{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:J4L6A42CL5YD5VELK4QO2QA64W","short_pith_number":"pith:J4L6A42C","canonical_record":{"source":{"id":"1101.5379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-27T20:18:39Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"58963120710b45f61ca625aa6fa55c8bae142ceacace4273d7fa2111dc43ecb3","abstract_canon_sha256":"f3d3929c55f5096717b2e83b53ce3102d0dbd0409abd4d057682338a7e3bc1f0"},"schema_version":"1.0"},"canonical_sha256":"4f17e073425f703ed48b5720ed401ee5aba7923927d0d57b1ff2c4a5fed3a6e9","source":{"kind":"arxiv","id":"1101.5379","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5379","created_at":"2026-05-18T03:23:03Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5379v3","created_at":"2026-05-18T03:23:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5379","created_at":"2026-05-18T03:23:03Z"},{"alias_kind":"pith_short_12","alias_value":"J4L6A42CL5YD","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J4L6A42CL5YD5VEL","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J4L6A42C","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:J4L6A42CL5YD5VELK4QO2QA64W","target":"record","payload":{"canonical_record":{"source":{"id":"1101.5379","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-27T20:18:39Z","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"title_canon_sha256":"58963120710b45f61ca625aa6fa55c8bae142ceacace4273d7fa2111dc43ecb3","abstract_canon_sha256":"f3d3929c55f5096717b2e83b53ce3102d0dbd0409abd4d057682338a7e3bc1f0"},"schema_version":"1.0"},"canonical_sha256":"4f17e073425f703ed48b5720ed401ee5aba7923927d0d57b1ff2c4a5fed3a6e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:23:03.395299Z","signature_b64":"1Yqx+/wsR50b0yOFQKEjLSX34ZhB6Rg8S5GOHLj1sdTUuS+anpdKtrdcXtyHndxnUdyp6fSzt6LVNeMP1t0oBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f17e073425f703ed48b5720ed401ee5aba7923927d0d57b1ff2c4a5fed3a6e9","last_reissued_at":"2026-05-18T03:23:03.394669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:23:03.394669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.5379","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:23:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"slXMrQa1961iwb6MLP5SnJzLj7siTfUP44PnnvIjKpJA0XXZndwuLDFPlopO0ZyiUCbdGWHsJkkFEIkKN7g7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:31:05.350240Z"},"content_sha256":"5394aac9fa2efe0abd95569e8bc2b78a9572c694a2000bd0b0799ac5c6a93367","schema_version":"1.0","event_id":"sha256:5394aac9fa2efe0abd95569e8bc2b78a9572c694a2000bd0b0799ac5c6a93367"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:J4L6A42CL5YD5VELK4QO2QA64W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How Many Nodes are Effectively Accessed in Complex Networks?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","cs.SI"],"primary_cat":"physics.soc-ph","authors_text":"Jo\\~ao L. B. Batista, Luciano da F. Costa, Matheus P. Viana","submitted_at":"2011-01-27T20:18:39Z","abstract_excerpt":"The measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports important results regarding the properties of the accessibility, including its relationship with the average minimal time to visit all nodes reachable after $h$ steps along a random walk starting from a source, as well as the number of nodes that are visited after a finite period of time. We characterize the relationship between accessibility and the average number of walks required in order to visit all reachable nodes (the e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5379","kind":"arxiv","version":3},"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":"2026-05-18T03:23:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h/K0Lqk45QoVmKllcAGOuZk8dqvugh2jymK0XpIy7ZMp/TKvOuX62X/tpdl9E/Cu2ZMqvZ7Ae5/yCoCrSop9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:31:05.350616Z"},"content_sha256":"3e27f8d12edb1413d5a787a20c46f6de930de760982b3f08a4805fa7e3d34535","schema_version":"1.0","event_id":"sha256:3e27f8d12edb1413d5a787a20c46f6de930de760982b3f08a4805fa7e3d34535"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J4L6A42CL5YD5VELK4QO2QA64W/bundle.json","state_url":"https://pith.science/pith/J4L6A42CL5YD