{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:N2YFPUVYVJ6MFQJZBPB4JW6IAY","short_pith_number":"pith:N2YFPUVY","canonical_record":{"source":{"id":"1707.06443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-20T11:02:48Z","cross_cats_sorted":[],"title_canon_sha256":"402a97a4e5912e6a1f120c499d1fa477da61e7f095f3e1abfab87389f3eb0264","abstract_canon_sha256":"c22962438412069f76ee9b2c10c3ce31b78f1030eb26fcfa7b9b9d11d638d234"},"schema_version":"1.0"},"canonical_sha256":"6eb057d2b8aa7cc2c1390bc3c4dbc80639765404d8414dd64b0b12c2d72f9f98","source":{"kind":"arxiv","id":"1707.06443","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06443","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06443v1","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06443","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"N2YFPUVYVJ6M","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N2YFPUVYVJ6MFQJZ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N2YFPUVY","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:N2YFPUVYVJ6MFQJZBPB4JW6IAY","target":"record","payload":{"canonical_record":{"source":{"id":"1707.06443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-20T11:02:48Z","cross_cats_sorted":[],"title_canon_sha256":"402a97a4e5912e6a1f120c499d1fa477da61e7f095f3e1abfab87389f3eb0264","abstract_canon_sha256":"c22962438412069f76ee9b2c10c3ce31b78f1030eb26fcfa7b9b9d11d638d234"},"schema_version":"1.0"},"canonical_sha256":"6eb057d2b8aa7cc2c1390bc3c4dbc80639765404d8414dd64b0b12c2d72f9f98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:53.807940Z","signature_b64":"EOAuIOgydQJJdevQtfmv2E7BM1MHud2piL9i8YmySZAhLjyM566VmxVGYk/c1MCYtw354iVSww6ft4yti9CzCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6eb057d2b8aa7cc2c1390bc3c4dbc80639765404d8414dd64b0b12c2d72f9f98","last_reissued_at":"2026-05-18T00:39:53.807444Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:53.807444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.06443","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":"2026-05-18T00:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cJw1gvFwSUPspJaYpvlGQqurK2S95VEpxMZA/FIUZiVq7WaQVPmUffT6O4y3uSEpOKtuNqMhIKYJaOh+dAmTCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T23:44:59.280156Z"},"content_sha256":"e7861ad3108098e9e895c7baf40148b8874fc78c38c0ba97fdf686f58e73f708","schema_version":"1.0","event_id":"sha256:e7861ad3108098e9e895c7baf40148b8874fc78c38c0ba97fdf686f58e73f708"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:N2YFPUVYVJ6MFQJZBPB4JW6IAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Linear Algorithm for Computing $\\gamma_{[1,2]}$-set in Generalized Series-Parallel Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"M.R. Hooshmandasl, P. Sharifani","submitted_at":"2017-07-20T11:02:48Z","abstract_excerpt":"For a graph $G=(V,E)$, a set $S \\subseteq V$ is a $[1,2]$-set if it is a dominating set for $G$ and each vertex $v \\in V \\setminus S$ is dominated by at most two vertices of $S$, i.e. $1 \\leq \\vert N(v) \\cap S \\vert \\leq 2$. Moreover a set $S \\subseteq V$ is a total $[1,2]$-set if for each vertex of $V$, it is the case that $1 \\leq \\vert N(v) \\cap S \\vert \\leq 2$. The $[1,2]$-domination number of $G$, denoted $\\gamma_{[1,2]}(G)$,is the minimum number of vertices in a $[1,2]$-set. Every $[1,2]$-set with cardinality of $\\gamma_{[1,2]}(G)$ is called a $\\gamma_{[1,2]}$-set. Total $[1,2]$-dominatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06443","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":"2026-05-18T00:39:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8rTZYL8BJqAU0oZZujY3CVLOL++o9Vw8GYSs/vCQNOZRpda5zscpkNZTw543hhGi5ZJpzVREtpkEDlN3IYOjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T23:44:59.280538Z"},"content_sha256":"a68017232b7463fb831b6eeb059a39fa9be0e1e03ab31c8059d0743fcccdad2c","schema_version":"1.0","event_id":"sha256:a68017232b7463fb831b6eeb059a39fa9be0e1e03ab31c8059d0743fcccdad2c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N2YFPUVYVJ6MFQJZBPB4JW6IAY/bundle.json","state_url":"https://pith.science/pith/