{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:U4JKBJA2CJRFWAMYGYWCG66KTE","short_pith_number":"pith:U4JKBJA2","canonical_record":{"source":{"id":"2605.17982","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T07:36:46Z","cross_cats_sorted":[],"title_canon_sha256":"e8da1f5464ec05fd59fbcbdc881999cfde147c2092e1a86cff6624cd3a8c1e31","abstract_canon_sha256":"11f0d213370a88d47149259b406571eba004f2d666cf937a36ca14fc11b97436"},"schema_version":"1.0"},"canonical_sha256":"a712a0a41a12625b0198362c237bca990dc9af9bd6743c4fd94ee331d0e97258","source":{"kind":"arxiv","id":"2605.17982","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17982","created_at":"2026-05-20T00:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17982v1","created_at":"2026-05-20T00:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17982","created_at":"2026-05-20T00:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"U4JKBJA2CJRF","created_at":"2026-05-20T00:05:09Z"},{"alias_kind":"pith_short_16","alias_value":"U4JKBJA2CJRFWAMY","created_at":"2026-05-20T00:05:09Z"},{"alias_kind":"pith_short_8","alias_value":"U4JKBJA2","created_at":"2026-05-20T00:05:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:U4JKBJA2CJRFWAMYGYWCG66KTE","target":"record","payload":{"canonical_record":{"source":{"id":"2605.17982","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T07:36:46Z","cross_cats_sorted":[],"title_canon_sha256":"e8da1f5464ec05fd59fbcbdc881999cfde147c2092e1a86cff6624cd3a8c1e31","abstract_canon_sha256":"11f0d213370a88d47149259b406571eba004f2d666cf937a36ca14fc11b97436"},"schema_version":"1.0"},"canonical_sha256":"a712a0a41a12625b0198362c237bca990dc9af9bd6743c4fd94ee331d0e97258","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:05:09.440366Z","signature_b64":"z0d8Jtxa775HhUhyBj3KgXWVbAY4B2/5xSxOgGyE4kZhRZQ/8ZHLFPW04EeuZa+KUKD1+SSglC9UxqIXrEr4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a712a0a41a12625b0198362c237bca990dc9af9bd6743c4fd94ee331d0e97258","last_reissued_at":"2026-05-20T00:05:09.439507Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:05:09.439507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.17982","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":"2026-05-20T00:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZyxbHp0KrbS5LSzoCSQ/oCZjde8Z4d2cQRPpyn4XPD295wKuEDfMnTFeTRsMX8TigA9l0W/QcWQBfavkUW8HAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:16:14.583434Z"},"content_sha256":"179d3a5c1358d39c2302e2437655db88f17fba713edc0a183fb5a794b2553184","schema_version":"1.0","event_id":"sha256:179d3a5c1358d39c2302e2437655db88f17fba713edc0a183fb5a794b2553184"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:U4JKBJA2CJRFWAMYGYWCG66KTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Benders Decomposition Approach for the k-Defensive Domination Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bilge Varol, K\\\"ubra Tan{\\i}nm{\\i}\\c{s}, T{\\i}naz Ekim","submitted_at":"2026-05-18T07:36:46Z","abstract_excerpt":"The k-defensive domination problem is a powerful modeling tool for strategic decision-making in network security and disaster/emergency management, where multiple nodes may be simultaneously under attack. Despite its practical relevance, the problem has been poorly studied, largely due to its high computational difficulty. This study investigates the application of Benders decomposition to the k-defensive domination problem, aiming to improve computational efficiency over standard integer programming formulations. Several cut generation strategies, including a combinatorial approach and the si"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17982","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/2605.17982/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.562558Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"af96b12dd1a26f857ae91d3c70eb0f179e4638541f5ea96e83f1606acf09ba8a"},"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":"2026-05-20T00:05:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jxWSKO2yEIYx9n4DErdDhKO6QTA+kHiQ+2THn3vqrqSXAq11t8VLuhhDjc3atVTEEnz9qMMy3VYwqu6yiwk/AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:16:14.583821Z"},"content_sha256":"4631f02abc27d40d2f119f25e17562748b978c5e8ab0cb753c6b35f09f1d44c9","schema_version":"1.0","event_id":"sha256:4631f02abc27d40d2f119f25e17562748b978c5e8ab0cb753c6b35f09f1d44c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U4JKBJA2CJRFWAMYGYWCG66KTE/bundle.json","state_url":"https://pith.science