{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QUMRRCS7UZPXFV73AIKJAUUBH3","short_pith_number":"pith:QUMRRCS7","canonical_record":{"source":{"id":"1506.00944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-06-02T16:22:46Z","cross_cats_sorted":[],"title_canon_sha256":"bf74483a0e82b64a7db8a79163209fe82150b3c5973d543d37ac79888c910fb9","abstract_canon_sha256":"d614f45a41ed73a8afc8f37bb18abaa8a04a8f6936018a0044b087c0c14d2101"},"schema_version":"1.0"},"canonical_sha256":"8519188a5fa65f72d7fb02149052813ecb6fd9ed45de3b9801731b0760e8b40c","source":{"kind":"arxiv","id":"1506.00944","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00944","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00944v1","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00944","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"QUMRRCS7UZPX","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QUMRRCS7UZPXFV73","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QUMRRCS7","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QUMRRCS7UZPXFV73AIKJAUUBH3","target":"record","payload":{"canonical_record":{"source":{"id":"1506.00944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-06-02T16:22:46Z","cross_cats_sorted":[],"title_canon_sha256":"bf74483a0e82b64a7db8a79163209fe82150b3c5973d543d37ac79888c910fb9","abstract_canon_sha256":"d614f45a41ed73a8afc8f37bb18abaa8a04a8f6936018a0044b087c0c14d2101"},"schema_version":"1.0"},"canonical_sha256":"8519188a5fa65f72d7fb02149052813ecb6fd9ed45de3b9801731b0760e8b40c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:34.023666Z","signature_b64":"r4bWwcJAQgjsK9FVupS0a5qsBn4CmWeGT8dZa3Gln24TLlYvuW6ghaaDt+HMJoQ8GdYjSguReOBGDBciQuGnBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8519188a5fa65f72d7fb02149052813ecb6fd9ed45de3b9801731b0760e8b40c","last_reissued_at":"2026-05-18T01:59:34.023060Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:34.023060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.00944","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":"2026-05-18T01:59:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EOsLM6ezgHIszuMb9mGt6vmpEMjUPhOP3W0pTaHDCJkTwfVaeMticqc5DpDjoGmY2PHF7KLLNFSY7yR3xCZbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:32:54.281897Z"},"content_sha256":"a32122140f29bc5fd9ae04bcbf6486ebfa5aee47c189f82f1f2abe54e42b2065","schema_version":"1.0","event_id":"sha256:a32122140f29bc5fd9ae04bcbf6486ebfa5aee47c189f82f1f2abe54e42b2065"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QUMRRCS7UZPXFV73AIKJAUUBH3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Parameterized mixed cluster editing via modular decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"F\\'abio Protti, Jayme Luiz Szwarcfiter, Maise Dantas da Silva","submitted_at":"2015-06-02T16:22:46Z","abstract_excerpt":"In this paper we introduce a natural generalization of the well-known problems Cluster Editing and Bicluster Editing, whose parameterized versions have been intensively investigated in the recent literature. The generalized problem, called Mixed Cluster Editing or ${\\cal M}$-Cluster Editing, is formulated as follows. Let ${\\cal M}$ be a family of graphs. Given a graph $G$ and a nonnegative integer $k$, transform $G$, through a sequence of at most $k$ edge editions, into a target graph $G'$ with the following property: $G'$ is a vertex-disjoint union of graphs $G_1, G_2, \\ldots$ such that every"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00944","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":"2026-05-18T01:59:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RqvKNT7kSSbndC5VUOb4lXZzxcIYLfa9GCTFrxU7sUeG7A6AC/MgjdbzXkRBZezQjqFbRSK2Fz2hJ3yrUfoyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:32:54.282340Z"},"content_sha256":"16f3a2c3e22ead0901c2f2032ebbb687cf2a449f579989615eceb6bec59d8d38","schema_version":"1.0","event_id":"sha256:16f3a2c3e22ead0901c2f2032ebbb687cf2a449f579989615eceb6bec59d8d38"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QUMRRCS7UZPXFV73AIKJAUUBH3/bundle.json","state_url":"https://pith.science/pith/QUMRRCS7UZPXFV73AIKJAUUBH3