{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3VXWG5KKLRGE7MK3Y57NSQFGSI","short_pith_number":"pith:3VXWG5KK","canonical_record":{"source":{"id":"1205.0388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-02T11:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"9a90813f8c96ec6eb8f84d1d4d278ecca4bc3d04e1865c4f3dfeefe1b0ae1377","abstract_canon_sha256":"75f8685bb33393849b829c9db4c43fd8b8e88c5e8c409698a62f25c3db4fd969"},"schema_version":"1.0"},"canonical_sha256":"dd6f63754a5c4c4fb15bc77ed940a6921966d85f1551488e75685fdc3b1bda81","source":{"kind":"arxiv","id":"1205.0388","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0388","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0388v1","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0388","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"3VXWG5KKLRGE","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3VXWG5KKLRGE7MK3","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3VXWG5KK","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3VXWG5KKLRGE7MK3Y57NSQFGSI","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-02T11:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"9a90813f8c96ec6eb8f84d1d4d278ecca4bc3d04e1865c4f3dfeefe1b0ae1377","abstract_canon_sha256":"75f8685bb33393849b829c9db4c43fd8b8e88c5e8c409698a62f25c3db4fd969"},"schema_version":"1.0"},"canonical_sha256":"dd6f63754a5c4c4fb15bc77ed940a6921966d85f1551488e75685fdc3b1bda81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:34.661039Z","signature_b64":"kQhgXmn+v7R2Kj39qcJyBrKXe5mskWJHuRrTjOpb8/d7MSUW0kIeaxy8pqB1pYe8Rz7NLREL9Ju9EftPBTvDDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd6f63754a5c4c4fb15bc77ed940a6921966d85f1551488e75685fdc3b1bda81","last_reissued_at":"2026-05-18T03:56:34.660559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:34.660559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0388","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":"2026-05-18T03:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CMC88FJlz1P02orZbqAZFMo7HOapD8rbpIysCT3x0WVKQitd66f8HTtmbXYCoRtABtSsLlMMPLgM6kcdPYwSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:56:56.086721Z"},"content_sha256":"637d8b1669db9aae286c26c6dc059788a1132b405c65c33e8fd90ef9df132323","schema_version":"1.0","event_id":"sha256:637d8b1669db9aae286c26c6dc059788a1132b405c65c33e8fd90ef9df132323"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3VXWG5KKLRGE7MK3Y57NSQFGSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic behavior of critical primitive multi-type branching processes with immigration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gyula Pap, M\\'arton Isp\\'any","submitted_at":"2012-05-02T11:41:49Z","abstract_excerpt":"Under natural assumptions a Feller type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved that a sequence of appropriately scaled random step functions formed from a sequence of critical primitive multi-type branching processes with immigration converges weakly towards a squared Bessel process supported by a ray determined by the Perron vector of the offspring mean matrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0388","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":"2026-05-18T03:56:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vnVuUpoM8cNtymlhzaMkwOeSIwzbxEsMuSKU6UKmtNFtQ6Dz4DGOh7WcQa7eDBi5ymyc/VGfpzqpopg93PKiDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:56:56.087066Z"},"content_sha256":"a66dd312c04857ad3dddd43d6855acf6973df34765638629a926ed5dc4da87b4","schema_version":"1.0","event_id":"sha256:a66dd312c04857ad3dddd43d6855acf6973df34765638629a926ed5dc4da87b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VXWG5KKLRGE7MK3Y57NSQFGSI/bundle.json","state_url":"https://pith.science/pith/3VXWG5KKLRGE7MK3Y57NSQFGSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VXWG5KKLRGE7MK3Y57NSQFGSI/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":"2026-06-26T00:56:56Z","links":{"resolver":"https://pith.science/pith/3VXWG5KKLRGE7MK3Y57NSQFGSI","bundle":"https://pith.science/pith/3VXWG5KKLRGE7MK3Y57NSQFGSI/bundle.json","state":"https://pith.science/pith/3VXWG5KKLRGE7MK3Y57NSQFGSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VXWG5KKLRGE7MK3Y57NSQFGSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3VXWG5KKLRGE7MK3Y57NSQFGSI","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":"75f8685bb33393849b829c9db4c43fd8b8e88c5e8c409698a62f25c3db4fd969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-02T11:41:49Z","title_canon_sha256":"9a90813f8c96ec6eb8f84d1d4d278ecca4bc3d04e1865c4f3dfeefe1b0ae1377"},"schema_version":"1.0","source":{"id":"1205.0388","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0388","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0388v1","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0388","created_at":"2026-05-18T03:56:34Z"},{"alias_kind":"pith_short_12","alias_value":"3VXWG5KKLRGE","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3VXWG5KKLRGE7MK3","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3VXWG5KK","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:a66dd312c04857ad3dddd43d6855acf6973df34765638629a926ed5dc4da87b4","target":"graph","created_at":"2026-05-18T03:56:34Z","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":"Under natural assumptions a Feller type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved that a sequence of appropriately scaled random step functions formed from a sequence of critical primitive multi-type branching processes with immigration converges weakly towards a squared Bessel process supported by a ray determined by the Perron vector of the offspring mean matrix.","authors_text":"Gyula Pap, M\\'arton Isp\\'any","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-02T11:41:49Z","title":"Asymptotic behavior of critical primitive multi-type branching processes with immigration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0388","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":"sha256:637d8b1669db9aae286c26c6dc059788a1132b405c65c33e8fd90ef9df132323","target":"record","created_at":"2026-05-18T03:56:34Z","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":"75f8685bb33393849b829c9db4c43fd8b8e88c5e8c409698a62f25c3db4fd969","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-05-02T11:41:49Z","title_canon_sha256":"9a90813f8c96ec6eb8f84d1d4d278ecca4bc3d04e1865c4f3dfeefe1b0ae1377"},"schema_version":"1.0","source":{"id":"1205.0388","kind":"arxiv","version":1}},"canonical_sha256":"dd6f63754a5c4c4fb15bc77ed940a6921966d85f1551488e75685fdc3b1bda81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd6f63754a5c4c4fb15bc77ed940a6921966d85f1551488e75685fdc3b1bda81","first_computed_at":"2026-05-18T03:56:34.660559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:34.660559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kQhgXmn+v7R2Kj39qcJyBrKXe5mskWJHuRrTjOpb8/d7MSUW0kIeaxy8pqB1pYe8Rz7NLREL9Ju9EftPBTvDDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:34.661039Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0388","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:637d8b1669db9aae286c26c6dc059788a1132b405c65c33e8fd90ef9df132323","sha256:a66dd312c04857ad3dddd43d6855acf6973df34765638629a926ed5dc4da87b4"],"state_sha256":"f98866c5b4188b20a2ac51787ddeeb5dbceb6adf122e2d088017568d059347bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/Otseq/N5INdKx4mOvMiW7e88V6UV6QDp4Lt4F4U5q5uCZzGdkX8d9NUA2+5pXnzm17i1vodNS0Zkydc7DmCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:56:56.089046Z","bundle_sha256":"9f21aa1e340881dd514c631ba72ae7c56332fa6e9b5f8f16b7f7b31ec009e559"}}