Identity as a First-In Cache: Anti-Aliasing, Monotone Fictionalization, and the Coherence Kernel

Humans misperceive autobiographical memory as a uniformly detailed film. In practice, it behaves like a rolling cache: a small working set of recent, high-resolution states plus aggressively compressed summaries of the past. We formalize this as a First-in Cache Identity (FCI) model in which perception is compressed by a channel C, maintained in a finite working set Wt, anti-aliased by a θ-independent operator Bthat hides cache rotation, and recalled by Rto produce a coherent narrative. Two invariants emerge: 1. Monotone fictionalization. Fisher information (phenomenal curvature) of recalled episodes is nonincreasing with temporal lag under memory channels independent of latent parameters; older memories become smoother and more confidently reconstructed yet less faithful. 2. Lyapunov coherence. Under generic forgetting flows the Fisher metric contracts; conti- nuity is a stable fixed point maintained by a minimal controller (the coherence kernel or “ego”). We connect psychology-scale cache dynamics to the broader Abzu corpus: QFI-based compiled law, sheaf-theoretic context gluing, and the QFI→TC bridge for phase transitions in cognition. We present falsifiable predictions, empirical protocols (human and model), and appendices with proofs, estimators, and a toy simulation spec. The thesis is simple: identity is the pointer and reconciliation map that keeps the narrative differentiable across cache rotations; blur is the shader that makes the film playable in real time.