{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YJV3UAS2BLY2EOJAN74MCHCJYH","short_pith_number":"pith:YJV3UAS2","canonical_record":{"source":{"id":"1107.4904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-25T11:42:17Z","cross_cats_sorted":[],"title_canon_sha256":"dd169904c1128bf5e65c855aad037e6a5f8ab4b5a8b811a58d337752ad37c990","abstract_canon_sha256":"d177780977ea2f43596bd000be19c870848e0b4bf2ae32aacd5b8e88e6931a71"},"schema_version":"1.0"},"canonical_sha256":"c26bba025a0af1a239206ff8c11c49c1ccd5d34c0d995edeb039d27ff6130dcf","source":{"kind":"arxiv","id":"1107.4904","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4904","created_at":"2026-05-18T02:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4904v1","created_at":"2026-05-18T02:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4904","created_at":"2026-05-18T02:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"YJV3UAS2BLY2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YJV3UAS2BLY2EOJA","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YJV3UAS2","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YJV3UAS2BLY2EOJAN74MCHCJYH","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-25T11:42:17Z","cross_cats_sorted":[],"title_canon_sha256":"dd169904c1128bf5e65c855aad037e6a5f8ab4b5a8b811a58d337752ad37c990","abstract_canon_sha256":"d177780977ea2f43596bd000be19c870848e0b4bf2ae32aacd5b8e88e6931a71"},"schema_version":"1.0"},"canonical_sha256":"c26bba025a0af1a239206ff8c11c49c1ccd5d34c0d995edeb039d27ff6130dcf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:10.612267Z","signature_b64":"HKTORbEwjFTwJvLk6vRpzaCJ8APz6pMvkPq1bBA8gZ7XINtrtQQLr7YDAmf3vqOxd+Fjj/IWB9/odjE4hwhLAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c26bba025a0af1a239206ff8c11c49c1ccd5d34c0d995edeb039d27ff6130dcf","last_reissued_at":"2026-05-18T02:01:10.611475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:10.611475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4904","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":"2026-05-18T02:01:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kzfZHtSdYG4q+CcaORWt+ai9wHmKbchp6XFQWHRFBbrYduWyTvcJuVKQzdgtauKhqMfynkTT0PXkA49wYAXrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:47:37.363785Z"},"content_sha256":"e7db6a68e6b458f81486ad5a5fa63711a86da6562bf4e651e971e8d00ecb3e4d","schema_version":"1.0","event_id":"sha256:e7db6a68e6b458f81486ad5a5fa63711a86da6562bf4e651e971e8d00ecb3e4d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YJV3UAS2BLY2EOJAN74MCHCJYH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enzo Orsingher, Valentina Cammarota","submitted_at":"2011-07-25T11:42:17Z","abstract_excerpt":"A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincar\\'e half-plane and Poincar\\'e disk) is examined. Each particle can split into two particles only once at Poisson paced times and deviates orthogonally when splitted. At time $t$, after $N(t)$ Poisson events, there are $N(t)+1$ particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4904","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":"2026-05-18T02:01:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u22tcL//7V/qK7CTxLPtHSZEKZd+8orxUB8b3z8WzU+c7zVkTfobu6rZVCXxrPixU9+A3+n+2FOdsOI5QaeLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T06:47:37.364147Z"},"content_sha256":"49d1c4610883cdbe925a5cea4d4f6f2ab2d876b0767af99013b9913a3d42dc51","schema_version":"1.0","event_id":"sha256:49d1c4610883cdbe925a5cea4d4f6f2ab2d876b0767af99013b9913a3d42dc51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YJV3UAS2BLY2EOJAN74MCHCJYH/bundle.json","state_url":"https://pith.science/pith/YJV3UAS2BLY2EOJAN74MCHCJYH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YJV3UAS2BLY2EOJAN74MCHCJYH/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":"2026-05-28T06:47:37Z","links":{"resolver":"https://pith.science/pith/YJV3UAS2BLY2EOJAN74MCHCJYH","bundle":"https://pith.science/pith/YJV3UAS2BLY2EOJAN74MCHCJYH/bundle.json","state":"https://pith.science/pith/YJV3UAS2BLY2EOJAN74MCHCJYH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YJV3UAS2BLY2EOJAN74MCHCJYH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YJV3UAS2BLY2EOJAN74MCHCJYH","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":"d177780977ea2f43596bd000be19c870848e0b4bf2ae32aacd5b8e88e6931a71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-25T11:42:17Z","title_canon_sha256":"dd169904c1128bf5e65c855aad037e6a5f8ab4b5a8b811a58d337752ad37c990"},"schema_version":"1.0","source":{"id":"1107.4904","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4904","created_at":"2026-05-18T02:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4904v1","created_at":"2026-05-18T02:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4904","created_at":"2026-05-18T02:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"YJV3UAS2BLY2","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YJV3UAS2BLY2EOJA","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YJV3UAS2","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:49d1c4610883cdbe925a5cea4d4f6f2ab2d876b0767af99013b9913a3d42dc51","target":"graph","created_at":"2026-05-18T02:01:10Z","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":"A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincar\\'e half-plane and Poincar\\'e disk) is examined. Each particle can split into two particles only once at Poisson paced times and deviates orthogonally when splitted. At time $t$, after $N(t)$ Poisson events, there are $N(t)+1$ particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and w","authors_text":"Enzo Orsingher, Valentina Cammarota","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-25T11:42:17Z","title":"Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4904","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:e7db6a68e6b458f81486ad5a5fa63711a86da6562bf4e651e971e8d00ecb3e4d","target":"record","created_at":"2026-05-18T02:01:10Z","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":"d177780977ea2f43596bd000be19c870848e0b4bf2ae32aacd5b8e88e6931a71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-25T11:42:17Z","title_canon_sha256":"dd169904c1128bf5e65c855aad037e6a5f8ab4b5a8b811a58d337752ad37c990"},"schema_version":"1.0","source":{"id":"1107.4904","kind":"arxiv","version":1}},"canonical_sha256":"c26bba025a0af1a239206ff8c11c49c1ccd5d34c0d995edeb039d27ff6130dcf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c26bba025a0af1a239206ff8c11c49c1ccd5d34c0d995edeb039d27ff6130dcf","first_computed_at":"2026-05-18T02:01:10.611475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:10.611475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HKTORbEwjFTwJvLk6vRpzaCJ8APz6pMvkPq1bBA8gZ7XINtrtQQLr7YDAmf3vqOxd+Fjj/IWB9/odjE4hwhLAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:10.612267Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4904","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7db6a68e6b458f81486ad5a5fa63711a86da6562bf4e651e971e8d00ecb3e4d","sha256:49d1c4610883cdbe925a5cea4d4f6f2ab2d876b0767af99013b9913a3d42dc51"],"state_sha256":"ec2cc9504c56c2bb25976b599be2bd94cdf555ad9a8446fdb2bc97a1b7dd9869"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U0vXf1744WibmPWRmMjoP5y88PUPA3cnNedx9PYN2Zxs8syhRlL6jXCnp64BskQtMZJ0CbcDbuHCTjs2dDpuCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T06:47:37.366539Z","bundle_sha256":"63b8e2c4d0ce85b8ef1c6b819bf74f8c9ab97c1ef9fe51716f2c8aa93934031c"}}