ExampleConstruction: AI-generatedVerification: AI-generatedPipeline-generated

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Keeping records on clients does not imply differential privacy

Example

Let the database be a finite record set, use add/remove adjacency, and let a distributed system release the exact number of records after each client has kept its own record locally. This deterministic count release is not $(ε, δ)$ -differentially private for any finite $ε \geq 0$ and any $0 \leq δ < 1$ .

Example references

Add/remove differential privacy

Facts & Assumptions

Given: The database domain and exact count mechanism in the Example.

[F1]

Differential privacy, databases, and add/remove adjacency: differential privacy requires the event inequality for every ordered neighboring database pair and every measurable output event.

[F2]

Measurable spaces and measurable sets, Probability measures and probability spaces, and Measure kernel and probability kernel: a deterministic count release is a probability kernel into the countable output space $N_{0}$ equipped with its power-set sigma algebra.

Proof technique: direct.

Proof

1.1F1F2givenconstruct

Let $D = \emptyset$ , $D^{'} = {r}$ , and let $M (E) = ∣ E ∣$ . These databases are add/remove neighbors. For the measurable event $A = {1}$ , $\Pr [M (D) \in A] = 0$ and $\Pr [M (D^{'}) \in A] = 1$ .

2.1F1step 1.1givenalgebra∎

The required privacy inequality in the order $(D^{'}, D)$ would read $1 \leq e^{ε} \cdot 0 + δ = δ$ , which is false whenever $δ < 1$ . Therefore the exact count mechanism is not $(ε, δ)$ -differentially private for the stated parameters.

Depends on

Used by

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Dependency tree · two levels

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