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QUMRRCS7UZPXFV73AIKJAUUBH3/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":"2026-06-11T07:32:54Z","links":{"resolver":"https://pith.science/pith/QUMRRCS7UZPXFV73AIKJAUUBH3","bundle":"https://pith.science/pith/QUMRRCS7UZPXFV73AIKJAUUBH3/bundle.json","state":"https://pith.science/pith/QUMRRCS7UZPXFV73AIKJAUUBH3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QUMRRCS7UZPXFV73AIKJAUUBH3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QUMRRCS7UZPXFV73AIKJAUUBH3","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":"d614f45a41ed73a8afc8f37bb18abaa8a04a8f6936018a0044b087c0c14d2101","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-06-02T16:22:46Z","title_canon_sha256":"bf74483a0e82b64a7db8a79163209fe82150b3c5973d543d37ac79888c910fb9"},"schema_version":"1.0","source":{"id":"1506.00944","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.00944","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"arxiv_version","alias_value":"1506.00944v1","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.00944","created_at":"2026-05-18T01:59:34Z"},{"alias_kind":"pith_short_12","alias_value":"QUMRRCS7UZPX","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QUMRRCS7UZPXFV73","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QUMRRCS7","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:16f3a2c3e22ead0901c2f2032ebbb687cf2a449f579989615eceb6bec59d8d38","target":"graph","created_at":"2026-05-18T01:59:34Z","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 this paper we introduce a natural generalization of the well-known problems Cluster Editing and Bicluster Editing, whose parameterized versions have been intensively investigated in the recent literature. The generalized problem, called Mixed Cluster Editing or ${\\cal M}$-Cluster Editing, is formulated as follows. Let ${\\cal M}$ be a family of graphs. Given a graph $G$ and a nonnegative integer $k$, transform $G$, through a sequence of at most $k$ edge editions, into a target graph $G'$ with the following property: $G'$ is a vertex-disjoint union of graphs $G_1, G_2, \\ldots$ such that every","authors_text":"F\\'abio Protti, Jayme Luiz Szwarcfiter, Maise Dantas da Silva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-06-02T16:22:46Z","title":"Parameterized mixed cluster editing via modular decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.00944","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:a32122140f29bc5fd9ae04bcbf6486ebfa5aee47c189f82f1f2abe54e42b2065","target":"record","created_at":"2026-05-18T01:59:34Z","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":"d614f45a41ed73a8afc8f37bb18abaa8a04a8f6936018a0044b087c0c14d2101","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-06-02T16:22:46Z","title_canon_sha256":"bf74483a0e82b64a7db8a79163209fe82150b3c5973d543d37ac79888c910fb9"},"schema_version":"1.0","source":{"id":"1506.00944","kind":"arxiv","version":1}},"canonical_sha256":"8519188a5fa65f72d7fb02149052813ecb6fd9ed45de3b9801731b0760e8b40c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8519188a5fa65f72d7fb02149052813ecb6fd9ed45de3b9801731b0760e8b40c","first_computed_at":"2026-05-18T01:59:34.023060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:34.023060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r4bWwcJAQgjsK9FVupS0a5qsBn4CmWeGT8dZa3Gln24TLlYvuW6ghaaDt+HMJoQ8GdYjSguReOBGDBciQuGnBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:34.023666Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.00944","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a32122140f29bc5fd9ae04bcbf6486ebfa5aee47c189f82f1f2abe54e42b2065","sha256:16f3a2c3e22ead0901c2f2032ebbb687cf2a449f579989615eceb6bec59d8d38"],"state_sha256":"05b40d99805b17cf948a55ec990a3d3e68f450cc14497c743f23fcf90371ae88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PTDymGrcW3eeZ3Z2U+qznrhcG+FC3BRaTqQZJm+tbeHWDeTu7/lJejbXSqksVWJN8CzUwn+PMg4JRWL8s2TACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T07:32:54.285268Z","bundle_sha256":"ddea89fd6eb84c9da760068d95095a2363203f1637b75d7a8f43c7b25f3169bf"}}