived at /nas/experiments/iccd/inputs and /nas/experiments/iccd/configs. Aggregated results (CSV/Parquet) are at /nas/experiments/iccd/outputs. Gossamer policy modules are proprietary; analysis notebooks and Leviathan configs are available from the corresponding author upon reasonable request.

References

[1] Shapiro, M., et al., “A Comprehensive Study of CRDTs,” 2011. [2] Cerf, V., et al., “Delay-Tolerant Networking Architecture,” 2007. [3] Burleigh, S., et al., “Contact Graph Routing,” 2003. [4] Vahdat, A., Becker, D., “Epidemic Routing for Partially Connected Ad Hoc Networks,” 2000. [5] Demers, A., et al., “Epidemic Algorithms for Replicated Database Maintenance,” 1987. [6] Kaul, S., Yates, R., Gruteser, M., “Real-Time Status: How Often Should One Update?,” 2012. [7] Reynolds, C., “Flocks, Herds, and Schools,” SIGGRAPH, 1987. [8] Dorigo, M., et al., “Ant Colony Optimization: Artificial Ants as a Computational Intelligence Technique,” 1999.

Appendix / Supplementary Material

Appendix A: Convergence of the Composite Intent CRDT

The intent registry is a product of two primitive CRDTs — a Last-Writer-Wins (LWW) register $L$ for scalar goal fields and an Observed-Remove Set (OR-Set) $O$ for constraint membership — joined via a vector-clock causal context. We must show the composite is itself a join-semilattice, not just that each primitive is.

Definitions. Let $(L, \sqcup_L)$ and $(O, \sqcup_O)$ be join-semilattices. Define the product state $S = L \times O$ with merge

Lemma 1 (Composition). If $(L, \sqcup_L)$ and $(O, \sqcup_O)$ are both commutative, associative, and idempotent join-semilattices, then $(S, \sqcup)$ as defined above is a commutative, associative, idempotent join-semilattice.

Proof. Associativity, commutativity, and idempotence each hold componentwise; the product operator inherits each property by direct computation on the pair. The partial order $s_1 \le s_2 \iff s_1 \sqcup s_2 = s_2$ on $S$ is exactly the product order $(\ell_1 \le_L \ell_2) \wedge (o_1 \le_O o_2)$, which is well-defined. ∎

Lemma 2 (Causal-context preservation). Augmenting $S$ with a vector-clock context $V$ — i.e. taking $S' = S \times V$ where $V$ has the standard pointwise-max merge — preserves the join-semilattice property, because $(V, \max_{\text{pointwise}})$ is itself a join-semilattice. Composition of join-semilattices is closed under finite products (Lemma 1).

Theorem 1 (Convergence). Let $A$ be a set of agents exchanging updates from $S' = L \times O \times V$ over an eventually-connected DTN with bounded message loss. For any agent $a \in A$ and any history $U$ of updates eventually delivered to $a$, the local state converges to $\bigsqcup_{u \in U} u$.

Proof Sketch.

1. Each primitive is a CRDT:
   • LWW register: merge keeps the entry with the lexicographically-greater (timestamp, agent-id), satisfying associativity, commutativity, idempotence (Shapiro et al., 2011).
   • OR-Set: each element carries unique add-tags; remove records observed tags. Merge is union-of-add-tags minus union-of-observed-remove-tags. Standard result.
   • Vector clock: pointwise max.
2. Composition is a CRDT by Lemmas 1–2.
3. Eventual delivery. The contact plan guarantees that any update generated at time $t_0$ is included in some bundle delivered to every reachable agent by $t_0 + T_{\max}$, where $T_{\max}$ is the contact-plan diameter. Bundles are subject to custody transfer, so no eventually-feasible delivery is lost.
4. Convergence. For any agent $a$, after time $t_0 + T_{\max}$ since the latest update in $U$, the local state equals $\bigsqcup_{u \in U} u$ by repeated application of the composite merge. ∎

This is sufficient to claim strong eventual consistency for the composite intent under the contact-plan model, which is what the §5 results assume.

Appendix B: Energy-Aware Relay Selection Algorithm

def select_relays(neighbors, current_soc, threshold_k, history_window):
    """
    Selects the minimal covering set of relays to maintain local
    connectivity while balancing energy consumption.
    """
    candidates = []
 
    # Calculate Centrality Score (Kappa)
    for n in neighbors:
        # Approximate betweenness via local ego-network clustering coeff
        kappa = (1.0 / (n.clustering_coeff + epsilon)) * (n.degree)
 
        # Energy penalty factor
        energy_weight = n.soc / BATTERY_CAPACITY_WH
 
        score = kappa * energy_weight
        candidates.append((n.id, score))
 
    # Sort by Score descending
    candidates.sort(key=lambda x: x[1], reverse=True)
 
    # Greedy selection for minimal cover
    selected_relays = set()
    covered_nodes = set()
 
    for c in candidates:
        if len(covered_nodes) == len(neighbors):
            break
 
        # Hypothetical function checking if node covers new neighbors
        new_cover = get_uncovered_neighbors(c.id, covered_nodes)
 
        if len(new_cover) > 0:
            selected_relays.add(c.id)
            covered_nodes.update(new_cover)
 
    return selected_relays

Appendix C: Simulation Parameters Table

Appendix D: Ablation Matrix (Summary)

We evaluate ICCD components in isolation to attribute gains: (i) CRDT intent without contact-plan scheduling, (ii) contact-plan scheduling without custody transfer, and (iii) relay rotation disabled. Table 2 reports AoI P50, coherence, and task completion deltas relative to the full ICCD configuration.

Appendix E: Reproducibility Checklist

Numbers in §5 derive from a single committed experiment.json (exp_id = exp_iccd_main_2026q2). Full runbook at /research/reproducibility/iccd. The provenance block in experiment.json records:

• Git hashes for gossamer-threaded-intelligence (v0.2.0) and leviathan-engine (py-0.2.0).
• Wheel SHA256s as installed at run time.
• pip freeze hash for the full Python lockfile.
• Hardware fingerprint (platform, CPU count, OpenMP build, CUDA presence).
• Full seed tree: exp_seed → gen_seed → candidate_seed → repeat_seed.
• Leviathan rng_state captured at every checkpoint so resumed runs are byte-identical to non-resumed runs.

All figures regenerate from the canonical Parquet outputs via the analysis notebooks in maneuver-map/notebooks/.

Appendix F: Unified Symbols (shared with DMB+TF-ACO and HMA papers)

See the shared appendix “Eventually Consistent State Abstractions” on the research index for the cross-paper CRDT framing used by ICCD intents, TF-ACO pheromone counters, and HMA depot inventory.