Cyclic Memory Residue Winding

A cyclic memory slot is a residue. A memory event also has a winding number: how many full turns through the memory bank have happened before this event.

Goal

Use residue plus winding to explain aliasing in a finite memory bank without pretending the residue alone proves freshness.

Concept

The circular object is the memory bank C_bank_size. Event t writes to slot t mod bank_size, while t div bank_size records the winding. Two events can share a slot and still be different writes because their windings differ.

event index = winding * bank_size + residue slot

That is the whole point of the contract: keep alias provenance explicit.

Example

The public fixture uses bank_size = 8, event_index = 23, and event_count = 32. The event sits in residue slot 7 with winding 2. The same residue class inside the trace is:

events:   7, 15, 23, 31
windings: 0,  1,  2,  3

python scripts/cyclic_memory_certify.py --format json
python scripts/circle_ai_contract_ready.py --kind cyclic_memory_residue_winding --digest --field same_residue_events --field same_residue_windings --field max_alias_load

Theorem Trail

Certificate Reading

The useful fields are:

residue_slot: the finite memory address.
winding: the full-turn count for the selected event.
same_residue_events: every event in the trace that aliases the same slot.
same_residue_windings: the corresponding provenance layer for those aliases.
max_alias_load: the largest finite alias class size in the declared trace.

Planner recommendations:

MEMORY-ATTACH-WINDING-ALIAS-PROVENANCE says a downstream system should preserve winding when slots alias.
MEMORY-AUDIT-FINITE-ALIAS-LOAD says the finite trace should expose the maximum observed alias load rather than hiding it behind a slot id.

This is a finite alias-provenance contract. It does not prove cache freshness, retrieval quality, long-term memory quality, or safety of any production memory system. Python fixtures are executable references, not proof artifacts and not performance claims.

Dictionary

Source Trail

Attention and memory paper: Coil Attention And Memory

Quickstart: Cyclic Memory Certifier