{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:P4RRVFDFSV5OG6RPWT4DEBSFLJ","short_pith_number":"pith:P4RRVFDF","canonical_record":{"source":{"id":"1904.00964","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-01T16:58:46Z","cross_cats_sorted":[],"title_canon_sha256":"86f516e21baeef3a4692a679af7b1f4e437e85b7e2d8fa862d675bff98eb7e66","abstract_canon_sha256":"94012de661f101cbc7ca3c850f0517f30505868cdc565d47a69ef2213b429eab"},"schema_version":"1.0"},"canonical_sha256":"7f231a9465957ae37a2fb4f83206455a7d02dd7230692f11545b956e581860dc","source":{"kind":"arxiv","id":"1904.00964","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00964","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00964v1","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00964","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"pith_short_12","alias_value":"P4RRVFDFSV5O","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"P4RRVFDFSV5OG6RP","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"P4RRVFDF","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:P4RRVFDFSV5OG6RPWT4DEBSFLJ","target":"record","payload":{"canonical_record":{"source":{"id":"1904.00964","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-01T16:58:46Z","cross_cats_sorted":[],"title_canon_sha256":"86f516e21baeef3a4692a679af7b1f4e437e85b7e2d8fa862d675bff98eb7e66","abstract_canon_sha256":"94012de661f101cbc7ca3c850f0517f30505868cdc565d47a69ef2213b429eab"},"schema_version":"1.0"},"canonical_sha256":"7f231a9465957ae37a2fb4f83206455a7d02dd7230692f11545b956e581860dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:44.741552Z","signature_b64":"36hIDy1uK/uM8CWx4J5hf3acQs9wm6cSwILA670PtRLHVABoYT4Lpv3US7cenFim866OhSQEJE1IQrN7bJYfCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f231a9465957ae37a2fb4f83206455a7d02dd7230692f11545b956e581860dc","last_reissued_at":"2026-05-17T23:49:44.741028Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:44.741028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.00964","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":"2026-05-17T23:49:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MEHEjUwPIjlHAViJBic0XMXyIQaLMGyaU0Nb3j+Hu/PXSaOHG+k+h0vnhyH+32ePuWzyt/c2mOo4hg/3DAhrBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:59:17.337119Z"},"content_sha256":"5e3941402983dd1feffa6913053481492a64c570cbfdf22bd9269fb8f316ecf7","schema_version":"1.0","event_id":"sha256:5e3941402983dd1feffa6913053481492a64c570cbfdf22bd9269fb8f316ecf7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:P4RRVFDFSV5OG6RPWT4DEBSFLJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity and Algorithms for Semipaired Domination in Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Arti Pandey, Michael A. Henning, Vikash Tripathi","submitted_at":"2019-04-01T16:58:46Z","abstract_excerpt":"For a graph $G=(V,E)$ with no isolated vertices, a set $D\\subseteq V$ is called a semipaired dominating set of G if $(i)$ $D$ is a dominating set of $G$, and $(ii)$ $D$ can be partitioned into two element subsets such that the vertices in each two element set are at distance at most two. The minimum cardinality of a semipaired dominating set of $G$ is called the semipaired domination number of $G$, and is denoted by $\\gamma_{pr2}(G)$. The \\textsc{Minimum Semipaired Domination} problem is to find a semipaired dominating set of $G$ of cardinality $\\gamma_{pr2}(G)$. In this paper, we initiate the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00964","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":""},"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":"2026-05-17T23:49:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SsjoDTulzoFpLQJCLpcKJvZ0cqyJ6ZpsSUWCoXu9X+L3Yew4rrbR1WGDa0Nu2Gd97HYqFnaxoByRxM5l/AbaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T03:59:17.337821Z"},"content_sha256":"3f40d12e6eed9652cff584cbec8cd3b5516168cbcd42ab7e7f0215e3640085ac","schema_version":"1.0","event_id":"sha256:3f40d12e6eed9652cff584cbec8cd3b5516168cbcd42ab7e7f0215e3640085ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P4RRVFDFSV5OG6RPWT4DEBSFLJ/bundle.json","state_url":"https://pith.science