Responsibility as an Error-Correcting Information Problem: Optimal Responsibility Codes, Legal Observability, and Verifiable Evidence in Autonomous Digital Systems

Autonomous digital systems distribute consequential action across users, operators, models, agents, tools, and cloud services, yet accountability can fail before investigation because responsibility-relevant evidence may be erased, corrupted, or never preserved. We formulate responsibility as an error-correcting information problem. Legal observability quantifies responsibility-separating information; responsibility capacity measures its worst-case survival under an explicit adversary. We introduce responsibility distance, code rate, adaptive capacity, transferability, Byzantine witness resilience, and a mixed error-erasure theorem showing that unique decoding is guaranteed when 2t + b < d_R^min, where t is the corruption budget, b is the erasure budget, and d_R^min is the minimum responsibility distance. We further formulate minimum-cost responsibility coding as a binary multicover optimization that minimizes telemetry cost subject to a required recovery radius. TRACE-R combines abstaining reconstruction, structural-causal analysis, Ed25519 cross-domain receipts, replay protection, Merkle checkpoints, and strict source/derived/inferred separation. AutoResponsibilityBench contributes 16,000 principal method-trials plus coding, adaptive-attack, identifiability-interval, cryptographic, transferability, and identical-outcome experiments. Fano and Bhattacharyya bounds bracket empirical decoding difficulty and expose information loss independently of any particular reconstruction algorithm. TRACE-R achieves zero false attribution on deliberately non-identifiable paired cases, while forced baselines always answer. The framework turns accountability from retrospective explanation into responsibility-identifiable system design without conflating technical reconstruction with evidentiary admissibility or legal liability.