{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:QUK2JM5MCVOECY65YBZIQ57BXS","short_pith_number":"pith:QUK2JM5M","canonical_record":{"source":{"id":"2011.09591","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-11-19T00:07:43Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"0d59a4f6e703dcc2e443275ec00b64061738dd0209c4120461d72088aaf05be6","abstract_canon_sha256":"d6ff03b1565b5b4076426e561020c48f1c7b822e507f0f1f78d28b6de6ae2046"},"schema_version":"1.0"},"canonical_sha256":"8515a4b3ac155c4163ddc0728877e1bc8ed5a590e2d351550523645115d0c5d3","source":{"kind":"arxiv","id":"2011.09591","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09591","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09591v1","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09591","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"QUK2JM5MCVOE","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_16","alias_value":"QUK2JM5MCVOECY65","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_8","alias_value":"QUK2JM5M","created_at":"2026-07-05T01:52:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:QUK2JM5MCVOECY65YBZIQ57BXS","target":"record","payload":{"canonical_record":{"source":{"id":"2011.09591","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-11-19T00:07:43Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"0d59a4f6e703dcc2e443275ec00b64061738dd0209c4120461d72088aaf05be6","abstract_canon_sha256":"d6ff03b1565b5b4076426e561020c48f1c7b822e507f0f1f78d28b6de6ae2046"},"schema_version":"1.0"},"canonical_sha256":"8515a4b3ac155c4163ddc0728877e1bc8ed5a590e2d351550523645115d0c5d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:50.203884Z","signature_b64":"KnpQbomf0J1PGKwvwYCE4rAU0F7K13w8B8WU5Gn4CJ27C21m3rSaOaOaV644M1ZUabWtEJlydrUFXwlfJiBaDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8515a4b3ac155c4163ddc0728877e1bc8ed5a590e2d351550523645115d0c5d3","last_reissued_at":"2026-07-05T01:52:50.203465Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:50.203465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2011.09591","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":"2026-07-05T01:52:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b7ZciRkNs9MG/dGKXl4knuIVHD8wmeeM6pIEzoJFWeb56t33G/oYKu5H8SGs9q/IjWtbr19wXpmmYVuGZPQ4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:42:16.214447Z"},"content_sha256":"b442a3cdf631a84c3790dd36ec251ab9d87c1fdd4ff105a2d78652dd670b66e5","schema_version":"1.0","event_id":"sha256:b442a3cdf631a84c3790dd36ec251ab9d87c1fdd4ff105a2d78652dd670b66e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:QUK2JM5MCVOECY65YBZIQ57BXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algorithms for Diameters of Unicycle Graphs and Diameter-Optimally Augmenting Trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Haitao Wang, Yiming Zhao","submitted_at":"2020-11-19T00:07:43Z","abstract_excerpt":"We consider the problem of computing the diameter of a unicycle graph (i.e., a graph with a unique cycle). We present an O(n) time algorithm for the problem, where n is the number of vertices of the graph. This improves the previous best O(n \\log n) time solution [Oh and Ahn, ISAAC 2016]. Using this algorithm as a subroutine, we solve the problem of adding a shortcut to a tree so that the diameter of the new graph (which is a unicycle graph) is minimized; our algorithm takes O(n^2 \\log n) time and O(n) space. The previous best algorithms solve the problem in O(n^2 \\log^3 n) time and O(n) space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09591","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/2011.09591/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":"2026-07-05T01:52:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QKZw7vEbQ9gFQWhg+BaZ7UtoEv5OqUopgBEqf4ZP0NUWThab1D+aTiheXcEv+zN2DPbjMg+CXIRNtYPtPD9eBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:42:16.214960Z"},"content_sha256":"836564d959b078dd62f1bdb64bd4ddb1d3273b6fd3f95aae6d0abbd140a18a32","schema_version":"1.0","event_id":"sha256:836564d959b078dd62f1bdb64bd4ddb1d3273b6fd3f95aae6d0abbd140a18a32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS/bundle.json","state_url":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