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Let $\\psi$ be a critical branching mechanism. We set $\\psi_\\theta(\\cdot)=\\psi(\\cdot+\\theta)-\\psi(\\theta)$. Let $\\Theta=(\\theta_\\infty,+\\infty)$ or $\\Theta=[\\theta_\\infty,+\\infty)$ be the set of values of $\\theta$ for which $\\psi_\\theta$ is a branching mechanism. The pruning procedure allows to construct a decreasing L\\'evy-CRT-value"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0904.4175","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-04-27T14:44:11Z","cross_cats_sorted":[],"title_canon_sha256":"2dd7f7eb1d9409815e9f29b395ea21dd68c55739157f672bd553651835a809ad","abstract_canon_sha256":"7cdbad717f8a9e86d14d1041d00643976d2c2ec1deece1d715df33057a769ae5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:06.366832Z","signature_b64":"MMKLeHqDgkQy4gY6/AV2sOpY5HdRKNiUS6wkymUlgDtU5rLxqjd3jAb7puGZMoMNhaeCZWld5+BDAjj7VZB8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5dc0861c12a911444247364e002480e41b1b5595840625ada87b6fd6c31f57e","last_reissued_at":"2026-05-18T03:54:06.366162Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:06.366162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A continuum-tree-valued Markov process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Delmas (CERMICS), Romain Abraham (MAPMO)","submitted_at":"2009-04-27T14:44:11Z","abstract_excerpt":"We present a construction of a L\\'evy continuum random tree (CRT) associated with a super-critical continuous state branching process using the so-called exploration process and a Girsanov's theorem. We also extend the pruning procedure to this super-critical case. Let $\\psi$ be a critical branching mechanism. We set $\\psi_\\theta(\\cdot)=\\psi(\\cdot+\\theta)-\\psi(\\theta)$. Let $\\Theta=(\\theta_\\infty,+\\infty)$ or $\\Theta=[\\theta_\\infty,+\\infty)$ be the set of values of $\\theta$ for which $\\psi_\\theta$ is a branching mechanism. 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