KV-Cache Ring Buffer Proof Audit

This appendix keeps the theorem-card trail for the KV-Cache Ring Buffer lesson. The lesson teaches the contract; this page is for checking the proof family.

These cards certify finite ring-buffer, retained-window, trace-freshness, stale-request, generated-live-window, and sink-window policy facts. They are not proof of a paging policy, GPU kernel, serving stack, throughput result, memory-saving result, retrieval-quality result, deployment-safety result, or model-quality result.

Audit Reading Order

Use this page as the proof-card appendix after reading the main lesson. The main lesson explains the contract and worked fixture; this page resolves the theorem ids.

Proof Family What To Check Here
Slot and retained-window core token slots are bounded, same-slot reuse has an exact period, and retained status matches the overwrite boundary
Generated live window the generated token interval is exactly the retained window and covers the slot range when full
Trace freshness and adapter requests passing and failing modeled read requests are equivalent to non-future, duplicate-free, trace-fresh token lists
Sink-window policy pinned seen-prefix tokens and rolling-window tokens have exact membership, count, and branch-separation fields

Slot And Retained-Window Core

Generated Live Window

Trace Freshness And Adapter Requests

Sink-Window Policy

Source Trail

Paper source: Coil Attention And Memory

Lean source: Circle/Applications/CircleAI.lean

Python source: circle_math/applications/circle_ai.py

CLI source: scripts/kv_cache_certify.py

Quickstart: KV-cache Certifier Quickstart