{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:QMCEV7KZDTCAKYUAXR7G52WWEC","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":"6ee900f6033131de0e32a14f08ac9598d3c1f50090a044fc43e526276e0d7719","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-10-12T14:27:07Z","title_canon_sha256":"a31f55e183e15390d8f63eef39f81a86efaaa5c102cc98b547c38c5fd8a8cf19"},"schema_version":"1.0","source":{"id":"2010.05733","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.05733","created_at":"2026-07-05T01:42:10Z"},{"alias_kind":"arxiv_version","alias_value":"2010.05733v1","created_at":"2026-07-05T01:42:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.05733","created_at":"2026-07-05T01:42:10Z"},{"alias_kind":"pith_short_12","alias_value":"QMCEV7KZDTCA","created_at":"2026-07-05T01:42:10Z"},{"alias_kind":"pith_short_16","alias_value":"QMCEV7KZDTCAKYUA","created_at":"2026-07-05T01:42:10Z"},{"alias_kind":"pith_short_8","alias_value":"QMCEV7KZ","created_at":"2026-07-05T01:42:10Z"}],"graph_snapshots":[{"event_id":"sha256:8f2bd575be41be8a8a6d864b1a84c033db9c4e4b6d806da95090e26298630908","target":"graph","created_at":"2026-07-05T01:42:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2010.05733/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a graph class $\\mathcal{H}$, the task of the $\\mathcal{H}$-Square Root problem is to decide, whether an input graph $G$ has a square root $H$ from $\\mathcal{H}$. We are interested in the parameterized complexity of the problem for classes $\\mathcal{H}$ that are composed by the graphs at vertex deletion distance at most $k$ from graphs of maximum degree at most one, that is, we are looking for a square root $H$ such that there is a modulator $S$ of size $k$ such that $H-S$ is the disjoint union of isolated vertices and disjoint edges. We show that different variants of the problems with c","authors_text":"Charis Papadopoulos, Paloma T. Lima, Petr A. Golovach","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-10-12T14:27:07Z","title":"Graph Square Roots of Small Distance from Degree One Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.05733","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":"sha256:062352f24515146d9847e94815139268206a86e1a22cddfc8a955c58cbccbedc","target":"record","created_at":"2026-07-05T01:42:10Z","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":"6ee900f6033131de0e32a14f08ac9598d3c1f50090a044fc43e526276e0d7719","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-10-12T14:27:07Z","title_canon_sha256":"a31f55e183e15390d8f63eef39f81a86efaaa5c102cc98b547c38c5fd8a8cf19"},"schema_version":"1.0","source":{"id":"2010.05733","kind":"arxiv","version":1}},"canonical_sha256":"83044afd591cc4056280bc7e6eead620ba2599fc8d843d76c9adc1e5ae8463f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83044afd591cc4056280bc7e6eead620ba2599fc8d843d76c9adc1e5ae8463f0","first_computed_at":"2026-07-05T01:42:10.199641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:42:10.199641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fb0z5DsT7f+PQ8LG1t6FMzmFiDNDLy8s3fYBzkwqFc4lwg7JGMePh3yvoFxw2GPPDll2WZP24gocfvJp+krzBA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:42:10.200081Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.05733","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:062352f24515146d9847e94815139268206a86e1a22cddfc8a955c58cbccbedc","sha256:8f2bd575be41be8a8a6d864b1a84c033db9c4e4b6d806da95090e26298630908"],"state_sha256":"3aa0de614f7e067755bd8a631ce5e502c319fb20f1ffd929a1cc4cd73a7e2e08"}