{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:O6JAOVFKJ2MN7IPRJ56FKLCBPY","short_pith_number":"pith:O6JAOVFK","canonical_record":{"source":{"id":"1305.1202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-06T14:06:04Z","cross_cats_sorted":[],"title_canon_sha256":"77891d23649c7263cf5067f17d276ef8ca63c631e2108a3ad6da1cc067eba537","abstract_canon_sha256":"4c440deedd157fcd506026cca41e947225b71cb1bcc358b242beb20bc792d735"},"schema_version":"1.0"},"canonical_sha256":"77920754aa4e98dfa1f14f7c552c417e1239ba5e3263e01cac1e2d75df64307f","source":{"kind":"arxiv","id":"1305.1202","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1202","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1202v1","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1202","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"O6JAOVFKJ2MN","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O6JAOVFKJ2MN7IPR","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O6JAOVFK","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:O6JAOVFKJ2MN7IPRJ56FKLCBPY","target":"record","payload":{"canonical_record":{"source":{"id":"1305.1202","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-06T14:06:04Z","cross_cats_sorted":[],"title_canon_sha256":"77891d23649c7263cf5067f17d276ef8ca63c631e2108a3ad6da1cc067eba537","abstract_canon_sha256":"4c440deedd157fcd506026cca41e947225b71cb1bcc358b242beb20bc792d735"},"schema_version":"1.0"},"canonical_sha256":"77920754aa4e98dfa1f14f7c552c417e1239ba5e3263e01cac1e2d75df64307f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:02.478126Z","signature_b64":"WL6JPKPSSeZFA6GWp1V0VAcPHcmoVp18EjWSNXOQMxiI6pCRJSWVm/HQNOKRA9G4sEFfRcb96qjFpXzokIjaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77920754aa4e98dfa1f14f7c552c417e1239ba5e3263e01cac1e2d75df64307f","last_reissued_at":"2026-05-18T02:31:02.477629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:02.477629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.1202","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":"2026-05-18T02:31:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ugwNcf+F2FZNUQzEEuARF7HHiFBsolI5yBN3x3DcXyRqTh6BKvM16lRzTuFElHd+4NVrbExKKpl7YgDYOsyjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:20:06.034157Z"},"content_sha256":"6d2580322c1dce643a5b10b3043b786e843d3c619def19e4611554e067efd31a","schema_version":"1.0","event_id":"sha256:6d2580322c1dce643a5b10b3043b786e843d3c619def19e4611554e067efd31a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:O6JAOVFKJ2MN7IPRJ56FKLCBPY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trees under attack: a Ray-Knight representation of Feller's branching diffusion with logistic growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Wakolbinger, Etienne Pardoux, Vi Le","submitted_at":"2013-05-06T14:06:04Z","abstract_excerpt":"We obtain a representation of Feller's branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion $H$ with a drift that is affine linear in the local time accumulated by $H$ at its current level. As in the classical Ray-Knight representation, the excursions of $H$ are the exploration paths of the trees of descendants of the ancestors at time $t=0$, and the local time of $H$ at height $t$ measures the population size at time $t$ (see e.g. \\cite{LG4}). We cope with the dependence in the reproduction by introducing a pecking order of individuals: an indivi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1202","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":""},"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":"2026-05-18T02:31:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pexT4tWuf1e4zQ6uAb0bIvZjxXyU/x6/AUzF3nnMidimkYRBuhlZsaf78khtmV3tYx2/lOgoH+2Fka7amyVhAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T18:20:06.034865Z"},"content_sha256":"7655bba0f3cc2727967802c24f15a68e723f96f308564014f811e78f0952bd71","schema_version":"1.0","event_id":"sha256:7655bba0f3cc2727967802c24f15a68e723f96f308564014f811e78f0952bd71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6JAOVFKJ2MN7IPRJ56FKLCBPY/bundle.json","state_url":"https://pith.science/pith/O