{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GOBMWEJ5TXDKYLTO6SCOIZNL2D","short_pith_number":"pith:GOBMWEJ5","canonical_record":{"source":{"id":"1605.03151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T03:36:28Z","cross_cats_sorted":[],"title_canon_sha256":"486a6dd72e96ff605bf478f7e90b5c74f6b7f304be394cf3b5e17c9c64e8b4a6","abstract_canon_sha256":"9a3ce8ee45e3e2d1243181a83e50ef9fb7e6031ff12205471f231e8f05c40104"},"schema_version":"1.0"},"canonical_sha256":"3382cb113d9dc6ac2e6ef484e465abd0f3e055bc51b72de9a89bf00b8fa59073","source":{"kind":"arxiv","id":"1605.03151","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03151","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03151v2","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03151","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"GOBMWEJ5TXDK","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GOBMWEJ5TXDKYLTO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GOBMWEJ5","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GOBMWEJ5TXDKYLTO6SCOIZNL2D","target":"record","payload":{"canonical_record":{"source":{"id":"1605.03151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T03:36:28Z","cross_cats_sorted":[],"title_canon_sha256":"486a6dd72e96ff605bf478f7e90b5c74f6b7f304be394cf3b5e17c9c64e8b4a6","abstract_canon_sha256":"9a3ce8ee45e3e2d1243181a83e50ef9fb7e6031ff12205471f231e8f05c40104"},"schema_version":"1.0"},"canonical_sha256":"3382cb113d9dc6ac2e6ef484e465abd0f3e055bc51b72de9a89bf00b8fa59073","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:52.104912Z","signature_b64":"PHtW/Mnniguz92CJcVXpEuBCh1545HVngse7yOqKNLZ6Sd2qXCw7A1V7vS7zKBt+XSFzrX8xj9t1uzOVzV3sCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3382cb113d9dc6ac2e6ef484e465abd0f3e055bc51b72de9a89bf00b8fa59073","last_reissued_at":"2026-05-18T01:14:52.104248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:52.104248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.03151","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":"2026-05-18T01:14:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tc20z7PVndEJw/BxIwOl6FWrdrnfEbfyZF20/mDtQm9oBoe2cQjUpDPN1teGsRR7GRsyXlau4YQqRyIBRY6rCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:42:54.562359Z"},"content_sha256":"c4a7f838615f760d880f9ad5a3fd7fc9810232f0e6ef5aa48250a674b3a61bd5","schema_version":"1.0","event_id":"sha256:c4a7f838615f760d880f9ad5a3fd7fc9810232f0e6ef5aa48250a674b3a61bd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GOBMWEJ5TXDKYLTO6SCOIZNL2D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Split Domination, Independence, and Irredundance in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fiona Knoll, Renu Laskar, Stephen Hedetniemi","submitted_at":"2016-05-06T03:36:28Z","abstract_excerpt":"In 1978, Kulli and Janakiram \\citep{KulliJanakiramSplit} defined the split dominating set: a dominating set $S$ of vertices in a graph $G = (V, E)$ is called {\\em split dominating} if the induced subgraph $\\langle V \\setminus S\\rangle$ is either disconnected or a $K_1$. In this paper we introduce the properties split independence and split irredundance. A set $S$ of vertices in a graph $G =(V,E)$ is called a {\\em split independent set} if $S$ is independent and the induced subgraph $\\langle V \\setminus S \\rangle$ is either disconnected or a $K_1$. A set $S$ of vertices in a graph $G = (V,E)$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03151","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":"2026-05-18T01:14:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WICiZJv3ByBe/SepJVu8e50wpYtekEKg1Tjv7tBuIYk4zE5g6HoDGFUa5VkpJ/dhX9QXNKJiFJr0IqOgScfLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:42:54.562763Z"},"content_sha256":"e697d535afb7385b4648ffca47461f86471a00b521529c4a8451e67b2caa4c0d","schema_version":"1.0","event_id":"sha256:e697d535afb7385b4648ffca47461f86471a00b521529c4a8451e67b2caa4c0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GOBMWEJ5TXDKYLTO6SCOIZNL2D/bundle.json","state_url":"https://pith.science/pith/GOBMWEJ5TXDKYLTO6SCOIZNL2D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GOBMWEJ5TXDKYLTO6SCOIZNL2D/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":"2026-06-02T04:42:54Z","links":{"resolver":"https://pith.science/pith/GOBMWEJ5TXDKYLTO6SCOIZNL2D","bundle":"https://pith.science/pith/GOBMWEJ5TXDKYLTO6SCOIZNL2D/bundle.json","state":"https://pith.science/pith/GOBMWEJ5TXDKYLTO6SCOIZNL2D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GOBMWEJ5TXDKYLTO6SCOIZNL2D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GOBMWEJ5TXDKYLTO6SCOIZNL2D","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":"9a3ce8ee45e3e2d1243181a83e50ef9fb7e6031ff12205471f231e8f05c40104","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T03:36:28Z","title_canon_sha256":"486a6dd72e96ff605bf478f7e90b5c74f6b7f304be394cf3b5e17c9c64e8b4a6"},"schema_version":"1.0","source":{"id":"1605.03151","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.03151","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1605.03151v2","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03151","created_at":"2026-05-18T01:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"GOBMWEJ5TXDK","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GOBMWEJ5TXDKYLTO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GOBMWEJ5","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:e697d535afb7385b4648ffca47461f86471a00b521529c4a8451e67b2caa4c0d","target":"graph","created_at":"2026-05-18T01:14:52Z","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":"In 1978, Kulli and Janakiram \\citep{KulliJanakiramSplit} defined the split dominating set: a dominating set $S$ of vertices in a graph $G = (V, E)$ is called {\\em split dominating} if the induced subgraph $\\langle V \\setminus S\\rangle$ is either disconnected or a $K_1$. In this paper we introduce the properties split independence and split irredundance. A set $S$ of vertices in a graph $G =(V,E)$ is called a {\\em split independent set} if $S$ is independent and the induced subgraph $\\langle V \\setminus S \\rangle$ is either disconnected or a $K_1$. A set $S$ of vertices in a graph $G = (V,E)$ i","authors_text":"Fiona Knoll, Renu Laskar, Stephen Hedetniemi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T03:36:28Z","title":"Split Domination, Independence, and Irredundance in Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03151","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:c4a7f838615f760d880f9ad5a3fd7fc9810232f0e6ef5aa48250a674b3a61bd5","target":"record","created_at":"2026-05-18T01:14:52Z","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":"9a3ce8ee45e3e2d1243181a83e50ef9fb7e6031ff12205471f231e8f05c40104","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-06T03:36:28Z","title_canon_sha256":"486a6dd72e96ff605bf478f7e90b5c74f6b7f304be394cf3b5e17c9c64e8b4a6"},"schema_version":"1.0","source":{"id":"1605.03151","kind":"arxiv","version":2}},"canonical_sha256":"3382cb113d9dc6ac2e6ef484e465abd0f3e055bc51b72de9a89bf00b8fa59073","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3382cb113d9dc6ac2e6ef484e465abd0f3e055bc51b72de9a89bf00b8fa59073","first_computed_at":"2026-05-18T01:14:52.104248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:52.104248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PHtW/Mnniguz92CJcVXpEuBCh1545HVngse7yOqKNLZ6Sd2qXCw7A1V7vS7zKBt+XSFzrX8xj9t1uzOVzV3sCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:52.104912Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.03151","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4a7f838615f760d880f9ad5a3fd7fc9810232f0e6ef5aa48250a674b3a61bd5","sha256:e697d535afb7385b4648ffca47461f86471a00b521529c4a8451e67b2caa4c0d"],"state_sha256":"325ea3bd987ed399c3bc7b0bd865f160d2d3de5a8ed151a53c8bf8249d6d0139"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWtjuKc4dNEle2AxW9aET2fV7KT/9tnhWTcCkaIzWvKe0SLIML5PeuiOmB5T4OW05TlRcN+iRJgW7j+0hWnaCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:42:54.565215Z","bundle_sha256":"6462976073445fe7512e2fa48045c6bc4258810068cf7538d893ac6cefd8cdde"}}