{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:V33G3YI43FULM4CHM23GWF3JIV","short_pith_number":"pith:V33G3YI4","canonical_record":{"source":{"id":"1110.3388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-15T06:07:49Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"c5a25be6a04ba298d1e58458ae1ec31ca7dcb477ff937068916e40415816cf6c","abstract_canon_sha256":"25597b146fe057e1f74ff87c1ff7ddffc486312684c81a28c083ffd1626f2abb"},"schema_version":"1.0"},"canonical_sha256":"aef66de11cd968b6704766b66b1769454f056e5282dc24884494e93a756383bc","source":{"kind":"arxiv","id":"1110.3388","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3388","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3388v1","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3388","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"V33G3YI43FUL","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V33G3YI43FULM4CH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V33G3YI4","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:V33G3YI43FULM4CHM23GWF3JIV","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-15T06:07:49Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"c5a25be6a04ba298d1e58458ae1ec31ca7dcb477ff937068916e40415816cf6c","abstract_canon_sha256":"25597b146fe057e1f74ff87c1ff7ddffc486312684c81a28c083ffd1626f2abb"},"schema_version":"1.0"},"canonical_sha256":"aef66de11cd968b6704766b66b1769454f056e5282dc24884494e93a756383bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:54.737880Z","signature_b64":"ungFF21XKnBqndF5ZnVOw16TkI2P+xF2JSeZHSKen2uiewqpak6Q+0UvHqMPLkc0C70wMaUqz5mJjKuf7N2cAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aef66de11cd968b6704766b66b1769454f056e5282dc24884494e93a756383bc","last_reissued_at":"2026-05-18T04:06:54.737367Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:54.737367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3388","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":"2026-05-18T04:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8TLSUuB7bvdiLTtUZRhUf86IU4gYnDl3TT5Kid6fx6SiliY1FZ/OSdxE1Zzo0oCLPuQ0pQAPX8xVhelhBQP6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:24:44.752195Z"},"content_sha256":"057333cc920d7f764334fe9513910b35d86661ce298b2350954e53b98ecf49ae","schema_version":"1.0","event_id":"sha256:057333cc920d7f764334fe9513910b35d86661ce298b2350954e53b98ecf49ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:V33G3YI43FULM4CHM23GWF3JIV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Role of fractal dimension in random walks on scale-free networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Shuyang Gao, Yihang Yang, Zhongzhi Zhang","submitted_at":"2011-10-15T06:07:49Z","abstract_excerpt":"Fractal dimension is central to understanding dynamical processes occurring on networks; however, the relation between fractal dimension and random walks on fractal scale-free networks has been rarely addressed, despite the fact that such networks are ubiquitous in real-life world. In this paper, we study the trapping problem on two families of networks. The first is deterministic, often called $(x,y)$-flowers; the other is random, which is a combination of $(1,3)$-flower and $(2,4)$-flower and thus called hybrid networks. The two network families display rich behavior as observed in various r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3388","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":"2026-05-18T04:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vfniWwg/dvvE219jzRbENj0HV/IJarAzORj4UbQpBRFg9IstKAYTNuHC5rpd8X7CZnXkJzHVYDgBDkJJUVyeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:24:44.752558Z"},"content_sha256":"1d7e15347de2658d92be3fb657490ecdded711ddc4461393dcb478f15f7c3035","schema_version":"1.0","event_id":"sha256:1d7e15347de2658d92be3fb657490ecdded711ddc4461393dcb478f15f7c3035"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V33G3YI43FULM4CHM23GWF3JIV/bundle.json","state_url":"https://pith.science/pith/V33G3YI43FULM4CHM23GWF3JIV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V33G3YI43FULM4CHM23GWF3JIV/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":"2026-06-02T14:24:44Z","links":{"resolver":"https://pith.science/pith/V33G3YI43FULM4CHM23GWF3JIV","bundle":"https://pith.science/pith/V33G3YI43FULM4CHM23GWF3JIV/bundle.json","state":"https://pith.science/pith/V33G3YI43FULM4CHM23GWF3JIV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V33G3YI43FULM4CHM23GWF3JIV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V33G3YI43FULM4CHM23GWF3JIV","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":"25597b146fe057e1f74ff87c1ff7ddffc486312684c81a28c083ffd1626f2abb","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-15T06:07:49Z","title_canon_sha256":"c5a25be6a04ba298d1e58458ae1ec31ca7dcb477ff937068916e40415816cf6c"},"schema_version":"1.0","source":{"id":"1110.3388","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3388","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3388v1","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3388","created_at":"2026-05-18T04:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"V33G3YI43FUL","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V33G3YI43FULM4CH","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V33G3YI4","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:1d7e15347de2658d92be3fb657490ecdded711ddc4461393dcb478f15f7c3035","target":"graph","created_at":"2026-05-18T04:06:54Z","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":"Fractal dimension is central to understanding dynamical processes occurring on networks; however, the relation between fractal dimension and random walks on fractal scale-free networks has been rarely addressed, despite the fact that such networks are ubiquitous in real-life world. In this paper, we study the trapping problem on two families of networks. The first is deterministic, often called $(x,y)$-flowers; the other is random, which is a combination of $(1,3)$-flower and $(2,4)$-flower and thus called hybrid networks. The two network families display rich behavior as observed in various r","authors_text":"Shuyang Gao, Yihang Yang, Zhongzhi Zhang","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-15T06:07:49Z","title":"Role of fractal dimension in random walks on scale-free networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3388","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":"sha256:057333cc920d7f764334fe9513910b35d86661ce298b2350954e53b98ecf49ae","target":"record","created_at":"2026-05-18T04:06:54Z","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":"25597b146fe057e1f74ff87c1ff7ddffc486312684c81a28c083ffd1626f2abb","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2011-10-15T06:07:49Z","title_canon_sha256":"c5a25be6a04ba298d1e58458ae1ec31ca7dcb477ff937068916e40415816cf6c"},"schema_version":"1.0","source":{"id":"1110.3388","kind":"arxiv","version":1}},"canonical_sha256":"aef66de11cd968b6704766b66b1769454f056e5282dc24884494e93a756383bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aef66de11cd968b6704766b66b1769454f056e5282dc24884494e93a756383bc","first_computed_at":"2026-05-18T04:06:54.737367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:54.737367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ungFF21XKnBqndF5ZnVOw16TkI2P+xF2JSeZHSKen2uiewqpak6Q+0UvHqMPLkc0C70wMaUqz5mJjKuf7N2cAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:54.737880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3388","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:057333cc920d7f764334fe9513910b35d86661ce298b2350954e53b98ecf49ae","sha256:1d7e15347de2658d92be3fb657490ecdded711ddc4461393dcb478f15f7c3035"],"state_sha256":"8c8738fd00bd7d8f60b625c1626a10ed1f690b6959aa0ce6256642f75882afa1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W24EUObFKCAyotAO/bYoqyjISR7tLjMvcts0PrL2RA0W/K5/DhA9JGNN/AIe68udD9h2fdXdstbNNsmI7p4aDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:24:44.754442Z","bundle_sha256":"c6fb28b705cb0e073700d5948c758954322ec5a4f823ff68915a70fea246a926"}}