Proof-of-Rigidity (PoR): A Sovereign Layer-1 Substrate Immutable Geometric Consensus and Brittle Semantic Security

Abstract

Traditional distributed consensus mechanisms rely on probabilistic assumptions, economic weighting (Proof-of-Stake), or arbitrary computational work (Proof-of-Work) to secure ledger state transitions. These models leave the application layer inherently vulnerable to Man-in-the-Middle (MITM) attacks, Maximal Extractable Value (MEV) extraction, and semantic exploits against critical infrastructure (SCADA/PLC). This manuscript introduces Proof-of-Rigidity (PoR), a deterministic state-validation framework that locks the consensus machine within a continuous 150-decimal-place geometric manifold ($G_{24}$ volume space). The paper formalizes three core components: The Brittle Acceptance Predicate: A Coq-verified mathematical boundary that enforces an absolute $10^{-80}$ validation tolerance, structurally denying unauthorized state mutations. Mantissa Tail Parity (The MEV Sieve): A mechanism utilizing Canonical Decimal Arithmetic ($\mathbb{D}_{150}$) to mathematically neutralize routing interception and front-running. Capability-Constrained Semantic Policies: A bipartite matrix that structurally subordinates LLM-based ontological analysis to strict cryptographic Role-Based Access Control (RBAC), preventing adversarial paraphrasing against industrial endpoints. By enforcing strict geometric determinism, PoR transforms network security from probabilistic difficulty into mathematical brittleness. Included in this deposit are the Coq formal verification proofs, a Python reference implementation of the Layer-1 substrate, and a computational benchmarking harness demonstrating throughput scalability. LEGAL, ETHICAL, AND SAFE HARBOR DISCLAIMER The mathematical models, formal Coq proofs, and Python reference implementations contained within this deposit are published strictly for academic research, cryptographic peer review, and educational purposes. The architectures described herein represent a theoretical substrate and an experimental prototype. They have not undergone formal, independent security auditing for production deployment. No Warranty (As-Is): The mathematical models and reference code are provided "AS IS", without warranty of any kind, express or implied. The continuous geometric bounds and mechanisms detailed herein are theoretical thresholds; physical hardware limitations, truncation errors, or implementation flaws may affect real-world execution. Limitation of Liability: Under no circumstances shall the author, contributors, or affiliated research entities be held liable for any direct, indirect, incidental, special, exemplary, or consequential damages (including, but not limited to, loss of use, data, stablecoin assets, or profits; business interruption; or industrial infrastructure failure) arising in any way out of the use, deployment, or misconfiguration of this protocol. Assumption of Risk: Any entity choosing to implement the $G_{24}$ volume space boundaries, the Topological Shatter mechanics, or any variant of the PoR consensus layer within a live environment does so entirely at their own risk, and is solely responsible for ensuring compliance with all applicable cybersecurity and financial regulations.