{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:YWUCE6METJJRBD7JGZ6R7DQGQP","short_pith_number":"pith:YWUCE6ME","canonical_record":{"source":{"id":"2506.04783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-05T09:11:44Z","cross_cats_sorted":[],"title_canon_sha256":"b8a04193b04f3a7d934b084c372fba1d4fd43773e588367ae3dd29c8f41c6a37","abstract_canon_sha256":"70879ab9e6a727800028f2b89f24fa9fccf412bec349b9453da791622f08f4b9"},"schema_version":"1.0"},"canonical_sha256":"c5a82279849a53108fe9367d1f8e0683de3b1061ca35aecf23edd862364d534e","source":{"kind":"arxiv","id":"2506.04783","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04783","created_at":"2026-07-05T11:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04783v1","created_at":"2026-07-05T11:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04783","created_at":"2026-07-05T11:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"YWUCE6METJJR","created_at":"2026-07-05T11:16:20Z"},{"alias_kind":"pith_short_16","alias_value":"YWUCE6METJJRBD7J","created_at":"2026-07-05T11:16:20Z"},{"alias_kind":"pith_short_8","alias_value":"YWUCE6ME","created_at":"2026-07-05T11:16:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:YWUCE6METJJRBD7JGZ6R7DQGQP","target":"record","payload":{"canonical_record":{"source":{"id":"2506.04783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-05T09:11:44Z","cross_cats_sorted":[],"title_canon_sha256":"b8a04193b04f3a7d934b084c372fba1d4fd43773e588367ae3dd29c8f41c6a37","abstract_canon_sha256":"70879ab9e6a727800028f2b89f24fa9fccf412bec349b9453da791622f08f4b9"},"schema_version":"1.0"},"canonical_sha256":"c5a82279849a53108fe9367d1f8e0683de3b1061ca35aecf23edd862364d534e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:16:20.173175Z","signature_b64":"MfB01iP+K3Hzukyb+WN/1Oys5c7k7sT8cu6ID8tSDD3sSwiBGcQ2+zk0okc9Od14vJsoz3wCm8o6hb2L5hiTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5a82279849a53108fe9367d1f8e0683de3b1061ca35aecf23edd862364d534e","last_reissued_at":"2026-07-05T11:16:20.172513Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:16:20.172513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.04783","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uaM+xVAG6LivTWmm6rwxXW0/h2cTJpzqs246TINsnkrOkDBwU4B4XOzsDOWtsRn5Sa5f/HFGKrBamscZDVa0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T13:48:13.721312Z"},"content_sha256":"4b75d3ab4aa31f0631e3941230ad5317896d92b5c31a315f98b88b3b6ac16f01","schema_version":"1.0","event_id":"sha256:4b75d3ab4aa31f0631e3941230ad5317896d92b5c31a315f98b88b3b6ac16f01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:YWUCE6METJJRBD7JGZ6R7DQGQP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Total progeny for spectrally negative branching L{\\'e}vy processes with absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christophe Profeta (LaMME)","submitted_at":"2025-06-05T09:11:44Z","abstract_excerpt":"We consider a spectrally negative branching L{\\'e}vy process in which particles are killed upon crossing below zero. It is known that such a process becomes extinct almost surely if the drift toward -$\\infty$ is sufficiently strong to counterbalance the reproduction rate. In this note, we study the tail asymptotics of the number of particles absorbed at the boundary during the lifetime of the process, in both the subcritical and critical regimes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04783","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.04783/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y05TCVos5tgV2FlE9xGgqFgU8J22/AoVEOzs6jR9RgYTJPFTviIIlynegGZPoAMGgEkdZDolSxQPvxFk9a4TAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T13:48:13.722467Z"},"content_sha256":"3d5cd061a49d13587d314c5927379e9b6b36760a784e5ef65b7bbbef9ecd2fac","schema_version":"1.0","event_id":"sha256:3d5cd061a49d13587d314c5927379e9b6b36760a784e5ef65b7bbbef9ecd2fac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWUCE6METJJRBD7JGZ6R7DQGQP/bundle.json","state_url":"https://pith.science/pith/YWUCE6METJJRBD7JGZ6R7DQGQP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWUCE6METJJRBD7JGZ6R7DQGQP/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":"2026-08-22T13:48:13Z","links":{"resolver":"https://pith.science/pith/YWUCE6METJJRBD7JGZ6R7DQGQP","bundle":"https://pith.science/pith/YWUCE6METJJRBD7JGZ6R7DQGQP/bundle.json","state":"https://pith.science/pith/YWUCE6METJJRBD7JGZ6R7DQGQP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWUCE6METJJRBD7JGZ6R7DQGQP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:YWUCE6METJJRBD7JGZ6R7DQGQP","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":"70879ab9e6a727800028f2b89f24fa9fccf412bec349b9453da791622f08f4b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-05T09:11:44Z","title_canon_sha256":"b8a04193b04f3a7d934b084c372fba1d4fd43773e588367ae3dd29c8f41c6a37"},"schema_version":"1.0","source":{"id":"2506.04783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.04783","created_at":"2026-07-05T11:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"2506.04783v1","created_at":"2026-07-05T11:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.04783","created_at":"2026-07-05T11:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"YWUCE6METJJR","created_at":"2026-07-05T11:16:20Z"},{"alias_kind":"pith_short_16","alias_value":"YWUCE6METJJRBD7J","created_at":"2026-07-05T11:16:20Z"},{"alias_kind":"pith_short_8","alias_value":"YWUCE6ME","created_at":"2026-07-05T11:16:20Z"}],"graph_snapshots":[{"event_id":"sha256:3d5cd061a49d13587d314c5927379e9b6b36760a784e5ef65b7bbbef9ecd2fac","target":"graph","created_at":"2026-07-05T11:16:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.04783/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a spectrally negative branching L{\\'e}vy process in which particles are killed upon crossing below zero. It is known that such a process becomes extinct almost surely if the drift toward -$\\infty$ is sufficiently strong to counterbalance the reproduction rate. In this note, we study the tail asymptotics of the number of particles absorbed at the boundary during the lifetime of the process, in both the subcritical and critical regimes.","authors_text":"Christophe Profeta (LaMME)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-05T09:11:44Z","title":"Total progeny for spectrally negative branching L{\\'e}vy processes with absorption"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04783","kind":"arxiv","version":1},"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":"sha256:4b75d3ab4aa31f0631e3941230ad5317896d92b5c31a315f98b88b3b6ac16f01","target":"record","created_at":"2026-07-05T11:16:20Z","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":"70879ab9e6a727800028f2b89f24fa9fccf412bec349b9453da791622f08f4b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-06-05T09:11:44Z","title_canon_sha256":"b8a04193b04f3a7d934b084c372fba1d4fd43773e588367ae3dd29c8f41c6a37"},"schema_version":"1.0","source":{"id":"2506.04783","kind":"arxiv","version":1}},"canonical_sha256":"c5a82279849a53108fe9367d1f8e0683de3b1061ca35aecf23edd862364d534e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5a82279849a53108fe9367d1f8e0683de3b1061ca35aecf23edd862364d534e","first_computed_at":"2026-07-05T11:16:20.172513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:16:20.172513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MfB01iP+K3Hzukyb+WN/1Oys5c7k7sT8cu6ID8tSDD3sSwiBGcQ2+zk0okc9Od14vJsoz3wCm8o6hb2L5hiTDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:16:20.173175Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.04783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b75d3ab4aa31f0631e3941230ad5317896d92b5c31a315f98b88b3b6ac16f01","sha256:3d5cd061a49d13587d314c5927379e9b6b36760a784e5ef65b7bbbef9ecd2fac"],"state_sha256":"b518f18d6b27dfe3ae45fbec5e631a456a260bce58eada3f8b3489a124ef956d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SN0ww6B3z5v5YhT2/Ht4w3V5G4PBApngFTa86wg08BCJE1z1PHt9INZGxIp5KhqRCjuwl+oa+gI70MO0v5tqDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T13:48:13.728345Z","bundle_sha256":"b23d8a03b8c0628cae5e005c5e207b9713cae4cf77cbf9c4b7c4b1c8b38e26e2"}}