C3: An Ultra-Lightweight, Self-Healing Time-Series Compression Algorithm for Resource-Constrained Embedded Telemetry.

This paper introduces C3, a novel, ultra-low memory, real-time lossless compression algorithm designed specifically for time-series telemetry in severely resource-constrained hardware environments (e.g., ESP32, ARM Cortex-M) operating over low-bandwidth, high-latency, and lossy networks such as LoRaWAN or CAN bus. Maintaining a core codec state machine footprint of less than 300 bytes of RAM and achieving zero-heap execution, C3 employs an asymmetric predictive history structure coupled with localized quantized anchor buffers. Furthermore, we formalize the deterministic state convergence property of C3, demonstrating its mathematical capacity for structural self-healing and state reconciliation post-packet loss without requiring centralized network consensus or heavy cryptographic handshakes. Update Log (v2.0): This version incorporates a complete peer-review revision. Key updates include: Refined memory footprint analysis clarifying the distinction between the codec state machine (<300 bytes) and auxiliary I/O buffers. Formal algebraic correction: definition of $\mathbb{Z}_{256}$ as a commutative ring. Rigorous formal proof of deterministic state convergence using component-wise limits. Integration of a robust transport layer assumption for bit-level alignment and synchronization. Clarification of state recovery bounds based on contextual stream transitions. Improved technical documentation regarding worst-case entropy expansion and absolute bit-budgeting.