QUK2JM5MCVOECY65YBZIQ57BXS/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":"2026-08-14T17:42:16Z","links":{"resolver":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS","bundle":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS/bundle.json","state":"https://pith.science/pith/QUK2JM5MCVOECY65YBZIQ57BXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QUK2JM5MCVOECY65YBZIQ57BXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:QUK2JM5MCVOECY65YBZIQ57BXS","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":"d6ff03b1565b5b4076426e561020c48f1c7b822e507f0f1f78d28b6de6ae2046","cross_cats_sorted":["cs.CG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-11-19T00:07:43Z","title_canon_sha256":"0d59a4f6e703dcc2e443275ec00b64061738dd0209c4120461d72088aaf05be6"},"schema_version":"1.0","source":{"id":"2011.09591","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2011.09591","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"2011.09591v1","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2011.09591","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"QUK2JM5MCVOE","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_16","alias_value":"QUK2JM5MCVOECY65","created_at":"2026-07-05T01:52:50Z"},{"alias_kind":"pith_short_8","alias_value":"QUK2JM5M","created_at":"2026-07-05T01:52:50Z"}],"graph_snapshots":[{"event_id":"sha256:836564d959b078dd62f1bdb64bd4ddb1d3273b6fd3f95aae6d0abbd140a18a32","target":"graph","created_at":"2026-07-05T01:52:50Z","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/2011.09591/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of computing the diameter of a unicycle graph (i.e., a graph with a unique cycle). We present an O(n) time algorithm for the problem, where n is the number of vertices of the graph. This improves the previous best O(n \\log n) time solution [Oh and Ahn, ISAAC 2016]. Using this algorithm as a subroutine, we solve the problem of adding a shortcut to a tree so that the diameter of the new graph (which is a unicycle graph) is minimized; our algorithm takes O(n^2 \\log n) time and O(n) space. The previous best algorithms solve the problem in O(n^2 \\log^3 n) time and O(n) space","authors_text":"Haitao Wang, Yiming Zhao","cross_cats":["cs.CG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-11-19T00:07:43Z","title":"Algorithms for Diameters of Unicycle Graphs and Diameter-Optimally Augmenting Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2011.09591","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:b442a3cdf631a84c3790dd36ec251ab9d87c1fdd4ff105a2d78652dd670b66e5","target":"record","created_at":"2026-07-05T01:52:50Z","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":"d6ff03b1565b5b4076426e561020c48f1c7b822e507f0f1f78d28b6de6ae2046","cross_cats_sorted":["cs.CG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-11-19T00:07:43Z","title_canon_sha256":"0d59a4f6e703dcc2e443275ec00b64061738dd0209c4120461d72088aaf05be6"},"schema_version":"1.0","source":{"id":"2011.09591","kind":"arxiv","version":1}},"canonical_sha256":"8515a4b3ac155c4163ddc0728877e1bc8ed5a590e2d351550523645115d0c5d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8515a4b3ac155c4163ddc0728877e1bc8ed5a590e2d351550523645115d0c5d3","first_computed_at":"2026-07-05T01:52:50.203465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:52:50.203465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KnpQbomf0J1PGKwvwYCE4rAU0F7K13w8B8WU5Gn4CJ27C21m3rSaOaOaV644M1ZUabWtEJlydrUFXwlfJiBaDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:52:50.203884Z","signed_message":"canonical_sha256_bytes"},"source_id":"2011.09591","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b442a3cdf631a84c3790dd36ec251ab9d87c1fdd4ff105a2d78652dd670b66e5","sha256:836564d959b078dd62f1bdb64bd4ddb1d3273b6fd3f95aae6d0abbd140a18a32"],"state_sha256":"ed209cee638762464e6f24042a274a854b920dc3cf91b954681f418689e624ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tt1J0hd+rxh5BDhE64INBZvx/BccfoM9ZQWn7mbEDlH237BNHCmDspR2KqehGoW+fKjv8nK5c/PafdhofuguDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T17:42:16.247090Z","bundle_sha256":"4a8e61a5cb826b38a23e1c2eda1aed838436d81d8975018551c6823e4288db94"}}