{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IUPO4L5P3OAY4NFL6IVKG3WD7N","short_pith_number":"pith:IUPO4L5P","canonical_record":{"source":{"id":"1902.00994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-03T23:45:41Z","cross_cats_sorted":[],"title_canon_sha256":"01fa1915d4c5453c51d50cb3f1556d5317fe563a1a8f03115b741f4717e2938b","abstract_canon_sha256":"4c6b7ad7193de06b85beb1ff30e6eb6c7a2b6dcb75bc590068c78bb1dca34197"},"schema_version":"1.0"},"canonical_sha256":"451eee2fafdb818e34abf22aa36ec3fb7b70d22853b178d2b32a3567a7a05a6d","source":{"kind":"arxiv","id":"1902.00994","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00994","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00994v1","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00994","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"IUPO4L5P3OAY","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"pith_short_16","alias_value":"IUPO4L5P3OAY4NFL","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"pith_short_8","alias_value":"IUPO4L5P","created_at":"2026-07-05T01:17:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IUPO4L5P3OAY4NFL6IVKG3WD7N","target":"record","payload":{"canonical_record":{"source":{"id":"1902.00994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-03T23:45:41Z","cross_cats_sorted":[],"title_canon_sha256":"01fa1915d4c5453c51d50cb3f1556d5317fe563a1a8f03115b741f4717e2938b","abstract_canon_sha256":"4c6b7ad7193de06b85beb1ff30e6eb6c7a2b6dcb75bc590068c78bb1dca34197"},"schema_version":"1.0"},"canonical_sha256":"451eee2fafdb818e34abf22aa36ec3fb7b70d22853b178d2b32a3567a7a05a6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:17:56.136912Z","signature_b64":"Uq1kTot0O4bA5JW6aTgg+gncZVJXay6EAbPul4iISXn9DHAtul4l7ieIezmAhC5X/G/X0ntOrkWo9zLkGWmzBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"451eee2fafdb818e34abf22aa36ec3fb7b70d22853b178d2b32a3567a7a05a6d","last_reissued_at":"2026-07-05T01:17:56.136498Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:17:56.136498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.00994","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":"2026-07-05T01:17:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXntxRnHaTPTx/OtGc4errLele+Vj98OlhyTcPmHYFj8cAZnW8pARK21lHENgNHMXt96XZHoRtqeJuqPAGERDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T23:27:16.285751Z"},"content_sha256":"8871d80657d7db12157db451a9e0551b25ff5c3c7bee0fd623dab3950adee3d4","schema_version":"1.0","event_id":"sha256:8871d80657d7db12157db451a9e0551b25ff5c3c7bee0fd623dab3950adee3d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IUPO4L5P3OAY4NFL6IVKG3WD7N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Catalytic Branching Random Walk with Semi-exponential Increments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ekaterina Vl. Bulinskaya","submitted_at":"2019-02-03T23:45:41Z","abstract_excerpt":"A catalytic branching random walk on a multidimensional lattice, with arbitrary finite number of catalysts, is studied in supercritical regime. The dynamics of spatial spread of the particles population is examined, upon normalization. The components of the vector random walk jump are assumed independent (or close to independent) and have semi-exponential distributions with, possibly, different parameters. A limit theorem on the almost sure normalized positions of the particles at the population ``front'' is established. Contrary to the case of the random walk increments with ``light'' distrib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00994","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/1902.00994/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":"2026-07-05T01:17:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DNLk2lyNHcCW1i5ir3IXSN/Zz2C+fNBwHX6ipu1LV53B7Reh3N6tJB6uYFKj0WZM4FGfwyaD/YTJ2O7gZy9jCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T23:27:16.286241Z"},"content_sha256":"9aa20d5a15a92d40ab95232ff98de4e98a27d3745ed9decfb8acc3bbb5ef745a","schema_version":"1.0","event_id":"sha256:9aa20d5a15a92d40ab95232ff98de4e98a27d3745ed9decfb8acc3bbb5ef745a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IUPO4L5P3OAY4NFL6IVKG3WD7N/bundle.json","