AxiomLimit · AI inference · for a technical reader
The least bookkeeping a shared AI cache needs, in a model: the lab’s exact wording
The lab’s own sentences and figures for this result, word for word, in its working terms, with its limits in plain words where the lab’s text cannot be reprinted. The plain account is on the result’s page; it says the same things in plain words.
The lab’s plain-English sentence
A computer-checked proof that a memory cache shared by many customers of an artificial-intelligence (AI) service, if it must never hand one customer's cached work to another yet always reuse it whenever that is allowed, has to keep at least one bit of permission bookkeeping for every (customer, cache block) pair — but only in the case where any block may be shared with any group of customers
- the lab says actually ships, the floor is n·log₂T bits, exponentially smaller.
Proved in the dense rights model
needs at least 2^(T*n) states, i.e. at least T*n bits
The limit to read first, in the lab’s words
T*n is the DENSE rights model -- every (tenant, block) right independent. It binds when a block may be authorized to an arbitrary SUBSET of tenants (group / shared-read ACLs).
If each block belongs to a single tenant
the tight floor is T^n states = n*log2(T) bits, exponentially smaller.
Claim
A zero-leak AND full-reuse pooled-KV policy over T tenants and n cache blocks needs at least 2^(T*n) states, i.e. at least T*n bits, as one machine-checked theorem general in T and n.
Part of the lab’s record (limits) is not reprinted here because it names internal files this site does not publish or uses internal working terms.
More
- The plain account of this result: the problem, what was shown, what it means for a buyer, who we expect would buy, why now, why you can trust the check, and what it does not show yet.
- This result’s file, the source of every sentence above.
- The formal statement of this result, set as a formula, with the other formal statements.