{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2C766IGILOGWTMDP62WM7QPGGE","short_pith_number":"pith:2C766IGI","canonical_record":{"source":{"id":"1801.04501","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-14T02:41:35Z","cross_cats_sorted":[],"title_canon_sha256":"6f04d91250c4e3dc64a84f754e73df410ab026691ed00dcf6e7386f5447648a1","abstract_canon_sha256":"aebcc7fe9c470a448ead143a444cd4119faf268213dbb886a55ce5d3961665be"},"schema_version":"1.0"},"canonical_sha256":"d0bfef20c85b8d69b06ff6accfc1e63122a650fa7eeeb92e02beba3988680969","source":{"kind":"arxiv","id":"1801.04501","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04501","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04501v3","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04501","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"2C766IGILOGW","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2C766IGILOGWTMDP","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2C766IGI","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2C766IGILOGWTMDP62WM7QPGGE","target":"record","payload":{"canonical_record":{"source":{"id":"1801.04501","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-14T02:41:35Z","cross_cats_sorted":[],"title_canon_sha256":"6f04d91250c4e3dc64a84f754e73df410ab026691ed00dcf6e7386f5447648a1","abstract_canon_sha256":"aebcc7fe9c470a448ead143a444cd4119faf268213dbb886a55ce5d3961665be"},"schema_version":"1.0"},"canonical_sha256":"d0bfef20c85b8d69b06ff6accfc1e63122a650fa7eeeb92e02beba3988680969","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:22.794892Z","signature_b64":"ncIv2rSX+Bde1rr618aYFYbk7Dt/jCaOg55E6MFgnz1+PfcPoY6d2r0bylPBlPFCuLWkTqs1n1Izot2SzMEsBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0bfef20c85b8d69b06ff6accfc1e63122a650fa7eeeb92e02beba3988680969","last_reissued_at":"2026-05-17T23:44:22.794346Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:22.794346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.04501","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AyH789MvcWCfMiQsUDELcipTL5RBdmGhw51UB0BciRAd60Xqe66De/dx7l2aJ4i66Iybm3skD4aY3XW9ulXkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:23:48.490385Z"},"content_sha256":"852f7026b06d90de8a2ec12438f5e1cfe244a8f8ea1ad2e59db296c0e101147e","schema_version":"1.0","event_id":"sha256:852f7026b06d90de8a2ec12438f5e1cfe244a8f8ea1ad2e59db296c0e101147e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2C766IGILOGWTMDP62WM7QPGGE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extinction and coming down from infinity of CB-processes with competition in a L\\'evy environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"H\\'el\\`ene Leman, Juan Carlos Pardo","submitted_at":"2018-01-14T02:41:35Z","abstract_excerpt":"In this note, we are interested on the event of extinction and the property of coming down from infinity of continuous state branching (or CB for short) processes with competition in a L\\'evy environment whose branching mechanism satisfies the so-called Grey's condition. In particular, we deduce, under the assumption that the L\\'evy environment does not drift towards infinity, that for any starting point the process becomes extinct in finite time a.s. Moreover if we impose an integrability condition on the competition mechanism, then the process comes down from infinity regardless the long ter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04501","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:44:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IN10KZL9LFkCwTpj5mC1B597YQltkPgdAWE1nYa9RxYS6OsYb9N4isd7cL7Gzdqh833wsl4W3O9DFX2PYSrXDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T22:23:48.491030Z"},"content_sha256":"51c9bc2ce8ec3056d51a15ac0fb2cba8e8355efeff1d65a6148c3e10e7935b9f","schema_version":"1.0","event_id":"sha256:51c9bc2ce8ec3056d51a15ac0fb2cba8e8355efeff1d65a6148c3e10e7935b9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2C766IGILOGWTMDP62WM7QPGGE/bundle.json","state_url":"https://pith.science/pith/2C766IGILOGWTMDP62WM7QPGGE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2C766IGILOGWTMDP62WM7QPGGE/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T22:23:48Z","links":{"resolver":"https://pith.science/pith/2C766IGILOGWTMDP62WM7QPGGE","bundle":"https://pith.science/pith/2C766IGILOGWTMDP62WM7QPGGE/bundle.json","state":"https://pith.science/pith/2C766IGILOGWTMDP62WM7QPGGE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2C766IGILOGWTMDP62WM7QPGGE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2C766IGILOGWTMDP62WM7QPGGE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"aebcc7fe9c470a448ead143a444cd4119faf268213dbb886a55ce5d3961665be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-14T02:41:35Z","title_canon_sha256":"6f04d91250c4e3dc64a84f754e73df410ab026691ed00dcf6e7386f5447648a1"},"schema_version":"1.0","source":{"id":"1801.04501","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.04501","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"arxiv_version","alias_value":"1801.04501v3","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.04501","created_at":"2026-05-17T23:44:22Z"},{"alias_kind":"pith_short_12","alias_value":"2C766IGILOGW","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2C766IGILOGWTMDP","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2C766IGI","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:51c9bc2ce8ec3056d51a15ac0fb2cba8e8355efeff1d65a6148c3e10e7935b9f","target":"graph","created_at":"2026-05-17T23:44:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this note, we are interested on the event of extinction and the property of coming down from infinity of continuous state branching (or CB for short) processes with competition in a L\\'evy environment whose branching mechanism satisfies the so-called Grey's condition. In particular, we deduce, under the assumption that the L\\'evy environment does not drift towards infinity, that for any starting point the process becomes extinct in finite time a.s. Moreover if we impose an integrability condition on the competition mechanism, then the process comes down from infinity regardless the long ter","authors_text":"H\\'el\\`ene Leman, Juan Carlos Pardo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-14T02:41:35Z","title":"Extinction and coming down from infinity of CB-processes with competition in a L\\'evy environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04501","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:852f7026b06d90de8a2ec12438f5e1cfe244a8f8ea1ad2e59db296c0e101147e","target":"record","created_at":"2026-05-17T23:44:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"aebcc7fe9c470a448ead143a444cd4119faf268213dbb886a55ce5d3961665be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-14T02:41:35Z","title_canon_sha256":"6f04d91250c4e3dc64a84f754e73df410ab026691ed00dcf6e7386f5447648a1"},"schema_version":"1.0","source":{"id":"1801.04501","kind":"arxiv","version":3}},"canonical_sha256":"d0bfef20c85b8d69b06ff6accfc1e63122a650fa7eeeb92e02beba3988680969","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0bfef20c85b8d69b06ff6accfc1e63122a650fa7eeeb92e02beba3988680969","first_computed_at":"2026-05-17T23:44:22.794346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:22.794346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ncIv2rSX+Bde1rr618aYFYbk7Dt/jCaOg55E6MFgnz1+PfcPoY6d2r0bylPBlPFCuLWkTqs1n1Izot2SzMEsBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:22.794892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.04501","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:852f7026b06d90de8a2ec12438f5e1cfe244a8f8ea1ad2e59db296c0e101147e","sha256:51c9bc2ce8ec3056d51a15ac0fb2cba8e8355efeff1d65a6148c3e10e7935b9f"],"state_sha256":"0cf79c08b75cb814604fc479edec94f9af666c170fbdeed15796a810ef9bb537"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y5tPwBob6P66sj+6YbR4Vci0XNpsmXojagOT36/VNh7TzA5PUob1/B8ntz0BnzRJzmFnAKiyLOkHCq3qipAZCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T22:23:48.494337Z","bundle_sha256":"3739c1ca76909725c3db1aed12e65a7960e7c18b3626639d6255032b5e4451ac"}}