5VELK4QO2QA64W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J4L6A42CL5YD5VELK4QO2QA64W/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":"2026-07-02T10:31:05Z","links":{"resolver":"https://pith.science/pith/J4L6A42CL5YD5VELK4QO2QA64W","bundle":"https://pith.science/pith/J4L6A42CL5YD5VELK4QO2QA64W/bundle.json","state":"https://pith.science/pith/J4L6A42CL5YD5VELK4QO2QA64W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J4L6A42CL5YD5VELK4QO2QA64W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:J4L6A42CL5YD5VELK4QO2QA64W","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":"f3d3929c55f5096717b2e83b53ce3102d0dbd0409abd4d057682338a7e3bc1f0","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-27T20:18:39Z","title_canon_sha256":"58963120710b45f61ca625aa6fa55c8bae142ceacace4273d7fa2111dc43ecb3"},"schema_version":"1.0","source":{"id":"1101.5379","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5379","created_at":"2026-05-18T03:23:03Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5379v3","created_at":"2026-05-18T03:23:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5379","created_at":"2026-05-18T03:23:03Z"},{"alias_kind":"pith_short_12","alias_value":"J4L6A42CL5YD","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"J4L6A42CL5YD5VEL","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"J4L6A42C","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:3e27f8d12edb1413d5a787a20c46f6de930de760982b3f08a4805fa7e3d34535","target":"graph","created_at":"2026-05-18T03:23:03Z","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 measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks. This article reports important results regarding the properties of the accessibility, including its relationship with the average minimal time to visit all nodes reachable after $h$ steps along a random walk starting from a source, as well as the number of nodes that are visited after a finite period of time. We characterize the relationship between accessibility and the average number of walks required in order to visit all reachable nodes (the e","authors_text":"Jo\\~ao L. B. Batista, Luciano da F. Costa, Matheus P. Viana","cross_cats":["cond-mat.stat-mech","cs.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-27T20:18:39Z","title":"How Many Nodes are Effectively Accessed in Complex Networks?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5379","kind":"arxiv","version":3},"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":"sha256:5394aac9fa2efe0abd95569e8bc2b78a9572c694a2000bd0b0799ac5c6a93367","target":"record","created_at":"2026-05-18T03:23:03Z","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":"f3d3929c55f5096717b2e83b53ce3102d0dbd0409abd4d057682338a7e3bc1f0","cross_cats_sorted":["cond-mat.stat-mech","cs.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2011-01-27T20:18:39Z","title_canon_sha256":"58963120710b45f61ca625aa6fa55c8bae142ceacace4273d7fa2111dc43ecb3"},"schema_version":"1.0","source":{"id":"1101.5379","kind":"arxiv","version":3}},"canonical_sha256":"4f17e073425f703ed48b5720ed401ee5aba7923927d0d57b1ff2c4a5fed3a6e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f17e073425f703ed48b5720ed401ee5aba7923927d0d57b1ff2c4a5fed3a6e9","first_computed_at":"2026-05-18T03:23:03.394669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:23:03.394669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Yqx+/wsR50b0yOFQKEjLSX34ZhB6Rg8S5GOHLj1sdTUuS+anpdKtrdcXtyHndxnUdyp6fSzt6LVNeMP1t0oBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:23:03.395299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.5379","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5394aac9fa2efe0abd95569e8bc2b78a9572c694a2000bd0b0799ac5c6a93367","sha256:3e27f8d12edb1413d5a787a20c46f6de930de760982b3f08a4805fa7e3d34535"],"state_sha256":"338dd57858edd31f0068c064393f605757cdca65e8c388a876ed09586464cac2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E9lP8oXFolOU0aGmdB/qpF8/e9V5J8zJwyw+s+/K2hI+bgvo4VFmPCYhLfPhto8pxknHu2w5Qie5u3FmvoLECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T10:31:05.352574Z","bundle_sha256":"df6132414f7ccf4f43f7e35d9e9ff1dd07289f576da3053f1aec48f10a9297b1"}}