{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XHR3XGHIKOU6HJ65RYZGJFVXW3","short_pith_number":"pith:XHR3XGHI","canonical_record":{"source":{"id":"1110.1510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-07T12:52:19Z","cross_cats_sorted":[],"title_canon_sha256":"2dd15892fd5afe88a2e4ed638d37a08cc8d44db59d476c496758d27ed44861e9","abstract_canon_sha256":"d040f9c424c85abee1ecc3472b1b39128b16c161bc8368fde62cd261938023e6"},"schema_version":"1.0"},"canonical_sha256":"b9e3bb98e853a9e3a7dd8e326496b7b6f0a9d16d01e667c056c46edba49f8956","source":{"kind":"arxiv","id":"1110.1510","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1510","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1510v2","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1510","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"XHR3XGHIKOU6","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XHR3XGHIKOU6HJ65","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XHR3XGHI","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XHR3XGHIKOU6HJ65RYZGJFVXW3","target":"record","payload":{"canonical_record":{"source":{"id":"1110.1510","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-07T12:52:19Z","cross_cats_sorted":[],"title_canon_sha256":"2dd15892fd5afe88a2e4ed638d37a08cc8d44db59d476c496758d27ed44861e9","abstract_canon_sha256":"d040f9c424c85abee1ecc3472b1b39128b16c161bc8368fde62cd261938023e6"},"schema_version":"1.0"},"canonical_sha256":"b9e3bb98e853a9e3a7dd8e326496b7b6f0a9d16d01e667c056c46edba49f8956","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:29.774213Z","signature_b64":"Er6sQR7d9CG0s+K6F4yCGqs0mC9/fLUoUIWv4hSiRHgb+PpoLv/T8E0OqaX1EBbcKfQoGhNqXjXYoTQDN+MFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9e3bb98e853a9e3a7dd8e326496b7b6f0a9d16d01e667c056c46edba49f8956","last_reissued_at":"2026-05-18T04:04:29.773486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:29.773486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.1510","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":"2026-05-18T04:04:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qko97k+kzy610Hp7x2UDPPNVQQTH4EdB8HsHxHvSgAFjIvZJ6/h819FT0RUd1FE8EYUUy795C3ovIiYJ1MZECg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:41:32.733610Z"},"content_sha256":"cf78ef1dc3f2df168d3f32d8953c8492ec7b692938b354ec6275f3109886217d","schema_version":"1.0","event_id":"sha256:cf78ef1dc3f2df168d3f32d8953c8492ec7b692938b354ec6275f3109886217d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XHR3XGHIKOU6HJ65RYZGJFVXW3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Andr\\'e Nichterlein, Sepp Hartung","submitted_at":"2011-10-07T12:52:19Z","abstract_excerpt":"In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the graph is directed or undirected. In contrary, we show NP-completeness for the problem of realizing a given sequence of pairs of positive integers (representing indegrees and outdegrees) with a directed acyclic graph, answering an open question of Berger and M\\\"uller-Hannemann [FCT 2011]. Furthermore, we classify the problem as fixed-parameter tractable with resp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1510","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":"2026-05-18T04:04:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eDWfB1NlxOZvX31Xv4Ozjrt4t+cyByaapjQsXl1zLT+BibSFS2/c7kTFO40MYWQeuxtK+OMKN+jEicNNnXOPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T01:41:32.734433Z"},"content_sha256":"e5e09f54c2b003cf7e7656a5f9b25e604d2a56a3d798faedfcff84386081c394","schema_version":"1.0","event_id":"sha256:e5e09f54c2b003cf7e7656a5f9b25e604d2a56a3d798faedfcff84386081c394"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XHR3XGHIKOU6HJ65RYZGJFVXW3/bundle.json","state_url":"https://pith.science/pith/XHR3XGHIKOU6HJ65RYZGJFVXW3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XHR3XGHIKOU6HJ65RYZGJFVXW3/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":"2026-06-01T01:41:32Z","links":{"resolver":"https://pith.science/pith/XHR3XGHIKOU6HJ65RYZGJFVXW3","bundle":"https://pith.science/pith/XHR3XGHIKOU6HJ65RYZGJFVXW3/bundle.json","state":"https://pith.science/pith/XHR3XGHIKOU6HJ65RYZGJFVXW3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XHR3XGHIKOU6HJ65RYZGJFVXW3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XHR3XGHIKOU6HJ65RYZGJFVXW3","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":"d040f9c424c85abee1ecc3472b1b39128b16c161bc8368fde62cd261938023e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-07T12:52:19Z","title_canon_sha256":"2dd15892fd5afe88a2e4ed638d37a08cc8d44db59d476c496758d27ed44861e9"},"schema_version":"1.0","source":{"id":"1110.1510","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1510","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1510v2","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1510","created_at":"2026-05-18T04:04:29Z"},{"alias_kind":"pith_short_12","alias_value":"XHR3XGHIKOU6","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XHR3XGHIKOU6HJ65","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XHR3XGHI","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:e5e09f54c2b003cf7e7656a5f9b25e604d2a56a3d798faedfcff84386081c394","target":"graph","created_at":"2026-05-18T04:04:29Z","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 graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the graph is directed or undirected. In contrary, we show NP-completeness for the problem of realizing a given sequence of pairs of positive integers (representing indegrees and outdegrees) with a directed acyclic graph, answering an open question of Berger and M\\\"uller-Hannemann [FCT 2011]. Furthermore, we classify the problem as fixed-parameter tractable with resp","authors_text":"Andr\\'e Nichterlein, Sepp Hartung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-07T12:52:19Z","title":"NP-Hardness and Fixed-Parameter Tractability of Realizing Degree Sequences with Directed Acyclic Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1510","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:cf78ef1dc3f2df168d3f32d8953c8492ec7b692938b354ec6275f3109886217d","target":"record","created_at":"2026-05-18T04:04:29Z","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":"d040f9c424c85abee1ecc3472b1b39128b16c161bc8368fde62cd261938023e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2011-10-07T12:52:19Z","title_canon_sha256":"2dd15892fd5afe88a2e4ed638d37a08cc8d44db59d476c496758d27ed44861e9"},"schema_version":"1.0","source":{"id":"1110.1510","kind":"arxiv","version":2}},"canonical_sha256":"b9e3bb98e853a9e3a7dd8e326496b7b6f0a9d16d01e667c056c46edba49f8956","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9e3bb98e853a9e3a7dd8e326496b7b6f0a9d16d01e667c056c46edba49f8956","first_computed_at":"2026-05-18T04:04:29.773486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:29.773486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Er6sQR7d9CG0s+K6F4yCGqs0mC9/fLUoUIWv4hSiRHgb+PpoLv/T8E0OqaX1EBbcKfQoGhNqXjXYoTQDN+MFBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:29.774213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1510","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf78ef1dc3f2df168d3f32d8953c8492ec7b692938b354ec6275f3109886217d","sha256:e5e09f54c2b003cf7e7656a5f9b25e604d2a56a3d798faedfcff84386081c394"],"state_sha256":"3e5a0e6649efbc2a7bca1b228ffc649670f48813158e6e50cb777e4073684294"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"owmAgY9elVsjWMf/YJFKBv6NIoTmqocQNoDQd2RQF9zIyN6UgRcqbEK7MouY+LzJqX27eMB3gY/Aeefxg3oPBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T01:41:32.738241Z","bundle_sha256":"57893f979bef12bab270cbdeba057fc1e56794b08311813c411f48199716baed"}}