/pith/U4JKBJA2CJRFWAMYGYWCG66KTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U4JKBJA2CJRFWAMYGYWCG66KTE/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":"2026-06-03T15:16:14Z","links":{"resolver":"https://pith.science/pith/U4JKBJA2CJRFWAMYGYWCG66KTE","bundle":"https://pith.science/pith/U4JKBJA2CJRFWAMYGYWCG66KTE/bundle.json","state":"https://pith.science/pith/U4JKBJA2CJRFWAMYGYWCG66KTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U4JKBJA2CJRFWAMYGYWCG66KTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:U4JKBJA2CJRFWAMYGYWCG66KTE","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":"11f0d213370a88d47149259b406571eba004f2d666cf937a36ca14fc11b97436","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T07:36:46Z","title_canon_sha256":"e8da1f5464ec05fd59fbcbdc881999cfde147c2092e1a86cff6624cd3a8c1e31"},"schema_version":"1.0","source":{"id":"2605.17982","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.17982","created_at":"2026-05-20T00:05:09Z"},{"alias_kind":"arxiv_version","alias_value":"2605.17982v1","created_at":"2026-05-20T00:05:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.17982","created_at":"2026-05-20T00:05:09Z"},{"alias_kind":"pith_short_12","alias_value":"U4JKBJA2CJRF","created_at":"2026-05-20T00:05:09Z"},{"alias_kind":"pith_short_16","alias_value":"U4JKBJA2CJRFWAMY","created_at":"2026-05-20T00:05:09Z"},{"alias_kind":"pith_short_8","alias_value":"U4JKBJA2","created_at":"2026-05-20T00:05:09Z"}],"graph_snapshots":[{"event_id":"sha256:4631f02abc27d40d2f119f25e17562748b978c5e8ab0cb753c6b35f09f1d44c9","target":"graph","created_at":"2026-05-20T00:05:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.562558Z","status":"skipped","version":"1.0.0"}],"endpoint":"/pith/2605.17982/integrity.json","findings":[],"snapshot_sha256":"af96b12dd1a26f857ae91d3c70eb0f179e4638541f5ea96e83f1606acf09ba8a","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The k-defensive domination problem is a powerful modeling tool for strategic decision-making in network security and disaster/emergency management, where multiple nodes may be simultaneously under attack. Despite its practical relevance, the problem has been poorly studied, largely due to its high computational difficulty. This study investigates the application of Benders decomposition to the k-defensive domination problem, aiming to improve computational efficiency over standard integer programming formulations. Several cut generation strategies, including a combinatorial approach and the si","authors_text":"Bilge Varol, K\\\"ubra Tan{\\i}nm{\\i}\\c{s}, T{\\i}naz Ekim","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T07:36:46Z","title":"A Benders Decomposition Approach for the k-Defensive Domination Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17982","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":"sha256:179d3a5c1358d39c2302e2437655db88f17fba713edc0a183fb5a794b2553184","target":"record","created_at":"2026-05-20T00:05:09Z","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":"11f0d213370a88d47149259b406571eba004f2d666cf937a36ca14fc11b97436","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-05-18T07:36:46Z","title_canon_sha256":"e8da1f5464ec05fd59fbcbdc881999cfde147c2092e1a86cff6624cd3a8c1e31"},"schema_version":"1.0","source":{"id":"2605.17982","kind":"arxiv","version":1}},"canonical_sha256":"a712a0a41a12625b0198362c237bca990dc9af9bd6743c4fd94ee331d0e97258","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a712a0a41a12625b0198362c237bca990dc9af9bd6743c4fd94ee331d0e97258","first_computed_at":"2026-05-20T00:05:09.439507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:09.439507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z0d8Jtxa775HhUhyBj3KgXWVbAY4B2/5xSxOgGyE4kZhRZQ/8ZHLFPW04EeuZa+KUKD1+SSglC9UxqIXrEr4Dw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:09.440366Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.17982","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:179d3a5c1358d39c2302e2437655db88f17fba713edc0a183fb5a794b2553184","sha256:4631f02abc27d40d2f119f25e17562748b978c5e8ab0cb753c6b35f09f1d44c9"],"state_sha256":"f0aea75af69da633e95c6cbd1b3097af2065afcd38c23192aa3c03d33a6ce8d1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zFkaILSNTSmvjosAYJGN3ZLvV35k0OIv+dnoMTpyhNT2PrPwjiQN31DoOCrKwcFOZDEQHrudhr5Fz8dHl3vHBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:16:14.586261Z","bundle_sha256":"92d9821dd1b825f7769a59eaa373512b9947a0e91f7282585c6cc480889f0c17"}}