N2YFPUVYVJ6MFQJZBPB4JW6IAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N2YFPUVYVJ6MFQJZBPB4JW6IAY/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":"2026-06-27T23:44:59Z","links":{"resolver":"https://pith.science/pith/N2YFPUVYVJ6MFQJZBPB4JW6IAY","bundle":"https://pith.science/pith/N2YFPUVYVJ6MFQJZBPB4JW6IAY/bundle.json","state":"https://pith.science/pith/N2YFPUVYVJ6MFQJZBPB4JW6IAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N2YFPUVYVJ6MFQJZBPB4JW6IAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:N2YFPUVYVJ6MFQJZBPB4JW6IAY","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":"c22962438412069f76ee9b2c10c3ce31b78f1030eb26fcfa7b9b9d11d638d234","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-20T11:02:48Z","title_canon_sha256":"402a97a4e5912e6a1f120c499d1fa477da61e7f095f3e1abfab87389f3eb0264"},"schema_version":"1.0","source":{"id":"1707.06443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.06443","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.06443v1","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06443","created_at":"2026-05-18T00:39:53Z"},{"alias_kind":"pith_short_12","alias_value":"N2YFPUVYVJ6M","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"N2YFPUVYVJ6MFQJZ","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"N2YFPUVY","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:a68017232b7463fb831b6eeb059a39fa9be0e1e03ab31c8059d0743fcccdad2c","target":"graph","created_at":"2026-05-18T00:39:53Z","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 $G=(V,E)$, a set $S \\subseteq V$ is a $[1,2]$-set if it is a dominating set for $G$ and each vertex $v \\in V \\setminus S$ is dominated by at most two vertices of $S$, i.e. $1 \\leq \\vert N(v) \\cap S \\vert \\leq 2$. Moreover a set $S \\subseteq V$ is a total $[1,2]$-set if for each vertex of $V$, it is the case that $1 \\leq \\vert N(v) \\cap S \\vert \\leq 2$. The $[1,2]$-domination number of $G$, denoted $\\gamma_{[1,2]}(G)$,is the minimum number of vertices in a $[1,2]$-set. Every $[1,2]$-set with cardinality of $\\gamma_{[1,2]}(G)$ is called a $\\gamma_{[1,2]}$-set. Total $[1,2]$-dominatio","authors_text":"M.R. Hooshmandasl, P. Sharifani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-20T11:02:48Z","title":"A Linear Algorithm for Computing $\\gamma_{[1,2]}$-set in Generalized Series-Parallel Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06443","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:e7861ad3108098e9e895c7baf40148b8874fc78c38c0ba97fdf686f58e73f708","target":"record","created_at":"2026-05-18T00:39:53Z","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":"c22962438412069f76ee9b2c10c3ce31b78f1030eb26fcfa7b9b9d11d638d234","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-20T11:02:48Z","title_canon_sha256":"402a97a4e5912e6a1f120c499d1fa477da61e7f095f3e1abfab87389f3eb0264"},"schema_version":"1.0","source":{"id":"1707.06443","kind":"arxiv","version":1}},"canonical_sha256":"6eb057d2b8aa7cc2c1390bc3c4dbc80639765404d8414dd64b0b12c2d72f9f98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6eb057d2b8aa7cc2c1390bc3c4dbc80639765404d8414dd64b0b12c2d72f9f98","first_computed_at":"2026-05-18T00:39:53.807444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:53.807444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EOAuIOgydQJJdevQtfmv2E7BM1MHud2piL9i8YmySZAhLjyM566VmxVGYk/c1MCYtw354iVSww6ft4yti9CzCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:53.807940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.06443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7861ad3108098e9e895c7baf40148b8874fc78c38c0ba97fdf686f58e73f708","sha256:a68017232b7463fb831b6eeb059a39fa9be0e1e03ab31c8059d0743fcccdad2c"],"state_sha256":"2b34f313c054bf9da6b14c0b38d83abfdd5e1f5644562304df30a9b008854be7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kZ8pfWrh9kFglOvk29k3UwaaRorVPJMHkGeupGeR6BwZZ8j8gM8oV9MriHVCBdBBwIs9BzcnZ8f4VO5Wc33VBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T23:44:59.282369Z","bundle_sha256":"abdba580499471a1dc4b41e0338b0640aa753dafbb3a31235f57b0e3b1cc3d34"}}