{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:TWYU6CILPKBCR64HLOAHBPVUXU","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":"fa1703fb8539ff7f3a8d291bd241e08a134a3e19a406cac27fb3d4a50804246d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T13:06:08Z","title_canon_sha256":"afaba75b9fee28b5e17f22d5cf9c59fcf7bee85297750ba1e382161d43a95517"},"schema_version":"1.0","source":{"id":"1503.04048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04048","created_at":"2026-05-18T02:23:57Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04048v1","created_at":"2026-05-18T02:23:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04048","created_at":"2026-05-18T02:23:57Z"},{"alias_kind":"pith_short_12","alias_value":"TWYU6CILPKBC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"TWYU6CILPKBCR64H","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"TWYU6CIL","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:c577a75c2b515018855f42f5ac0b77d211ba5d9769e93d73cc0f133735faba03","target":"graph","created_at":"2026-05-18T02:23:57Z","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":"Given a graph G = (V,E), a subset S of V is dominating if for every v in V - S there exists u in S such that uv is in E. A dominating subset S of V is secure if for every v in V - S there exists u in S such that (S - {u}) U {v} is dominating. In this work we extend the concept of secure dominating set to digraphs in four different ways, all of them with interesting applications, and prove some results regarding each of them.","authors_text":"Karam Ebadi, Martin Manrique, Morteza Ebrahimi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T13:06:08Z","title":"Secure Domination in Digraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04048","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":"sha256:58f2d5599d082605c269d2e18dbf6abdfb85301ff30b7ebd45b72166698fcf51","target":"record","created_at":"2026-05-18T02:23:57Z","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":"fa1703fb8539ff7f3a8d291bd241e08a134a3e19a406cac27fb3d4a50804246d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-13T13:06:08Z","title_canon_sha256":"afaba75b9fee28b5e17f22d5cf9c59fcf7bee85297750ba1e382161d43a95517"},"schema_version":"1.0","source":{"id":"1503.04048","kind":"arxiv","version":1}},"canonical_sha256":"9db14f090b7a8228fb875b8070beb4bd0be9139d4871284c35fa6d0ca2c089dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9db14f090b7a8228fb875b8070beb4bd0be9139d4871284c35fa6d0ca2c089dc","first_computed_at":"2026-05-18T02:23:57.250686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:57.250686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bNzlfOdeCKINUYJ97YP5bQ3zR65LEgko2EQuNBdrve+yuev05c6YZRxvnxhu47XE/PytUOB5BI9mESVPnAD4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:57.251393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58f2d5599d082605c269d2e18dbf6abdfb85301ff30b7ebd45b72166698fcf51","sha256:c577a75c2b515018855f42f5ac0b77d211ba5d9769e93d73cc0f133735faba03"],"state_sha256":"9a722934ce5b679010c4c7ccad837a7c45837e73111839ddb07c016ffbb9b182"}