{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:LD5UHAHXIHZCP3R2WNCRDKUIRA","short_pith_number":"pith:LD5UHAHX","canonical_record":{"source":{"id":"2107.13962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2021-07-29T13:51:17Z","cross_cats_sorted":[],"title_canon_sha256":"78842fb742dc537a993cce4316dadf0f10b39f712c8941f0a02bf6fe19f1cc50","abstract_canon_sha256":"90094f198bb515fb430adb5bb0786cfd82f97110be0f44c34bc7f1a679d5bd2e"},"schema_version":"1.0"},"canonical_sha256":"58fb4380f741f227ee3ab34511aa888822b9cfde07cd7b3baa0799c80194a503","source":{"kind":"arxiv","id":"2107.13962","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.13962","created_at":"2026-07-05T03:01:42Z"},{"alias_kind":"arxiv_version","alias_value":"2107.13962v1","created_at":"2026-07-05T03:01:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.13962","created_at":"2026-07-05T03:01:42Z"},{"alias_kind":"pith_short_12","alias_value":"LD5UHAHXIHZC","created_at":"2026-07-05T03:01:42Z"},{"alias_kind":"pith_short_16","alias_value":"LD5UHAHXIHZCP3R2","created_at":"2026-07-05T03:01:42Z"},{"alias_kind":"pith_short_8","alias_value":"LD5UHAHX","created_at":"2026-07-05T03:01:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:LD5UHAHXIHZCP3R2WNCRDKUIRA","target":"record","payload":{"canonical_record":{"source":{"id":"2107.13962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2021-07-29T13:51:17Z","cross_cats_sorted":[],"title_canon_sha256":"78842fb742dc537a993cce4316dadf0f10b39f712c8941f0a02bf6fe19f1cc50","abstract_canon_sha256":"90094f198bb515fb430adb5bb0786cfd82f97110be0f44c34bc7f1a679d5bd2e"},"schema_version":"1.0"},"canonical_sha256":"58fb4380f741f227ee3ab34511aa888822b9cfde07cd7b3baa0799c80194a503","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:01:42.346360Z","signature_b64":"orxTdhldTAdayRgAj77jCG6yKcUO2rHPN+63F68NnQGqniVSBChwl85WZD+ST1oPzXFXuNmWdTTvnxae7SivCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58fb4380f741f227ee3ab34511aa888822b9cfde07cd7b3baa0799c80194a503","last_reissued_at":"2026-07-05T03:01:42.345885Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:01:42.345885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2107.13962","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":"2026-07-05T03:01:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rnt1Yxdb/re1l3ssMMaRJ2QxNeyuZK9QyCfKtoBgmRe5jQyxsE8qhgbiFh9Xe3/UHFycq1kg+9y7mhDmsUnwCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-24T21:01:08.108002Z"},"content_sha256":"5c66ba039fbd25b746e8cb285c0ac3e7869c59fd94f7d7efbf1b8c01de4ea806","schema_version":"1.0","event_id":"sha256:5c66ba039fbd25b746e8cb285c0ac3e7869c59fd94f7d7efbf1b8c01de4ea806"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:LD5UHAHXIHZCP3R2WNCRDKUIRA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Robustness of Graph k-shell Structure under Adversarial Attacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SI","authors_text":"B. Zhou, J. H. Wang, Q. Xuan, S. Q. Yu, Y. C. Mao, Y. Q. Lv","submitted_at":"2021-07-29T13:51:17Z","abstract_excerpt":"The k-shell decomposition plays an important role in unveiling the structural properties of a network, i.e., it is widely adopted to find the densest part of a network across a broad range of scientific fields, including Internet, biological networks, social networks, etc. However, there arises concern about the robustness of the k-shell structure when networks suffer from adversarial attacks. Here, we introduce and formalize the problem of the k-shell attack and develop an efficient strategy to attack the k-shell structure by rewiring a small number of links. To the best of our knowledge, it "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.13962","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2107.13962/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:01:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLIe37KnYiOOj0zvW7S/aKj5q4YzBnkGhpIIWDNyB7mXH1ZLYtiYzY/t5wkmPMkz+MXi1RLng8PCOZPC9aaPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-24T21:01:08.108389Z"},"content_sha256":"3a51a622eb5075c56e370826de095dcd8ac43daf3bc23ee077ded582ef1ec01f","schema_version":"1.0","event_id":"sha256:3a51a622eb5075c56e370826de095dcd8ac43daf3bc23ee077ded582ef1ec01f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LD5UHAHXIHZCP3R2WNCRDKUIRA/bundle.json","state_url":"https://pith.science/pith/LD5UHAHXIHZCP3R2WNCRDKUIRA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LD5UHAHXIHZCP3R2WNCRDKUIRA/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":"2026-07-24T21:01:08Z","links":{"resolver":"https://pith.science/pith/LD5UHAHXIHZCP3R2WNCRDKUIRA","bundle":"https://pith.science/pith/LD5UHAHXIHZCP3R2WNCRDKUIRA/bundle.json","state":"https://pith.science/pith/LD5UHAHXIHZCP3R2WNCRDKUIRA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LD5UHAHXIHZCP3R2WNCRDKUIRA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LD5UHAHXIHZCP3R2WNCRDKUIRA","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":"90094f198bb515fb430adb5bb0786cfd82f97110be0f44c34bc7f1a679d5bd2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2021-07-29T13:51:17Z","title_canon_sha256":"78842fb742dc537a993cce4316dadf0f10b39f712c8941f0a02bf6fe19f1cc50"},"schema_version":"1.0","source":{"id":"2107.13962","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2107.13962","created_at":"2026-07-05T03:01:42Z"},{"alias_kind":"arxiv_version","alias_value":"2107.13962v1","created_at":"2026-07-05T03:01:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2107.13962","created_at":"2026-07-05T03:01:42Z"},{"alias_kind":"pith_short_12","alias_value":"LD5UHAHXIHZC","created_at":"2026-07-05T03:01:42Z"},{"alias_kind":"pith_short_16","alias_value":"LD5UHAHXIHZCP3R2","created_at":"2026-07-05T03:01:42Z"},{"alias_kind":"pith_short_8","alias_value":"LD5UHAHX","created_at":"2026-07-05T03:01:42Z"}],"graph_snapshots":[{"event_id":"sha256:3a51a622eb5075c56e370826de095dcd8ac43daf3bc23ee077ded582ef1ec01f","target":"graph","created_at":"2026-07-05T03:01:42Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2107.13962/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The k-shell decomposition plays an important role in unveiling the structural properties of a network, i.e., it is widely adopted to find the densest part of a network across a broad range of scientific fields, including Internet, biological networks, social networks, etc. However, there arises concern about the robustness of the k-shell structure when networks suffer from adversarial attacks. Here, we introduce and formalize the problem of the k-shell attack and develop an efficient strategy to attack the k-shell structure by rewiring a small number of links. To the best of our knowledge, it ","authors_text":"B. Zhou, J. H. Wang, Q. Xuan, S. Q. Yu, Y. C. Mao, Y. Q. Lv","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2021-07-29T13:51:17Z","title":"The Robustness of Graph k-shell Structure under Adversarial Attacks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.13962","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":"sha256:5c66ba039fbd25b746e8cb285c0ac3e7869c59fd94f7d7efbf1b8c01de4ea806","target":"record","created_at":"2026-07-05T03:01:42Z","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":"90094f198bb515fb430adb5bb0786cfd82f97110be0f44c34bc7f1a679d5bd2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SI","submitted_at":"2021-07-29T13:51:17Z","title_canon_sha256":"78842fb742dc537a993cce4316dadf0f10b39f712c8941f0a02bf6fe19f1cc50"},"schema_version":"1.0","source":{"id":"2107.13962","kind":"arxiv","version":1}},"canonical_sha256":"58fb4380f741f227ee3ab34511aa888822b9cfde07cd7b3baa0799c80194a503","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58fb4380f741f227ee3ab34511aa888822b9cfde07cd7b3baa0799c80194a503","first_computed_at":"2026-07-05T03:01:42.345885Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:01:42.345885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"orxTdhldTAdayRgAj77jCG6yKcUO2rHPN+63F68NnQGqniVSBChwl85WZD+ST1oPzXFXuNmWdTTvnxae7SivCg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:01:42.346360Z","signed_message":"canonical_sha256_bytes"},"source_id":"2107.13962","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c66ba039fbd25b746e8cb285c0ac3e7869c59fd94f7d7efbf1b8c01de4ea806","sha256:3a51a622eb5075c56e370826de095dcd8ac43daf3bc23ee077ded582ef1ec01f"],"state_sha256":"a387a94c147e27708eae0222ea3aba17e626769ea6bb8767a0d4c7f354b36092"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cBHqXXrdEBKVoEbwIfoGfH5oKGtdKtiPBHdLdyZwSBfnBlD/tf901ksmZDWzGsdvyUc1tjy+hvqsvEFSeld5Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-24T21:01:08.111051Z","bundle_sha256":"22d73d2e6cb612ad0378fe5ae98c41f839815d707884bf72669d5ef3ff9dcf48"}}