The Low-Rank Alignment Control Surface

Lean

Machine-checked descriptive formalization of the gate.

The role-provenance gate has a companion Lean 4 development that gives its ablation structure a machine-checked descriptive form — the formal counterpart to the empirical RPCG5 layer-ablation chain.

RoleGateReachability.lean

File: LeanMining/SteadyState/RoleGateReachability.lean5 theorems, sorry count 0, mathlib base axioms only.

Theorem
logit_full_ablation
logit_mono
logit_no_ablation_le_base
logit_le_base
ablation_monotonically_reaches_base

The model: the gated logit of an out-of-role primitive is a base value plus a finite family of rank-one suppression components. The capstone, ablation_monotonically_reaches_base, proves that ablating more components monotonically raises every out-of-role logit, and that full ablation reaches the un-gated base — for every out-of-role primitive simultaneously. The empirical RPCG5 greedy-ablation chain (strictly monotone, decreasing to the un-gated value) instantiates it.

The development is descriptive: it formalizes the gate’s monotone-reachability shape. It makes no minimality or optimality claim — matching the experiments’ v1 scope.

Source: LeanMining/SteadyState/RoleGateReachability.lean, status/theorem-status.yaml.