Recursive Self-Improvement Stability under Endogenous Yardstick Drift

This paper develops a first-principles interface theory for recursive self-improvement under endogenous yardstick drift: the setting in which a system does not merely improve policies or code, but also changes its own evaluator, benchmark, parser, routing logic, memory substrate, and verification process. The central problem is not whether self-modification can produce short-term gains, but whether a self-editing system can still distinguish claimed improvement from stable improvement when the ruler itself moves. The framework is organized around replayable observable interfaces rather than privileged semantic oversight. It separates four layers that are often conflated in self-improving systems: base admissibility, certified stable gain, debt-bounded stability, and governance safety. The formal development includes typed-noise comparator certificates, replayable state lifts, lower-oracle stable-gain intervals for ruler-editing proposals, delayed shadow certification with logged challenge routing and confidence-sequence lower bounds, contradiction obligations with protected reserve exposure, semantic-retention and refreezing margins, proof-carrying escalation lanes, unresolved-downside debt reserves, and capability-dependent verification throughput. The paper’s main results show how stability and growth claims must be stated conditionally on published replayable instrumentation and conservative envelope objects. It derives small-gain style stability wrappers for the coupled improver–evaluator–memory–queue loop, constructive conditions for certified window contraction, replayable lower certificates under delayed audit, and comparison theorems for explicit regime–policy pairs. It also shows that some governance edits can be frontier-expanding investments even when they do not yield immediate productive capability increments, provided that replay, challenge, contradiction preservation, promotion, proof, and verification interfaces are sufficiently strong under fixed admission thresholds. The framework is model-architecture-neutral but not infrastructure-free. It does not assume a privileged overseer, a fixed benchmark, or a specific training rule, but it does require replayable governance-relevant interfaces, protected service lanes, contradiction-obligation logs, attestation roots, transport and calibration envelopes, and explicit resource escrows. Under those conditions, recursive self-improvement can be analyzed as a scientifically auditable stability problem rather than as an informal narrative about open-ended growth.Archived on Arweave (Data Tx ID)PDF: 51A0D9zDVmlRcAMOAxSEjt8g1A9ckC5QD-_mQQnl_UsTeX source: KOMcMbaEecUL0I39Ft8Rtkb-JSM79-ioZxCWBN2zGPI