DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedverified 2026-10-22 (gpt-6.1-sol)

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.

Split and coverage condition for a multicast design

Definition

For a finite-tree probe design $C = ((C_{d}, N_{d}))_{d = 1}^{D}$ , a receiver $r \in R$ is covered if $r \in C_{d}$ for some $d$ . For a nonroot internal vertex $v$ , a design $C_{d}$ splits $v$ if there are distinct children $c, c^{'}$ of $v$ and receivers $r, s \in C_{d}$ such that $r$ lies in the subtree rooted at $c$ and $s$ lies in the subtree rooted at $c^{'}$ . The design satisfies the split/coverage condition if every receiver is covered and every nonroot internal vertex is split by at least one design.

Definition references

Finite-tree multicast loss experiments

Xi, Michailidis, and Nair, §3.2, Proposition 1

Lawrence, Michailidis, and Nair, §3.1

Depends on

Finite-tree multicast loss experiments

Used by

Link-loss identifiability from split and coverage Theorem

Dependency tree · two levels

2 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

B. Xi, G. Michailidis, and V. N. Nair, Estimating Network Loss Rates Using Active Tomography, Journal of the American Statistical Association 101 (2006), 1430–1448 (standard reference, not scraped)
E. Lawrence, G. Michailidis, and V. N. Nair, Statistical Inverse Problems in Active Network Tomography, IMS Lecture Notes–Monograph Series 54 (2007), 24–44 (standard reference, not scraped)