{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:57H7QAV4KJJFWGIAIGKKDR55LC","short_pith_number":"pith:57H7QAV4","canonical_record":{"source":{"id":"2005.06419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-05-13T16:49:55Z","cross_cats_sorted":[],"title_canon_sha256":"bbf0c9ef3ebe277f23aac0bc4466f8d00d098b1d6fa74efc2872d672204687ce","abstract_canon_sha256":"fbf6f4907844fb3e5745d814217ad47917a5c158d6262587b76fa90a86ef0c08"},"schema_version":"1.0"},"canonical_sha256":"efcff802bc52525b19004194a1c7bd58802fc11d08c1c3d064c3678b9aa1a0b9","source":{"kind":"arxiv","id":"2005.06419","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.06419","created_at":"2026-07-05T01:02:41Z"},{"alias_kind":"arxiv_version","alias_value":"2005.06419v1","created_at":"2026-07-05T01:02:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.06419","created_at":"2026-07-05T01:02:41Z"},{"alias_kind":"pith_short_12","alias_value":"57H7QAV4KJJF","created_at":"2026-07-05T01:02:41Z"},{"alias_kind":"pith_short_16","alias_value":"57H7QAV4KJJFWGIA","created_at":"2026-07-05T01:02:41Z"},{"alias_kind":"pith_short_8","alias_value":"57H7QAV4","created_at":"2026-07-05T01:02:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:57H7QAV4KJJFWGIAIGKKDR55LC","target":"record","payload":{"canonical_record":{"source":{"id":"2005.06419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-05-13T16:49:55Z","cross_cats_sorted":[],"title_canon_sha256":"bbf0c9ef3ebe277f23aac0bc4466f8d00d098b1d6fa74efc2872d672204687ce","abstract_canon_sha256":"fbf6f4907844fb3e5745d814217ad47917a5c158d6262587b76fa90a86ef0c08"},"schema_version":"1.0"},"canonical_sha256":"efcff802bc52525b19004194a1c7bd58802fc11d08c1c3d064c3678b9aa1a0b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:02:41.225407Z","signature_b64":"1SVEcKkKnHmfn+7sAXwEuUU56V34rgk0q6fPC2y+5LPizkLh2zn7pxHLJirBeldbnYUn2CqapvBQhaSz11suBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efcff802bc52525b19004194a1c7bd58802fc11d08c1c3d064c3678b9aa1a0b9","last_reissued_at":"2026-07-05T01:02:41.224973Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:02:41.224973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2005.06419","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":"2026-07-05T01:02:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Px75NQgC4AT5GHTofHWVyrs9fbSEeCQlhr1x8/A6fHbWdKOc8OmJ8LVlmvWLLOyc9QGVLmN0AG7zTfLWW3sZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:55:37.424765Z"},"content_sha256":"55ec4731c644349a08f82a23ebdb49d7ae7c32bc09ea321045d3742d4e615668","schema_version":"1.0","event_id":"sha256:55ec4731c644349a08f82a23ebdb49d7ae7c32bc09ea321045d3742d4e615668"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:57H7QAV4KJJFWGIAIGKKDR55LC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time Space Optimal Algorithm for Computing Separators in Bounded Genus Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Chetan Gupta, Raghunath Tewari, Rahul Jain","submitted_at":"2020-05-13T16:49:55Z","abstract_excerpt":"A graph separator is a subset of vertices of a graph whose removal divides the graph into small components. Computing small graph separators for various classes of graphs is an important computational task. In this paper, we present a polynomial time algorithm that uses $O(g^{1/2}n^{1/2}\\log n)$-space to find an $O(g^{1/2}n^{1/2})$-sized separator of a graph having $n$ vertices and embedded on a surface of genus $g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.06419","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2005.06419/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:02:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9HIBUMPDiKqP7L8EcG7UfdfCcmOh7bSciGmC3kK8HMk2IYjh+i6dJv31XkvGuw0sIrs6U/vpBONhasdZL+VDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:55:37.425138Z"},"content_sha256":"0d907b3eb4057262cb7a5843f1a30a68977168b64f702513f247ad87d0505b5a","schema_version":"1.0","event_id":"sha256:0d907b3eb4057262cb7a5843f1a30a68977168b64f702513f247ad87d0505b5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57H7QAV4KJJFWGIAIGKKDR55LC/bundle.json","state_url":"https://pith.science/pith/57H7QAV4KJJFWGIAIGKKDR55LC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57H7QAV4KJJFWGIAIGKKDR55LC/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":"2026-08-12T22:55:37Z","links":{"resolver":"https://pith.science/pith/57H7QAV4KJJFWGIAIGKKDR55LC","bundle":"https://pith.science/pith/57H7QAV4KJJFWGIAIGKKDR55LC/bundle.json","state":"https://pith.science/pith/57H7QAV4KJJFWGIAIGKKDR55LC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57H7QAV4KJJFWGIAIGKKDR55LC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:57H7QAV4KJJFWGIAIGKKDR55LC","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":"fbf6f4907844fb3e5745d814217ad47917a5c158d6262587b76fa90a86ef0c08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-05-13T16:49:55Z","title_canon_sha256":"bbf0c9ef3ebe277f23aac0bc4466f8d00d098b1d6fa74efc2872d672204687ce"},"schema_version":"1.0","source":{"id":"2005.06419","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2005.06419","created_at":"2026-07-05T01:02:41Z"},{"alias_kind":"arxiv_version","alias_value":"2005.06419v1","created_at":"2026-07-05T01:02:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2005.06419","created_at":"2026-07-05T01:02:41Z"},{"alias_kind":"pith_short_12","alias_value":"57H7QAV4KJJF","created_at":"2026-07-05T01:02:41Z"},{"alias_kind":"pith_short_16","alias_value":"57H7QAV4KJJFWGIA","created_at":"2026-07-05T01:02:41Z"},{"alias_kind":"pith_short_8","alias_value":"57H7QAV4","created_at":"2026-07-05T01:02:41Z"}],"graph_snapshots":[{"event_id":"sha256:0d907b3eb4057262cb7a5843f1a30a68977168b64f702513f247ad87d0505b5a","target":"graph","created_at":"2026-07-05T01:02:41Z","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/2005.06419/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A graph separator is a subset of vertices of a graph whose removal divides the graph into small components. Computing small graph separators for various classes of graphs is an important computational task. In this paper, we present a polynomial time algorithm that uses $O(g^{1/2}n^{1/2}\\log n)$-space to find an $O(g^{1/2}n^{1/2})$-sized separator of a graph having $n$ vertices and embedded on a surface of genus $g$.","authors_text":"Chetan Gupta, Raghunath Tewari, Rahul Jain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-05-13T16:49:55Z","title":"Time Space Optimal Algorithm for Computing Separators in Bounded Genus Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.06419","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":"sha256:55ec4731c644349a08f82a23ebdb49d7ae7c32bc09ea321045d3742d4e615668","target":"record","created_at":"2026-07-05T01:02:41Z","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":"fbf6f4907844fb3e5745d814217ad47917a5c158d6262587b76fa90a86ef0c08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2020-05-13T16:49:55Z","title_canon_sha256":"bbf0c9ef3ebe277f23aac0bc4466f8d00d098b1d6fa74efc2872d672204687ce"},"schema_version":"1.0","source":{"id":"2005.06419","kind":"arxiv","version":1}},"canonical_sha256":"efcff802bc52525b19004194a1c7bd58802fc11d08c1c3d064c3678b9aa1a0b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efcff802bc52525b19004194a1c7bd58802fc11d08c1c3d064c3678b9aa1a0b9","first_computed_at":"2026-07-05T01:02:41.224973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:02:41.224973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1SVEcKkKnHmfn+7sAXwEuUU56V34rgk0q6fPC2y+5LPizkLh2zn7pxHLJirBeldbnYUn2CqapvBQhaSz11suBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:02:41.225407Z","signed_message":"canonical_sha256_bytes"},"source_id":"2005.06419","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55ec4731c644349a08f82a23ebdb49d7ae7c32bc09ea321045d3742d4e615668","sha256:0d907b3eb4057262cb7a5843f1a30a68977168b64f702513f247ad87d0505b5a"],"state_sha256":"f578f9ecd9846baa100e5c7355aeb70ae2eab1a6e8c060dbffbaf03d020f226e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o+gWDTDaQMhdtgNJeMl1EFdKzlbAyvDZw+hz5LyY3YbsHUI67om/qPCR+CkkE1RfnqwJFhjVT1pV+sup6ThHBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:55:37.427822Z","bundle_sha256":"335b394381618b46a3f340ccaaa746ba37b5bbf59faff15da0c3ccacbd5ad53b"}}