DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

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.

Local-Stochastic Fault-Set Law

Definition

Let $L$ be a finite set of elementary fault-location labels and let $(Ω, w)$ be a finite probability space as in Finite probability spaces, outcome weights, events, and event probabilities. A fault-set random variable is a map $F : Ω \to P (L)$ . For a parameter $η \in [0, 1]$ , the fault-set law is $η$ -local-stochastic if, for every subset $S \subseteq L$ ,

P {ω \in Ω : S \subseteq F (ω)} \leq η^{∣ S ∣} .

Here $η^{k}$ is the ordinary $k$ -fold product, with $η^{0} = 1$ . This condition allows correlations among fault indicators; it does not assert mutual independence.

Depends on

Used by

Local-Stochastic Correlated Quantum Noise Definition
Local-Stochastic Fault-Witness Bound Lemma

Dependency tree · two levels

12 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

D. Aharonov and M. Ben-Or, Fault-Tolerant Quantum Computation With Constant Error (standard reference, not scraped)
P. Aliferis, D. Gottesman, J. Preskill, Accuracy Threshold for Postselected Quantum Computation (standard reference, not scraped)