Algebraic Identities and Stochastic Walsh Smoothing for Rule 30 Damage Dynamics

This record contains the paper Algebraic Identities and Stochastic Walsh Smoothing for Rule 30 Damage Dynamics and its separately scoped reproducibility archive. The paper establishes algebraic identities for Rule 30 damage dynamics and exact graph-Walsh smoothing and contraction results for a skew-product with independent Bernoulli driver fields. It also records finite algebraic, linear-programming, and empirical computations. The archive preserves the canonical PDF, an unchanged retained R41 campaign archive, an unchanged archival recovery gate, exact recovered verifier sources inside that gate, explicitly labelled new reconstruction verifiers, fresh deterministic logs, a complete provenance and recovery ledger, and replay instructions. Nine exact verifier source names listed in Appendix B were not found in the retained bytes; no reconstruction is represented as a recovered original. The exact final manuscript source was also not found, and the included Markdown source is labelled as an earlier historical skeleton. The stochastic iid-driver theorems are not a proof of deterministic Rule 30 mixing. The record does not claim a proof of the Sole Anomaly conjecture or of any of Wolfram's three Rule 30 prize problems. The deposit archive replays successfully with explicit caveats documented inside the archive. Files deposited separately are the principal paper PDF and the complete archival and reproducibility package. SHA-256 of rule30_walsh_smoothing.pdf: caede90027f8d46819d6a8a3272d246e1ca2774b637dfdc79409f5a735ae916a. SHA-256 of RULE30_WALSH_SMOOTHING_ZENODO_DEPOSIT_V1.zip: be15b31c691e4286225acebcaa17d112e023b944189e993a4686008882e5cd1c.