{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:Z5BDZJB4EDJQXIRRVXXDGXQA3G","short_pith_number":"pith:Z5BDZJB4","schema_version":"1.0","canonical_sha256":"cf423ca43c20d30ba231adee335e00d99b185f4695231c1c470ab5a526617cba","source":{"kind":"arxiv","id":"1310.5469","version":1},"attestation_state":"computed","paper":{"title":"Parameterized Algorithms for Finding Square Roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dani\\\"el Paulusma, Dieter Kratsch, Jean-Fran\\c{c}ois Couturier, Manfred Cochefert, Petr A. Golovach","submitted_at":"2013-10-21T08:57:19Z","abstract_excerpt":"We show that the following two problems are fixed-parameter tractable with parameter k: testing whether a connected n-vertex graph with m edges has a square root with at most n-1+k edges and testing whether such a graph has a square root with at least m-k edges. Our first result implies that squares of graphs obtained from trees by adding at most k edges can be recognized in polynomial time for every fixed k>=0; previously this result was known only for k=0. Our second result is equivalent to stating that deciding whether a graph can be modified into a square root of itself by at most k edge d"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.5469","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-10-21T08:57:19Z","cross_cats_sorted":[],"title_canon_sha256":"94bfc4ca78a3a885f2c16412218b23dd180f26ac3d615815f22c13bb786803da","abstract_canon_sha256":"bc1cf1f9fa9d51fb4c135eaefc1897a12afa43df3c7cca11844a86022001b668"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:35.544128Z","signature_b64":"0VOHv9bS3oBaoPhgJCVy+b94nBvamlgYE4CbrC1xSr4MUpvS9ltgGPuo6hwfbNxjytRmhIglf8SIl3v9ypZjCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf423ca43c20d30ba231adee335e00d99b185f4695231c1c470ab5a526617cba","last_reissued_at":"2026-05-18T03:09:35.543313Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:35.543313Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parameterized Algorithms for Finding Square Roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Dani\\\"el Paulusma, Dieter Kratsch, Jean-Fran\\c{c}ois Couturier, Manfred Cochefert, Petr A. Golovach","submitted_at":"2013-10-21T08:57:19Z","abstract_excerpt":"We show that the following two problems are fixed-parameter tractable with parameter k: testing whether a connected n-vertex graph with m edges has a square root with at most n-1+k edges and testing whether such a graph has a square root with at least m-k edges. Our first result implies that squares of graphs obtained from trees by adding at most k edges can be recognized in polynomial time for every fixed k>=0; previously this result was known only for k=0. Our second result is equivalent to stating that deciding whether a graph can be modified into a square root of itself by at most k edge d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5469","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.5469","created_at":"2026-05-18T03:09:35.543448+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.5469v1","created_at":"2026-05-18T03:09:35.543448+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5469","created_at":"2026-05-18T03:09:35.543448+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z5BDZJB4EDJQ","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z5BDZJB4EDJQXIRR","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z5BDZJB4","created_at":"2026-05-18T12:28:09.283467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z5BDZJB4EDJQXIRRVXXDGXQA3G","json":"https://pith.science/pith/Z5BDZJB4EDJQXIRRVXXDGXQA3G.json","graph_json":"https://pith.science/api/pith-number/Z5BDZJB4EDJQXIRRVXXDGXQA3G/graph.json","events_json":"https://pith.science/api/pith-number/Z5BDZJB4EDJQXIRRVXXDGXQA3G/events.json","paper":"https://pith.science/paper/Z5BDZJB4"},"agent_actions":{"view_html":"https://pith.science/pith/Z5BDZJB4EDJQXIRRVXXDGXQA3G","download_json":"https://pith.science/pith/Z5BDZJB4EDJQXIRRVXXDGXQA3G.json","view_paper":"https://pith.science/paper/Z5BDZJB4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.5469&json=true","fetch_graph":"https://pith.science/api/pith-number/Z5BDZJB4EDJQXIRRVXXDGXQA3G/graph.json","fetch_events":"https://pith.science/api/pith-number/Z5BDZJB4EDJQXIRRVXXDGXQA3G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z5BDZJB4EDJQXIRRVXXDGXQA3G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z5BDZJB4EDJQXIRRVXXDGXQA3G/action/storage_attestation","attest_author":"https://pith.science/pith/Z5BDZJB4EDJQXIRRVXXDGXQA3G/action/author_attestation","sign_citation":"https://pith.science/pith/Z5BDZJB4EDJQXIRRVXXDGXQA3G/action/citation_signature","submit_replication":"https://pith.science/pith/Z5BDZJB4EDJQXIRRVXXDGXQA3G/action/replication_record"}},"created_at":"2026-05-18T03:09:35.543448+00:00","updated_at":"2026-05-18T03:09:35.543448+00:00"}