{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FNPLM2CKHTLZ2WBDVCTKXIAVSA","short_pith_number":"pith:FNPLM2CK","canonical_record":{"source":{"id":"1504.06900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-27T01:15:45Z","cross_cats_sorted":[],"title_canon_sha256":"c4a6351abb7356e9a24f8bec9074fb40bca22727d274d926cef3220dd7302b5e","abstract_canon_sha256":"607783d993e3aaa737237ab3ebedbab3b58e7ada195230cf6984519f9d7edb87"},"schema_version":"1.0"},"canonical_sha256":"2b5eb6684a3cd79d5823a8a6aba01590211f108ebe6716a39d185542461c25c7","source":{"kind":"arxiv","id":"1504.06900","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06900","created_at":"2026-05-18T01:32:29Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06900v2","created_at":"2026-05-18T01:32:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06900","created_at":"2026-05-18T01:32:29Z"},{"alias_kind":"pith_short_12","alias_value":"FNPLM2CKHTLZ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FNPLM2CKHTLZ2WBD","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FNPLM2CK","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FNPLM2CKHTLZ2WBDVCTKXIAVSA","target":"record","payload":{"canonical_record":{"source":{"id":"1504.06900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-27T01:15:45Z","cross_cats_sorted":[],"title_canon_sha256":"c4a6351abb7356e9a24f8bec9074fb40bca22727d274d926cef3220dd7302b5e","abstract_canon_sha256":"607783d993e3aaa737237ab3ebedbab3b58e7ada195230cf6984519f9d7edb87"},"schema_version":"1.0"},"canonical_sha256":"2b5eb6684a3cd79d5823a8a6aba01590211f108ebe6716a39d185542461c25c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:29.660516Z","signature_b64":"F9Y4DuFb7FkjOUJPj8iSAbUCSjZO9eNd+45ec+Yp9ctn4bwwGKjFvR9iTKauOKLhOWuAvHdkgPnsNkS23yIBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b5eb6684a3cd79d5823a8a6aba01590211f108ebe6716a39d185542461c25c7","last_reissued_at":"2026-05-18T01:32:29.659981Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:29.659981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.06900","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:32:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qbUxfoZ607rmcfhc8U/737xvbmgLLdAibCx642u5bvabjMzzUhHKf0HLYlhG17lbpwtSH7K3ZcxGm5EUjQJSBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:52:03.089543Z"},"content_sha256":"fb060ca021178dba2d11af363fa2ed4f5761cc0f9b7689b4b4df2f10fa73803e","schema_version":"1.0","event_id":"sha256:fb060ca021178dba2d11af363fa2ed4f5761cc0f9b7689b4b4df2f10fa73803e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FNPLM2CKHTLZ2WBDVCTKXIAVSA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The influence of the broadness of the degree distribution on network's robustness: comparing localized attack and random attack","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.soc-ph","authors_text":"H. Eugene Stanley, Shlomo Havlin, Shuai Shao, Xin Yuan","submitted_at":"2015-04-27T01:15:45Z","abstract_excerpt":"The stability of networks is greatly influenced by their degree distributions and in particular by their broadness. Networks with broader degree distributions are usually more robust to random failures but less robust to localized attacks. To better understand the effect of the broadness of the degree distribution we study here two models where the broadness is controlled and compare their robustness against localized attacks (LA) and random attacks (RA). We study analytically and by numerical simulations the cases where the degrees in the networks follow a Bi-Poisson distribution $P(k)=\\alpha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06900","kind":"arxiv","version":2},"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":"2026-05-18T01:32:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b0FNFjP0RSNiQyCS9O7rahjQpKuaYqOR8E5NIYO3BSuLY8iuniO6DQQeJnGHXlxQB9aPSwbpa1yaAaiFlraGAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:52:03.089892Z"},"content_sha256":"bc8c6e5ebc821862a8f55dcc64083bcc4344c3a559d6225ee1286b48f3c514d6","schema_version":"1.0","event_id":"sha256:bc8c6e5ebc821862a8f55dcc64083bcc4344c3a559d6225ee1286b48f3c514d6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FNPLM2CKHTLZ2WBDVCTKXIAVSA/bundle.json","state_url":"https://pith.science/pith/FNPLM2CKHTLZ2WBDVCTKXIAVSA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FNPLM2CKHTLZ2WBDVCTKXIAVSA/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":"2026-05-28T03:52:03Z","links":{"resolver":"https://pith.science/pith/FNPLM2CKHTLZ2WBDVCTKXIAVSA","bundle":"https://pith.science/pith/FNPLM2CKHTLZ2WBDVCTKXIAVSA/bundle.json","state":"https://pith.science/pith/FNPLM2CKHTLZ2WBDVCTKXIAVSA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FNPLM2CKHTLZ2WBDVCTKXIAVSA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FNPLM2CKHTLZ2WBDVCTKXIAVSA","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":"607783d993e3aaa737237ab3ebedbab3b58e7ada195230cf6984519f9d7edb87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-27T01:15:45Z","title_canon_sha256":"c4a6351abb7356e9a24f8bec9074fb40bca22727d274d926cef3220dd7302b5e"},"schema_version":"1.0","source":{"id":"1504.06900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.06900","created_at":"2026-05-18T01:32:29Z"},{"alias_kind":"arxiv_version","alias_value":"1504.06900v2","created_at":"2026-05-18T01:32:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.06900","created_at":"2026-05-18T01:32:29Z"},{"alias_kind":"pith_short_12","alias_value":"FNPLM2CKHTLZ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FNPLM2CKHTLZ2WBD","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FNPLM2CK","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:bc8c6e5ebc821862a8f55dcc64083bcc4344c3a559d6225ee1286b48f3c514d6","target":"graph","created_at":"2026-05-18T01:32:29Z","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 stability of networks is greatly influenced by their degree distributions and in particular by their broadness. Networks with broader degree distributions are usually more robust to random failures but less robust to localized attacks. To better understand the effect of the broadness of the degree distribution we study here two models where the broadness is controlled and compare their robustness against localized attacks (LA) and random attacks (RA). We study analytically and by numerical simulations the cases where the degrees in the networks follow a Bi-Poisson distribution $P(k)=\\alpha","authors_text":"H. Eugene Stanley, Shlomo Havlin, Shuai Shao, Xin Yuan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-27T01:15:45Z","title":"The influence of the broadness of the degree distribution on network's robustness: comparing localized attack and random attack"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06900","kind":"arxiv","version":2},"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:fb060ca021178dba2d11af363fa2ed4f5761cc0f9b7689b4b4df2f10fa73803e","target":"record","created_at":"2026-05-18T01:32:29Z","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":"607783d993e3aaa737237ab3ebedbab3b58e7ada195230cf6984519f9d7edb87","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.soc-ph","submitted_at":"2015-04-27T01:15:45Z","title_canon_sha256":"c4a6351abb7356e9a24f8bec9074fb40bca22727d274d926cef3220dd7302b5e"},"schema_version":"1.0","source":{"id":"1504.06900","kind":"arxiv","version":2}},"canonical_sha256":"2b5eb6684a3cd79d5823a8a6aba01590211f108ebe6716a39d185542461c25c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b5eb6684a3cd79d5823a8a6aba01590211f108ebe6716a39d185542461c25c7","first_computed_at":"2026-05-18T01:32:29.659981Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:32:29.659981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F9Y4DuFb7FkjOUJPj8iSAbUCSjZO9eNd+45ec+Yp9ctn4bwwGKjFvR9iTKauOKLhOWuAvHdkgPnsNkS23yIBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:32:29.660516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.06900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb060ca021178dba2d11af363fa2ed4f5761cc0f9b7689b4b4df2f10fa73803e","sha256:bc8c6e5ebc821862a8f55dcc64083bcc4344c3a559d6225ee1286b48f3c514d6"],"state_sha256":"d496ff2b7bacfcd48098867ee3c6f3a160a51243671dfffd9e5f83f4fec12cd1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ci5vEpygHCyD4SQzOtcpipFhD0a3cA3SgRhsplx1W+DJ7dUdugI/sQcK2NtBU/6LP5Fia/wht2K6ueiz9iseBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:52:03.092455Z","bundle_sha256":"d4c0fdb397192ed711dd88dcb69a63cafc9fb86bf069ea1f8b9b77d4710058c0"}}