{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:VTEP7NCZSRPDBSVKHR4PHOEAFV","short_pith_number":"pith:VTEP7NCZ","canonical_record":{"source":{"id":"1111.3548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-15T15:06:54Z","cross_cats_sorted":[],"title_canon_sha256":"00ebc21535c3ec8706375296d43706581f9734c76db3ef5de5ed287cd5060198","abstract_canon_sha256":"16aa9ceb87175b354878a54ed622c1461d85e5a8f739bb17670c469cca66ccd2"},"schema_version":"1.0"},"canonical_sha256":"acc8ffb459945e30caaa3c78f3b8802d7a3b2a95ab8a8cec096640b4364da273","source":{"kind":"arxiv","id":"1111.3548","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3548","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3548v1","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3548","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"pith_short_12","alias_value":"VTEP7NCZSRPD","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VTEP7NCZSRPDBSVK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VTEP7NCZ","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:VTEP7NCZSRPDBSVKHR4PHOEAFV","target":"record","payload":{"canonical_record":{"source":{"id":"1111.3548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-15T15:06:54Z","cross_cats_sorted":[],"title_canon_sha256":"00ebc21535c3ec8706375296d43706581f9734c76db3ef5de5ed287cd5060198","abstract_canon_sha256":"16aa9ceb87175b354878a54ed622c1461d85e5a8f739bb17670c469cca66ccd2"},"schema_version":"1.0"},"canonical_sha256":"acc8ffb459945e30caaa3c78f3b8802d7a3b2a95ab8a8cec096640b4364da273","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:12.861878Z","signature_b64":"tVsrEAwvqMEhITg0pf/KMNUZXUhBu3PzYC6iCDnZjuuH3nSk/6tSuGYoqbojz2mHxCEf/13os3QrzttUrMguAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acc8ffb459945e30caaa3c78f3b8802d7a3b2a95ab8a8cec096640b4364da273","last_reissued_at":"2026-05-18T02:45:12.861327Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:12.861327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.3548","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":"2026-05-18T02:45:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3pi/sfznTAdSMDZBj2ORRVTTTFRpRh0/QCvchkg5+beb+g9ABA+OcbqU9faoC6/OHf3wzangSswu1j6R6zhkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:36:36.338371Z"},"content_sha256":"0b6b9720d45293655342d72de88dd76cece501e48b1796c6d3cb2a54cc261f33","schema_version":"1.0","event_id":"sha256:0b6b9720d45293655342d72de88dd76cece501e48b1796c6d3cb2a54cc261f33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:VTEP7NCZSRPDBSVKHR4PHOEAFV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fully dynamic recognition of proper circular-arc graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Francisco J. Soulignac","submitted_at":"2011-11-15T15:06:54Z","abstract_excerpt":"We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations cost O(log n) time, where n is the number of vertices of the graph, while vertex operations cost O(log n + d) time, where d is the degree of the modified vertex. We also show incremental and decremental algorithms that work in O(1) time per inserted or removed edge. As part of our algorithm, fully dynamic connectivity and co-connectivity algorithms that work in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3548","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":"2026-05-18T02:45:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4PrRUqBE7LWpwOUbJXTT9CG0NPdwFUS8GVDc5d5IUrCjpGPww9tXpGmlesapBZwZLnhjMC/jT0CK20OUoKzbAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:36:36.338929Z"},"content_sha256":"40868d39eb46cd3651473e724bac72a0c57e523a806e62c478c1398f0efe2912","schema_version":"1.0","event_id":"sha256:40868d39eb46cd3651473e724bac72a0c57e523a806e62c478c1398f0efe2912"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VTEP7NCZSRPDBSVKHR4PHOEAFV/bundle.json","state_url":"https://pith.science/pith/VTEP7NCZSRPDBSVKHR4PHOEAFV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VTEP7NCZSRPDBSVKHR4PHOEAFV/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":"2026-06-07T01:36:36Z","links":{"resolver":"https://pith.science/pith/VTEP7NCZSRPDBSVKHR4PHOEAFV","bundle":"https://pith.science/pith/VTEP7NCZSRPDBSVKHR4PHOEAFV/bundle.json","state":"https://pith.science/pith/VTEP7NCZSRPDBSVKHR4PHOEAFV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VTEP7NCZSRPDBSVKHR4PHOEAFV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:VTEP7NCZSRPDBSVKHR4PHOEAFV","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":"16aa9ceb87175b354878a54ed622c1461d85e5a8f739bb17670c469cca66ccd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-15T15:06:54Z","title_canon_sha256":"00ebc21535c3ec8706375296d43706581f9734c76db3ef5de5ed287cd5060198"},"schema_version":"1.0","source":{"id":"1111.3548","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.3548","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"arxiv_version","alias_value":"1111.3548v1","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.3548","created_at":"2026-05-18T02:45:12Z"},{"alias_kind":"pith_short_12","alias_value":"VTEP7NCZSRPD","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"VTEP7NCZSRPDBSVK","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"VTEP7NCZ","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:40868d39eb46cd3651473e724bac72a0c57e523a806e62c478c1398f0efe2912","target":"graph","created_at":"2026-05-18T02:45:12Z","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":"We present a fully dynamic algorithm for the recognition of proper circular-arc (PCA) graphs. The allowed operations on the graph involve the insertion and removal of vertices (together with its incident edges) or edges. Edge operations cost O(log n) time, where n is the number of vertices of the graph, while vertex operations cost O(log n + d) time, where d is the degree of the modified vertex. We also show incremental and decremental algorithms that work in O(1) time per inserted or removed edge. As part of our algorithm, fully dynamic connectivity and co-connectivity algorithms that work in","authors_text":"Francisco J. Soulignac","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-15T15:06:54Z","title":"Fully dynamic recognition of proper circular-arc graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3548","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":"sha256:0b6b9720d45293655342d72de88dd76cece501e48b1796c6d3cb2a54cc261f33","target":"record","created_at":"2026-05-18T02:45:12Z","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":"16aa9ceb87175b354878a54ed622c1461d85e5a8f739bb17670c469cca66ccd2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-15T15:06:54Z","title_canon_sha256":"00ebc21535c3ec8706375296d43706581f9734c76db3ef5de5ed287cd5060198"},"schema_version":"1.0","source":{"id":"1111.3548","kind":"arxiv","version":1}},"canonical_sha256":"acc8ffb459945e30caaa3c78f3b8802d7a3b2a95ab8a8cec096640b4364da273","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acc8ffb459945e30caaa3c78f3b8802d7a3b2a95ab8a8cec096640b4364da273","first_computed_at":"2026-05-18T02:45:12.861327Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:12.861327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tVsrEAwvqMEhITg0pf/KMNUZXUhBu3PzYC6iCDnZjuuH3nSk/6tSuGYoqbojz2mHxCEf/13os3QrzttUrMguAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:12.861878Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.3548","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b6b9720d45293655342d72de88dd76cece501e48b1796c6d3cb2a54cc261f33","sha256:40868d39eb46cd3651473e724bac72a0c57e523a806e62c478c1398f0efe2912"],"state_sha256":"5df37021b46feace07ed048033679fa93f0a43dfe91bae78427fd5a3af4bd55d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G9SahvDHpMDzyMHH/2j5wYheYUAIopeXvc7/Nn78OqRFhKsx5oao+fxxlA3MdbU/2Fyw3d9uQom9f9uA/dhsBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T01:36:36.342528Z","bundle_sha256":"8fda20947ed0ab93a4c3aeb8e6d29dcc5fe935e17e042962270d397f4338ae19"}}