6JAOVFKJ2MN7IPRJ56FKLCBPY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6JAOVFKJ2MN7IPRJ56FKLCBPY/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":"2026-06-08T18:20:06Z","links":{"resolver":"https://pith.science/pith/O6JAOVFKJ2MN7IPRJ56FKLCBPY","bundle":"https://pith.science/pith/O6JAOVFKJ2MN7IPRJ56FKLCBPY/bundle.json","state":"https://pith.science/pith/O6JAOVFKJ2MN7IPRJ56FKLCBPY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6JAOVFKJ2MN7IPRJ56FKLCBPY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O6JAOVFKJ2MN7IPRJ56FKLCBPY","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":"4c440deedd157fcd506026cca41e947225b71cb1bcc358b242beb20bc792d735","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-06T14:06:04Z","title_canon_sha256":"77891d23649c7263cf5067f17d276ef8ca63c631e2108a3ad6da1cc067eba537"},"schema_version":"1.0","source":{"id":"1305.1202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.1202","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"arxiv_version","alias_value":"1305.1202v1","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.1202","created_at":"2026-05-18T02:31:02Z"},{"alias_kind":"pith_short_12","alias_value":"O6JAOVFKJ2MN","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O6JAOVFKJ2MN7IPR","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O6JAOVFK","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:7655bba0f3cc2727967802c24f15a68e723f96f308564014f811e78f0952bd71","target":"graph","created_at":"2026-05-18T02:31:02Z","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":"We obtain a representation of Feller's branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion $H$ with a drift that is affine linear in the local time accumulated by $H$ at its current level. As in the classical Ray-Knight representation, the excursions of $H$ are the exploration paths of the trees of descendants of the ancestors at time $t=0$, and the local time of $H$ at height $t$ measures the population size at time $t$ (see e.g. \\cite{LG4}). We cope with the dependence in the reproduction by introducing a pecking order of individuals: an indivi","authors_text":"Anton Wakolbinger, Etienne Pardoux, Vi Le","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-06T14:06:04Z","title":"Trees under attack: a Ray-Knight representation of Feller's branching diffusion with logistic growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1202","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":"sha256:6d2580322c1dce643a5b10b3043b786e843d3c619def19e4611554e067efd31a","target":"record","created_at":"2026-05-18T02:31:02Z","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":"4c440deedd157fcd506026cca41e947225b71cb1bcc358b242beb20bc792d735","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-06T14:06:04Z","title_canon_sha256":"77891d23649c7263cf5067f17d276ef8ca63c631e2108a3ad6da1cc067eba537"},"schema_version":"1.0","source":{"id":"1305.1202","kind":"arxiv","version":1}},"canonical_sha256":"77920754aa4e98dfa1f14f7c552c417e1239ba5e3263e01cac1e2d75df64307f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77920754aa4e98dfa1f14f7c552c417e1239ba5e3263e01cac1e2d75df64307f","first_computed_at":"2026-05-18T02:31:02.477629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:02.477629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WL6JPKPSSeZFA6GWp1V0VAcPHcmoVp18EjWSNXOQMxiI6pCRJSWVm/HQNOKRA9G4sEFfRcb96qjFpXzokIjaBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:02.478126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.1202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d2580322c1dce643a5b10b3043b786e843d3c619def19e4611554e067efd31a","sha256:7655bba0f3cc2727967802c24f15a68e723f96f308564014f811e78f0952bd71"],"state_sha256":"b42d576602a4b0c2a15c28c44978dd7d13c547e335793f106d5cb45eefbaf682"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+gr6mKlrqyX6dlWI2Jpri50CdIt57dvzlVPdmfMpiJ4e7UywkuH2ROyO/KVTjZcPbEviPKLDpritC+X0z/MxDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T18:20:06.038312Z","bundle_sha256":"36c364978ed3f67ed2a796d984ea48e34417c03043a6bcf4fe76630219655347"}}