{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ULRWWO5OUC7NWZ4L67PIDKZJY4","short_pith_number":"pith:ULRWWO5O","canonical_record":{"source":{"id":"1305.6802","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T13:53:07Z","cross_cats_sorted":[],"title_canon_sha256":"dbc06c2c7ec0767d29966bb71a4f42e3c6f3b9ebb8622c6580bca8634d9ac927","abstract_canon_sha256":"71ede65a2cf8f6581e0d0d3872ec1ef9fd115ed82454ff5c77d8c5b9f09e6d7f"},"schema_version":"1.0"},"canonical_sha256":"a2e36b3baea0bedb678bf7de81ab29c706c754697ebc938f1bfc82d4fec9f9ca","source":{"kind":"arxiv","id":"1305.6802","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6802","created_at":"2026-05-18T01:49:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6802v1","created_at":"2026-05-18T01:49:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6802","created_at":"2026-05-18T01:49:40Z"},{"alias_kind":"pith_short_12","alias_value":"ULRWWO5OUC7N","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"ULRWWO5OUC7NWZ4L","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"ULRWWO5O","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ULRWWO5OUC7NWZ4L67PIDKZJY4","target":"record","payload":{"canonical_record":{"source":{"id":"1305.6802","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T13:53:07Z","cross_cats_sorted":[],"title_canon_sha256":"dbc06c2c7ec0767d29966bb71a4f42e3c6f3b9ebb8622c6580bca8634d9ac927","abstract_canon_sha256":"71ede65a2cf8f6581e0d0d3872ec1ef9fd115ed82454ff5c77d8c5b9f09e6d7f"},"schema_version":"1.0"},"canonical_sha256":"a2e36b3baea0bedb678bf7de81ab29c706c754697ebc938f1bfc82d4fec9f9ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:40.240133Z","signature_b64":"JAiTOxQjmUqp+1TtbsPnr0qs6BL2hyKEGK9iyUN1CbnlEz9RPJt3z0mSbiDpb6aU+6gUdc7hgFR4+4qygprYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2e36b3baea0bedb678bf7de81ab29c706c754697ebc938f1bfc82d4fec9f9ca","last_reissued_at":"2026-05-18T01:49:40.239494Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:40.239494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.6802","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":"2026-05-18T01:49:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O8pxDUvmE6ksT991FkWf7jF+xMdGjXO+nZJZXZ+PcdmmILiWcrmBgLSYID3Z9pSWfC26Tq86gqz37x/OIAySCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:44:54.006712Z"},"content_sha256":"55e67e07558d8655a6513feebf514f746503cc60397942b3e9e6c2058c8624b2","schema_version":"1.0","event_id":"sha256:55e67e07558d8655a6513feebf514f746503cc60397942b3e9e6c2058c8624b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ULRWWO5OUC7NWZ4L67PIDKZJY4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rumor processes in random environment on N and on Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniela Bertacchi, Fabio Zucca","submitted_at":"2013-05-29T13:53:07Z","abstract_excerpt":"The aim of this paper is to study rumor processes in random environment. In a rumor process a signal starts from the stations of a fixed vertex (the root) and travels on a graph from vertex to vertex. We consider two rumor processes. In the firework process each station, when reached by the signal, transmits it up to a random distance. In the reverse firework process, on the other hand, stations do not send any signal but they \"listen\" for it up to a random distance. The first random environment that we consider is the deterministic 1-dimensional tree N with a random number of stations on each"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6802","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":"2026-05-18T01:49:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gtn16MrVqTYHE4GcAQowMuijIhz5Wl40cwCv5QAnnVYCe7/EwMf091GrWC8cPgKnBB/XCzfIr/hRwpdsm07IAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:44:54.007224Z"},"content_sha256":"3622ddb011b57c370284a074d7508f8a828523031913fe0048c5e9c27cbe5b2a","schema_version":"1.0","event_id":"sha256:3622ddb011b57c370284a074d7508f8a828523031913fe0048c5e9c27cbe5b2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULRWWO5OUC7NWZ4L67PIDKZJY4/bundle.json","state_url":"https://pith.science/pith/ULRWWO5OUC7NWZ4L67PIDKZJY4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULRWWO5OUC7NWZ4L67PIDKZJY4/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":"2026-05-28T20:44:54Z","links":{"resolver":"https://pith.science/pith/ULRWWO5OUC7NWZ4L67PIDKZJY4","bundle":"https://pith.science/pith/ULRWWO5OUC7NWZ4L67PIDKZJY4/bundle.json","state":"https://pith.science/pith/ULRWWO5OUC7NWZ4L67PIDKZJY4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULRWWO5OUC7NWZ4L67PIDKZJY4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ULRWWO5OUC7NWZ4L67PIDKZJY4","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":"71ede65a2cf8f6581e0d0d3872ec1ef9fd115ed82454ff5c77d8c5b9f09e6d7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T13:53:07Z","title_canon_sha256":"dbc06c2c7ec0767d29966bb71a4f42e3c6f3b9ebb8622c6580bca8634d9ac927"},"schema_version":"1.0","source":{"id":"1305.6802","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6802","created_at":"2026-05-18T01:49:40Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6802v1","created_at":"2026-05-18T01:49:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6802","created_at":"2026-05-18T01:49:40Z"},{"alias_kind":"pith_short_12","alias_value":"ULRWWO5OUC7N","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"ULRWWO5OUC7NWZ4L","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"ULRWWO5O","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:3622ddb011b57c370284a074d7508f8a828523031913fe0048c5e9c27cbe5b2a","target":"graph","created_at":"2026-05-18T01:49:40Z","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":"The aim of this paper is to study rumor processes in random environment. In a rumor process a signal starts from the stations of a fixed vertex (the root) and travels on a graph from vertex to vertex. We consider two rumor processes. In the firework process each station, when reached by the signal, transmits it up to a random distance. In the reverse firework process, on the other hand, stations do not send any signal but they \"listen\" for it up to a random distance. The first random environment that we consider is the deterministic 1-dimensional tree N with a random number of stations on each","authors_text":"Daniela Bertacchi, Fabio Zucca","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T13:53:07Z","title":"Rumor processes in random environment on N and on Galton-Watson trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6802","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":"sha256:55e67e07558d8655a6513feebf514f746503cc60397942b3e9e6c2058c8624b2","target":"record","created_at":"2026-05-18T01:49:40Z","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":"71ede65a2cf8f6581e0d0d3872ec1ef9fd115ed82454ff5c77d8c5b9f09e6d7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-29T13:53:07Z","title_canon_sha256":"dbc06c2c7ec0767d29966bb71a4f42e3c6f3b9ebb8622c6580bca8634d9ac927"},"schema_version":"1.0","source":{"id":"1305.6802","kind":"arxiv","version":1}},"canonical_sha256":"a2e36b3baea0bedb678bf7de81ab29c706c754697ebc938f1bfc82d4fec9f9ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2e36b3baea0bedb678bf7de81ab29c706c754697ebc938f1bfc82d4fec9f9ca","first_computed_at":"2026-05-18T01:49:40.239494Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:40.239494Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JAiTOxQjmUqp+1TtbsPnr0qs6BL2hyKEGK9iyUN1CbnlEz9RPJt3z0mSbiDpb6aU+6gUdc7hgFR4+4qygprYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:40.240133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6802","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55e67e07558d8655a6513feebf514f746503cc60397942b3e9e6c2058c8624b2","sha256:3622ddb011b57c370284a074d7508f8a828523031913fe0048c5e9c27cbe5b2a"],"state_sha256":"2c8873793e3b694b0d2d0777539b8c337facc57062816d9903e2ee4e2b11a249"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mP4GTRB8C/DF7KZJemOAyCqlB/pA/u1c6x40Qb+bVv57UliHrfH5GK9FY5ZF3nE4NtANXSjkePxuyn0i84LVAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:44:54.009930Z","bundle_sha256":"3a0000189e4c04d34f392e59c97f1807e622c390dc58f10b3e2cc4b85453f579"}}