/pith/P4RRVFDFSV5OG6RPWT4DEBSFLJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P4RRVFDFSV5OG6RPWT4DEBSFLJ/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":"2026-06-11T03:59:17Z","links":{"resolver":"https://pith.science/pith/P4RRVFDFSV5OG6RPWT4DEBSFLJ","bundle":"https://pith.science/pith/P4RRVFDFSV5OG6RPWT4DEBSFLJ/bundle.json","state":"https://pith.science/pith/P4RRVFDFSV5OG6RPWT4DEBSFLJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P4RRVFDFSV5OG6RPWT4DEBSFLJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:P4RRVFDFSV5OG6RPWT4DEBSFLJ","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":"94012de661f101cbc7ca3c850f0517f30505868cdc565d47a69ef2213b429eab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-01T16:58:46Z","title_canon_sha256":"86f516e21baeef3a4692a679af7b1f4e437e85b7e2d8fa862d675bff98eb7e66"},"schema_version":"1.0","source":{"id":"1904.00964","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.00964","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"arxiv_version","alias_value":"1904.00964v1","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.00964","created_at":"2026-05-17T23:49:44Z"},{"alias_kind":"pith_short_12","alias_value":"P4RRVFDFSV5O","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"P4RRVFDFSV5OG6RP","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"P4RRVFDF","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:3f40d12e6eed9652cff584cbec8cd3b5516168cbcd42ab7e7f0215e3640085ac","target":"graph","created_at":"2026-05-17T23:49:44Z","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":"For a graph $G=(V,E)$ with no isolated vertices, a set $D\\subseteq V$ is called a semipaired dominating set of G if $(i)$ $D$ is a dominating set of $G$, and $(ii)$ $D$ can be partitioned into two element subsets such that the vertices in each two element set are at distance at most two. The minimum cardinality of a semipaired dominating set of $G$ is called the semipaired domination number of $G$, and is denoted by $\\gamma_{pr2}(G)$. The \\textsc{Minimum Semipaired Domination} problem is to find a semipaired dominating set of $G$ of cardinality $\\gamma_{pr2}(G)$. In this paper, we initiate the","authors_text":"Arti Pandey, Michael A. Henning, Vikash Tripathi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-01T16:58:46Z","title":"Complexity and Algorithms for Semipaired Domination in Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00964","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":"sha256:5e3941402983dd1feffa6913053481492a64c570cbfdf22bd9269fb8f316ecf7","target":"record","created_at":"2026-05-17T23:49:44Z","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":"94012de661f101cbc7ca3c850f0517f30505868cdc565d47a69ef2213b429eab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2019-04-01T16:58:46Z","title_canon_sha256":"86f516e21baeef3a4692a679af7b1f4e437e85b7e2d8fa862d675bff98eb7e66"},"schema_version":"1.0","source":{"id":"1904.00964","kind":"arxiv","version":1}},"canonical_sha256":"7f231a9465957ae37a2fb4f83206455a7d02dd7230692f11545b956e581860dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f231a9465957ae37a2fb4f83206455a7d02dd7230692f11545b956e581860dc","first_computed_at":"2026-05-17T23:49:44.741028Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:44.741028Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"36hIDy1uK/uM8CWx4J5hf3acQs9wm6cSwILA670PtRLHVABoYT4Lpv3US7cenFim866OhSQEJE1IQrN7bJYfCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:44.741552Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.00964","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e3941402983dd1feffa6913053481492a64c570cbfdf22bd9269fb8f316ecf7","sha256:3f40d12e6eed9652cff584cbec8cd3b5516168cbcd42ab7e7f0215e3640085ac"],"state_sha256":"c5465f5ddf8b46baefd6dce4d2aa011d094a416db48e9c9a085e2e73761e4575"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Ynxfm/ZWinoXmBWGhU+zzhUwTORECrmRuOo/qDNEDFN3li14xhIw4/V7x9FPm7+jrYQKcNDHsgwwWvKZXOiDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T03:59:17.341434Z","bundle_sha256":"91bbb7822a7bdd2a9cec3f28f651eaf6542ed1b02fc09e436d67d38abfd4ba48"}}