{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ACAFODMEKQAM6M6JWHWO3NMWQO","short_pith_number":"pith:ACAFODME","canonical_record":{"source":{"id":"1112.6079","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T08:32:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"45ab5784abb0a1d8aeb5d17ade997fe55165326b9a978c472f2f7f07aa3dd1ed","abstract_canon_sha256":"0f8bfc240d4eeb898323dee9f787e975a516517df9ea92db77f9b061eae272d0"},"schema_version":"1.0"},"canonical_sha256":"0080570d845400cf33c9b1ecedb596839d52666a932bc2cc2cf72c831286447c","source":{"kind":"arxiv","id":"1112.6079","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6079","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6079v2","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6079","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"pith_short_12","alias_value":"ACAFODMEKQAM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ACAFODMEKQAM6M6J","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ACAFODME","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ACAFODMEKQAM6M6JWHWO3NMWQO","target":"record","payload":{"canonical_record":{"source":{"id":"1112.6079","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T08:32:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"45ab5784abb0a1d8aeb5d17ade997fe55165326b9a978c472f2f7f07aa3dd1ed","abstract_canon_sha256":"0f8bfc240d4eeb898323dee9f787e975a516517df9ea92db77f9b061eae272d0"},"schema_version":"1.0"},"canonical_sha256":"0080570d845400cf33c9b1ecedb596839d52666a932bc2cc2cf72c831286447c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:09.189026Z","signature_b64":"OuHEhfwthmoZ3FWVfZ5zHEU9HDO3441HmnBIRn51/Rawdn0c8LaQ3vNLyc+YudtO0iuxcbEUOsz6JWuBLEYyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0080570d845400cf33c9b1ecedb596839d52666a932bc2cc2cf72c831286447c","last_reissued_at":"2026-05-18T02:31:09.188370Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:09.188370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.6079","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":"2026-05-18T02:31:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k/gg9DleLjiwi+NOXQU8kSorz+NZjW3ytoIeTFczxcch81MTuWrMXdXvWmDyhmpFDzuP5Y5XrA9dZeLO8ZhODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:08:11.972150Z"},"content_sha256":"f8a5c296a1b93276cfa7a8e75ebd6ecefd98bdbc0716f7782e69c47f84abef0c","schema_version":"1.0","event_id":"sha256:f8a5c296a1b93276cfa7a8e75ebd6ecefd98bdbc0716f7782e69c47f84abef0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ACAFODMEKQAM6M6JWHWO3NMWQO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Determining the Solution Space of Vertex-Cover by Interactions and Backbones","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Binghui Guo, Renquan Zhang, Wei Wei, Zhiming Zheng","submitted_at":"2011-12-28T08:32:37Z","abstract_excerpt":"To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of Vertex-cover, a new structure named interaction between nodes is defined and discovered for random graph, which results in the emergence of the frustration and long-range correlation phenomenon. Based on the backbones and interactions with a node adding process, we propose an Interaction and Backbone Evolution Algorithm to achieve the reduced solution graph, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6079","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":"2026-05-18T02:31:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wt2QSaK8y8ureLWpLl4tzSZv0NH+Hqfi1NsKTf3cu7MKTKyXvfW1iXRQV0iXLBpu+0njdR9T6sOiBT6gO7p+DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T19:08:11.972693Z"},"content_sha256":"6cd0d769266680f1bf914f9b95e1ea09c3224e54a0168918fc4f7d34501a95e9","schema_version":"1.0","event_id":"sha256:6cd0d769266680f1bf914f9b95e1ea09c3224e54a0168918fc4f7d34501a95e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/bundle.json","state_url":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/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":"2026-05-26T19:08:11Z","links":{"resolver":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO","bundle":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/bundle.json","state":"https://pith.science/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ACAFODMEKQAM6M6JWHWO3NMWQO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ACAFODMEKQAM6M6JWHWO3NMWQO","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":"0f8bfc240d4eeb898323dee9f787e975a516517df9ea92db77f9b061eae272d0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T08:32:37Z","title_canon_sha256":"45ab5784abb0a1d8aeb5d17ade997fe55165326b9a978c472f2f7f07aa3dd1ed"},"schema_version":"1.0","source":{"id":"1112.6079","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6079","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6079v2","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6079","created_at":"2026-05-18T02:31:09Z"},{"alias_kind":"pith_short_12","alias_value":"ACAFODMEKQAM","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"ACAFODMEKQAM6M6J","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"ACAFODME","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:6cd0d769266680f1bf914f9b95e1ea09c3224e54a0168918fc4f7d34501a95e9","target":"graph","created_at":"2026-05-18T02:31:09Z","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":"To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of Vertex-cover, a new structure named interaction between nodes is defined and discovered for random graph, which results in the emergence of the frustration and long-range correlation phenomenon. Based on the backbones and interactions with a node adding process, we propose an Interaction and Backbone Evolution Algorithm to achieve the reduced solution graph, whi","authors_text":"Binghui Guo, Renquan Zhang, Wei Wei, Zhiming Zheng","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T08:32:37Z","title":"Determining the Solution Space of Vertex-Cover by Interactions and Backbones"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6079","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:f8a5c296a1b93276cfa7a8e75ebd6ecefd98bdbc0716f7782e69c47f84abef0c","target":"record","created_at":"2026-05-18T02:31:09Z","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":"0f8bfc240d4eeb898323dee9f787e975a516517df9ea92db77f9b061eae272d0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-12-28T08:32:37Z","title_canon_sha256":"45ab5784abb0a1d8aeb5d17ade997fe55165326b9a978c472f2f7f07aa3dd1ed"},"schema_version":"1.0","source":{"id":"1112.6079","kind":"arxiv","version":2}},"canonical_sha256":"0080570d845400cf33c9b1ecedb596839d52666a932bc2cc2cf72c831286447c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0080570d845400cf33c9b1ecedb596839d52666a932bc2cc2cf72c831286447c","first_computed_at":"2026-05-18T02:31:09.188370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:09.188370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OuHEhfwthmoZ3FWVfZ5zHEU9HDO3441HmnBIRn51/Rawdn0c8LaQ3vNLyc+YudtO0iuxcbEUOsz6JWuBLEYyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:09.189026Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.6079","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8a5c296a1b93276cfa7a8e75ebd6ecefd98bdbc0716f7782e69c47f84abef0c","sha256:6cd0d769266680f1bf914f9b95e1ea09c3224e54a0168918fc4f7d34501a95e9"],"state_sha256":"8e8a1445f1375cc19ecc91a4c4ababd86e77859b38d269d35a3c1014229f199c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QVnx66aGQDHkJWhxgWhPSJSJxhBVOGmrAbsb9T4NSs5hWXyJ+dvnnUNJYVt+kBPw4xXhVgbK5NBlC/bipBEvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T19:08:11.976207Z","bundle_sha256":"ee754c9c0909c65e1d98284544835af5cd7064697216f7e3f0eafd70ede7d9bb"}}