arXiv:2610.08262v1 Announce Type: cross Abstract: Can authentication make memory, rather than computational hardness, the attacker's bottleneck? Contextual Chain is a lightweight continuity protocol for intermittently connected devices that share evolving physical or operational context. An honest device follows one realized history, updating a compact accumulator and fixed hash-based readiness lanes; outages cause pause or bounded rollback, not branch search. After the epoch is frozen, a fresh challenge selects one lane under a short deadline. An outsider that missed context may therefore need to prepare for many mature histories before learning which one will be tested. In the standard random-oracle model, a causal counting theorem lower-bounds the deadline-accessible retained state required for a target success probability against arbitrary nonlinear preselection encoding and adaptive post-selection queries, accounting for sequential depth, candidate queries, and cross-target protected information obtained online. Honest readiness memory remains fixed and independent of the number of plausible histories. Contextual Chain thus converts shared-experience uncertainty into a tunable preparation requirement without transferring combinatorial complexity to lightweight devices.