state_url":"https://pith.science/pith/IUPO4L5P3OAY4NFL6IVKG3WD7N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IUPO4L5P3OAY4NFL6IVKG3WD7N/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":"2026-08-16T23:27:16Z","links":{"resolver":"https://pith.science/pith/IUPO4L5P3OAY4NFL6IVKG3WD7N","bundle":"https://pith.science/pith/IUPO4L5P3OAY4NFL6IVKG3WD7N/bundle.json","state":"https://pith.science/pith/IUPO4L5P3OAY4NFL6IVKG3WD7N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IUPO4L5P3OAY4NFL6IVKG3WD7N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IUPO4L5P3OAY4NFL6IVKG3WD7N","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":"4c6b7ad7193de06b85beb1ff30e6eb6c7a2b6dcb75bc590068c78bb1dca34197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-03T23:45:41Z","title_canon_sha256":"01fa1915d4c5453c51d50cb3f1556d5317fe563a1a8f03115b741f4717e2938b"},"schema_version":"1.0","source":{"id":"1902.00994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00994","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00994v1","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00994","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"IUPO4L5P3OAY","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"pith_short_16","alias_value":"IUPO4L5P3OAY4NFL","created_at":"2026-07-05T01:17:56Z"},{"alias_kind":"pith_short_8","alias_value":"IUPO4L5P","created_at":"2026-07-05T01:17:56Z"}],"graph_snapshots":[{"event_id":"sha256:9aa20d5a15a92d40ab95232ff98de4e98a27d3745ed9decfb8acc3bbb5ef745a","target":"graph","created_at":"2026-07-05T01:17:56Z","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/1902.00994/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A catalytic branching random walk on a multidimensional lattice, with arbitrary finite number of catalysts, is studied in supercritical regime. The dynamics of spatial spread of the particles population is examined, upon normalization. The components of the vector random walk jump are assumed independent (or close to independent) and have semi-exponential distributions with, possibly, different parameters. A limit theorem on the almost sure normalized positions of the particles at the population ``front'' is established. Contrary to the case of the random walk increments with ``light'' distrib","authors_text":"Ekaterina Vl. Bulinskaya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-03T23:45:41Z","title":"Catalytic Branching Random Walk with Semi-exponential Increments"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00994","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":"sha256:8871d80657d7db12157db451a9e0551b25ff5c3c7bee0fd623dab3950adee3d4","target":"record","created_at":"2026-07-05T01:17:56Z","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":"4c6b7ad7193de06b85beb1ff30e6eb6c7a2b6dcb75bc590068c78bb1dca34197","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-02-03T23:45:41Z","title_canon_sha256":"01fa1915d4c5453c51d50cb3f1556d5317fe563a1a8f03115b741f4717e2938b"},"schema_version":"1.0","source":{"id":"1902.00994","kind":"arxiv","version":1}},"canonical_sha256":"451eee2fafdb818e34abf22aa36ec3fb7b70d22853b178d2b32a3567a7a05a6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"451eee2fafdb818e34abf22aa36ec3fb7b70d22853b178d2b32a3567a7a05a6d","first_computed_at":"2026-07-05T01:17:56.136498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:17:56.136498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uq1kTot0O4bA5JW6aTgg+gncZVJXay6EAbPul4iISXn9DHAtul4l7ieIezmAhC5X/G/X0ntOrkWo9zLkGWmzBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:17:56.136912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8871d80657d7db12157db451a9e0551b25ff5c3c7bee0fd623dab3950adee3d4","sha256:9aa20d5a15a92d40ab95232ff98de4e98a27d3745ed9decfb8acc3bbb5ef745a"],"state_sha256":"b17b0dc2dcf68dff825e0680823e2b2ab104b9a5cc57716f8ea6914dd1d57b66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"knVztFo1z7X9G1Ao7VLgTtpeDt0XrBscxPP5DUjMMrawGrdEiMMRUS2QOZ818PWVvSJlV9MpBn8F6T+pKcI3Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T23:27:16.291449Z","bundle_sha256":"2bc900819cdb32ae81839063447a2b6f7f36f56ea119b0ca510c4f72cea769df"}}