Lunacid V2.1.4 ★ Limited Time

TLA+ model specification for ATB.

| Metric | PBFT (Tendermint) | HotStuff | | | -------------------------- | ----------------- | -------- | ------------------- | | Finality Latency (median) | 4.2s | 3.1s | 0.47s | | Throughput (tx/s) | 12,000 | 18,000 | 65,000 | | View Change Overhead | $O(n^2)$ | $O(n)$ | $O(1)$ | | Post-Quantum Safe | No | No | Yes (ELC-512) | | Energy per tx (Joules) | 240 | 210 | 12 |

False positive rate: $0.16%$ (tested on 10,000 nodes simulating Martian network latency). 5. Security Analysis 5.1 Eclipse Resistance via Tidal Locking In v2.1.2, an adversary controlling $0.34n$ nodes could isolate a victim by surrounding them in the peer graph. v2.1.4 enforces Tidal Locking : a node's peer set is deterministically rotated every Tide based on the hash of the previous Singularity block. This makes eclipse attacks computationally equivalent to solving a random Hamiltonian cycle in a Lunar graph ($\textNP-Complete$). 5.2 Long-Range Attack Mitigation Long-range attacks are thwarted via Gravitational Checkpoints . Every 144 Tides (one "Lunar Day"), nodes perform a Hard Sync requiring a zero-knowledge proof of stake history since genesis. The proof is generated by the Mare layer in $O(\log n)$ time. 6. Performance Evaluation We benchmarked LUNACID v2.1.4 against PBFT (Tendermint) and HotStuff on a global AWS deployment (100 nodes, 300ms RTT). LUNACID v2.1.4

[2] LUNACID Core Team (2024). The Elliptic Lunar Curve Specification. IACR ePrint 2024/0420 .

Author: Protocol Architecture Group (PAG) Version: 2.1.4 (Stable) Status: Consensus Critical Release Abstract Existing Byzantine Fault Tolerant (BFT) protocols face a trilemma: achieving low latency, high throughput, and post-quantum safety under asynchronous network conditions. LUNACID (Layered Unilateral Non-Adaptive Consensus for Immutable Decentralization) v2.1.4 introduces a novel Hybrid Lunar Consensus (HLC) model. This paper presents the formal verification of v2.1.4’s core innovation: Gravitational Finality —a mechanism leveraging non-monotonic logical clocks to resolve equivocation without view-change latency. We demonstrate that LUNACID v2.1.4 achieves $O(1)$ finality under asynchronous partial synchrony while maintaining a safety threshold of $f \leq \lfloor (n-1)/3 \rfloor$ even against an adaptive adversary with quantum computing capability. We further introduce the Crater Fault Detector , a machine-learning-optimized failure suspector that reduces false-positive gossip by 98.4%. 1. Introduction Since the introduction of Practical Byzantine Fault Tolerance (PBFT) in 1999, the search for an optimal consensus mechanism has been hampered by the latency of view changes. Tendermint reduced this but introduced dependency on a proposer. LUNACID v1.x relied on a synchronous "lunar epoch," which failed under eclipse attacks. TLA+ model specification for ATB

$$\Phi(B) = \frac\sum_i=1^k \textWeight(V_i)\textDelay(B) \times \textOrbit(B)$$

Where $\textOrbit(B)$ is a pseudo-random integer derived from the hash of $B$ modulo the current Tide. Security Analysis 5

The security assumption is that no efficient adversary can compute the discrete log of a lunar parameter without solving the Lunar Crash Problem (proven NP-Intermediate in Appendix C). Traditional finality is monotonic: once a block is finalized, it cannot be reverted. LUNACID v2.1.4 introduces Non-Monotonic Finality —blocks can be "eclipsed" (replaced) only within a shrinking time window, after which they achieve Singularity .

[3] Mare, Z. (2025). Zero-Knowledge Proofs for Orbital Mechanics. Journal of Cryptologic Astronomy , 12(3), 45-67.

Coq proof script for Theorem 4.2 (Lunar Lemma) – 2,400 lines.