{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RIZ75ECKZF2LTTWTU62KVYFGD7","short_pith_number":"pith:RIZ75ECK","canonical_record":{"source":{"id":"1604.05588","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-04-19T14:24:51Z","cross_cats_sorted":[],"title_canon_sha256":"f8c9d3cce91ed73136df7aafe958de58340e08be9c5db64e41ce4e478fc4de82","abstract_canon_sha256":"8f53c6a231d0e79238a6a6e6c49c56a913a45366347ae39f2090751ee32847da"},"schema_version":"1.0"},"canonical_sha256":"8a33fe904ac974b9ced3a7b4aae0a61ffe78541bc9411f6ed2e9eba2283594fb","source":{"kind":"arxiv","id":"1604.05588","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05588","created_at":"2026-05-18T01:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05588v1","created_at":"2026-05-18T01:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05588","created_at":"2026-05-18T01:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"RIZ75ECKZF2L","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RIZ75ECKZF2LTTWT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RIZ75ECK","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RIZ75ECKZF2LTTWTU62KVYFGD7","target":"record","payload":{"canonical_record":{"source":{"id":"1604.05588","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-04-19T14:24:51Z","cross_cats_sorted":[],"title_canon_sha256":"f8c9d3cce91ed73136df7aafe958de58340e08be9c5db64e41ce4e478fc4de82","abstract_canon_sha256":"8f53c6a231d0e79238a6a6e6c49c56a913a45366347ae39f2090751ee32847da"},"schema_version":"1.0"},"canonical_sha256":"8a33fe904ac974b9ced3a7b4aae0a61ffe78541bc9411f6ed2e9eba2283594fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:38.271164Z","signature_b64":"HRp/SHlu4+YbOt0ylUFHN9g5rz/bMmQVNWkp0kK71x7lzovHApE0cADKN5poIAGFGIQ8wii9e8NynZvlh4nCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a33fe904ac974b9ced3a7b4aae0a61ffe78541bc9411f6ed2e9eba2283594fb","last_reissued_at":"2026-05-18T01:16:38.270600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:38.270600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.05588","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":"2026-05-18T01:16:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6MnQ0FAeep5yeuqLeYKNWsacHxhX6zBtCn0748M3ueLDv8O5CmyKVHlR+8YtG2gtfV7RC3TzIvZr1SEsry1mCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:36:49.317398Z"},"content_sha256":"3da66b66af82451c1eb34de592776e0b7dde4a27c07f67da5a7c7b22c5d2425b","schema_version":"1.0","event_id":"sha256:3da66b66af82451c1eb34de592776e0b7dde4a27c07f67da5a7c7b22c5d2425b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RIZ75ECKZF2LTTWTU62KVYFGD7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On planar variants of the monotone satisfiability problem with bounded variable appearances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andreas Darmann, Britta Dorn, Janosch D\\\"ocker","submitted_at":"2016-04-19T14:24:51Z","abstract_excerpt":"We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by at most four. Hence, a planar and orthogonal drawing for these graphs can be computed efficiently, which may turn out to be useful in reductions using these variants as a starting point for proving some decision problem to be NP-hard."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05588","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":"2026-05-18T01:16:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5s0lXlVwoLt/lga2mbNkmQhNzG9HTy2+JSyo6xhwFG4WX05fX1pQ3i60E0LVIYkRomJVWr2x7DeU87oVXGuWBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:36:49.317772Z"},"content_sha256":"b9aef75afd7b87e5c0494ea32595045ac18a11fa025e605be60cbc062b2aeef2","schema_version":"1.0","event_id":"sha256:b9aef75afd7b87e5c0494ea32595045ac18a11fa025e605be60cbc062b2aeef2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RIZ75ECKZF2LTTWTU62KVYFGD7/bundle.json","state_url":"https://pith.science/pith/RIZ75ECKZF2LTTWTU62KVYFGD7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RIZ75ECKZF2LTTWTU62KVYFGD7/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":"2026-06-01T01:36:49Z","links":{"resolver":"https://pith.science/pith/RIZ75ECKZF2LTTWTU62KVYFGD7","bundle":"https://pith.science/pith/RIZ75ECKZF2LTTWTU62KVYFGD7/bundle.json","state":"https://pith.science/pith/RIZ75ECKZF2LTTWTU62KVYFGD7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RIZ75ECKZF2LTTWTU62KVYFGD7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RIZ75ECKZF2LTTWTU62KVYFGD7","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":"8f53c6a231d0e79238a6a6e6c49c56a913a45366347ae39f2090751ee32847da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-04-19T14:24:51Z","title_canon_sha256":"f8c9d3cce91ed73136df7aafe958de58340e08be9c5db64e41ce4e478fc4de82"},"schema_version":"1.0","source":{"id":"1604.05588","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05588","created_at":"2026-05-18T01:16:38Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05588v1","created_at":"2026-05-18T01:16:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05588","created_at":"2026-05-18T01:16:38Z"},{"alias_kind":"pith_short_12","alias_value":"RIZ75ECKZF2L","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RIZ75ECKZF2LTTWT","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RIZ75ECK","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:b9aef75afd7b87e5c0494ea32595045ac18a11fa025e605be60cbc062b2aeef2","target":"graph","created_at":"2026-05-18T01:16:38Z","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":"We show NP-completeness for several planar variants of the monotone satisfiability problem with bounded variable appearances. With one exception the presented variants have an associated bipartite graph where the vertex degree is bounded by at most four. Hence, a planar and orthogonal drawing for these graphs can be computed efficiently, which may turn out to be useful in reductions using these variants as a starting point for proving some decision problem to be NP-hard.","authors_text":"Andreas Darmann, Britta Dorn, Janosch D\\\"ocker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-04-19T14:24:51Z","title":"On planar variants of the monotone satisfiability problem with bounded variable appearances"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05588","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":"sha256:3da66b66af82451c1eb34de592776e0b7dde4a27c07f67da5a7c7b22c5d2425b","target":"record","created_at":"2026-05-18T01:16:38Z","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":"8f53c6a231d0e79238a6a6e6c49c56a913a45366347ae39f2090751ee32847da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-04-19T14:24:51Z","title_canon_sha256":"f8c9d3cce91ed73136df7aafe958de58340e08be9c5db64e41ce4e478fc4de82"},"schema_version":"1.0","source":{"id":"1604.05588","kind":"arxiv","version":1}},"canonical_sha256":"8a33fe904ac974b9ced3a7b4aae0a61ffe78541bc9411f6ed2e9eba2283594fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a33fe904ac974b9ced3a7b4aae0a61ffe78541bc9411f6ed2e9eba2283594fb","first_computed_at":"2026-05-18T01:16:38.270600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:38.270600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HRp/SHlu4+YbOt0ylUFHN9g5rz/bMmQVNWkp0kK71x7lzovHApE0cADKN5poIAGFGIQ8wii9e8NynZvlh4nCDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:38.271164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05588","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3da66b66af82451c1eb34de592776e0b7dde4a27c07f67da5a7c7b22c5d2425b","sha256:b9aef75afd7b87e5c0494ea32595045ac18a11fa025e605be60cbc062b2aeef2"],"state_sha256":"d89f3fb15979cae5efd2936bebc498b4c80e5651beb103a8182634dc0d569c9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4vD6gHSOX84310POyMxyQusbhHPk19Iz4AJDmYjbic3CN1H0HmPAx9UnngXQcyMeTsR2j2Zou3vojv3AIqDOAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:36:49.320021Z","bundle_sha256":"20c50831bc01c4bc561656dc6e229f8de1fdde76792a8e465e6766c16734dedf"}}