Formal proof that a categorical phase-skip detector catches what CUSUM/GLR can't(academia.edu)

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Formal proof that a categorical phase-skip detector catches what CUSUM/GLR can't

https://www.academia.edu/164981853/Resonant_Symbolic_Operator_Calculus_RSOC_Formal_Convergence_Proof_of_%CF%87_t_Under_Adversarial_Phase_Conditions_including_Lemma_5_One_Step_Simultaneous_Detection

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nicbogaert4 माह पहले

Statistical change-point detectors (CUSUM, GLR, Page's test) share a structural vulnerability: an adversary who knows the sufficient statistic can steer the post-change distribution toward the pre-change distribution and suppress the alarm indefinitely. This is documented in the 2024 covert detection literature, not a theoretical edge case.

For categorical architectural violations — a system jumping from phase state S5 to S8 in one step, bypassing required stages — there is no distribution to match. The skip is its own fingerprint.

I built a formal convergence proof for a deterministic binary predicate (d_score) and event-triggered corrective controller (χ(t)) in a hybrid discrete/continuous monitor. The main result: under β > Pmax/ρmin, χ(t) converges before structural drift reaches the hard ceiling at all recursion depths. The convergence condition is satisfied analytically — no empirical benchmarking required.

Paper (22pp, includes annotated implementation): https://www.academia.edu/164981853/Resonant_Symbolic_Operato...

Known limitations are documented: single-step adversary only (multi-step acceleration attack is an open problem, engineering extension exists), baseline integrity is a precondition not a theorem.