{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:T7OFDYDKQ6PKJNJDVYPDGOUSBL","short_pith_number":"pith:T7OFDYDK","canonical_record":{"source":{"id":"1904.03117","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-05T15:20:32Z","cross_cats_sorted":[],"title_canon_sha256":"08a255fbc6878953b00738f55d5d5b97421433f1fb2dd559e250f128eb049fee","abstract_canon_sha256":"de24f5c5362a1bbf33f0f6ed1298ea3b361634e49dadb7c9ca75ca77a3c1193c"},"schema_version":"1.0"},"canonical_sha256":"9fdc51e06a879ea4b523ae1e333a920ac803b6989ccbe7035e3a82a08d248654","source":{"kind":"arxiv","id":"1904.03117","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03117","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03117v2","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03117","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"T7OFDYDKQ6PK","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T7OFDYDKQ6PKJNJD","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T7OFDYDK","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:T7OFDYDKQ6PKJNJDVYPDGOUSBL","target":"record","payload":{"canonical_record":{"source":{"id":"1904.03117","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-05T15:20:32Z","cross_cats_sorted":[],"title_canon_sha256":"08a255fbc6878953b00738f55d5d5b97421433f1fb2dd559e250f128eb049fee","abstract_canon_sha256":"de24f5c5362a1bbf33f0f6ed1298ea3b361634e49dadb7c9ca75ca77a3c1193c"},"schema_version":"1.0"},"canonical_sha256":"9fdc51e06a879ea4b523ae1e333a920ac803b6989ccbe7035e3a82a08d248654","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:08.500629Z","signature_b64":"p59euXRqQBS/AVAazVlB68YGdr63gqHMUFJOX8b28I3P0PBadfOknbTLPwW5qAeTK5sWalZv5AK4oY4acHeRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fdc51e06a879ea4b523ae1e333a920ac803b6989ccbe7035e3a82a08d248654","last_reissued_at":"2026-05-17T23:49:08.499990Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:08.499990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.03117","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:49:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P2r/Lv2o7P6CfvIBeCkOyDBsBBvkLvd/BFOBmpo0Ss3bNvBwl+gxOk911CCJuYFQRCApKirAwR8mC1Jra1pnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:55:32.735952Z"},"content_sha256":"a98f8d77f87d0e7649385c92cae7bc91c7b1630cbbe4c71880d47b948be805ee","schema_version":"1.0","event_id":"sha256:a98f8d77f87d0e7649385c92cae7bc91c7b1630cbbe4c71880d47b948be805ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:T7OFDYDKQ6PKJNJDVYPDGOUSBL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Knot Diagrams of Treewidth Two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alexander Grigoriev, Benjamin Burton, Fedor V. Fomin, Hans L. Bodlaender","submitted_at":"2019-04-05T15:20:32Z","abstract_excerpt":"In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the unknot? We also show that for a link diagram of treewidth two we can test in linear time if it represents the unlink. From the algorithm, it follows that a diagram of the unknot of treewidth 2 can always be reduced to the trivial diagram with at most $n$ (un)twist and (un)poke Reidemeister moves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03117","kind":"arxiv","version":2},"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":"2026-05-17T23:49:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J4iiiqE271Md9SGCplffhX53+K1xIXJsqPL1Q1n6AMuaMw/tKX0CfFRppEyny4qEFMnd7YVJbuZO0eIRQlSdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:55:32.736631Z"},"content_sha256":"babe3cd4c3c708733e20e37456ef7b26dafee09940933ea8d4ce99961c54abec","schema_version":"1.0","event_id":"sha256:babe3cd4c3c708733e20e37456ef7b26dafee09940933ea8d4ce99961c54abec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7OFDYDKQ6PKJNJDVYPDGOUSBL/bundle.json","state_url":"https://pith.science/pith/T7OFDYDKQ6PKJNJDVYPDGOUSBL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7OFDYDKQ6PKJNJDVYPDGOUSBL/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":"2026-05-27T00:55:32Z","links":{"resolver":"https://pith.science/pith/T7OFDYDKQ6PKJNJDVYPDGOUSBL","bundle":"https://pith.science/pith/T7OFDYDKQ6PKJNJDVYPDGOUSBL/bundle.json","state":"https://pith.science/pith/T7OFDYDKQ6PKJNJDVYPDGOUSBL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7OFDYDKQ6PKJNJDVYPDGOUSBL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:T7OFDYDKQ6PKJNJDVYPDGOUSBL","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":"de24f5c5362a1bbf33f0f6ed1298ea3b361634e49dadb7c9ca75ca77a3c1193c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-05T15:20:32Z","title_canon_sha256":"08a255fbc6878953b00738f55d5d5b97421433f1fb2dd559e250f128eb049fee"},"schema_version":"1.0","source":{"id":"1904.03117","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.03117","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"arxiv_version","alias_value":"1904.03117v2","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03117","created_at":"2026-05-17T23:49:08Z"},{"alias_kind":"pith_short_12","alias_value":"T7OFDYDKQ6PK","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"T7OFDYDKQ6PKJNJD","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"T7OFDYDK","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:babe3cd4c3c708733e20e37456ef7b26dafee09940933ea8d4ce99961c54abec","target":"graph","created_at":"2026-05-17T23:49:08Z","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":"In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the unknot? We also show that for a link diagram of treewidth two we can test in linear time if it represents the unlink. From the algorithm, it follows that a diagram of the unknot of treewidth 2 can always be reduced to the trivial diagram with at most $n$ (un)twist and (un)poke Reidemeister moves.","authors_text":"Alexander Grigoriev, Benjamin Burton, Fedor V. Fomin, Hans L. Bodlaender","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-05T15:20:32Z","title":"Knot Diagrams of Treewidth Two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03117","kind":"arxiv","version":2},"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:a98f8d77f87d0e7649385c92cae7bc91c7b1630cbbe4c71880d47b948be805ee","target":"record","created_at":"2026-05-17T23:49:08Z","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":"de24f5c5362a1bbf33f0f6ed1298ea3b361634e49dadb7c9ca75ca77a3c1193c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-05T15:20:32Z","title_canon_sha256":"08a255fbc6878953b00738f55d5d5b97421433f1fb2dd559e250f128eb049fee"},"schema_version":"1.0","source":{"id":"1904.03117","kind":"arxiv","version":2}},"canonical_sha256":"9fdc51e06a879ea4b523ae1e333a920ac803b6989ccbe7035e3a82a08d248654","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fdc51e06a879ea4b523ae1e333a920ac803b6989ccbe7035e3a82a08d248654","first_computed_at":"2026-05-17T23:49:08.499990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:08.499990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p59euXRqQBS/AVAazVlB68YGdr63gqHMUFJOX8b28I3P0PBadfOknbTLPwW5qAeTK5sWalZv5AK4oY4acHeRDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:08.500629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.03117","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a98f8d77f87d0e7649385c92cae7bc91c7b1630cbbe4c71880d47b948be805ee","sha256:babe3cd4c3c708733e20e37456ef7b26dafee09940933ea8d4ce99961c54abec"],"state_sha256":"1c187796a5fecc07d680d24872fe17f9f30ad33696b07770b59b91166e605218"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ao3ysBQWiK2rY43Uk5KRnw+kLVsT1F4NyO8TEyDqL1zb+RvRyXljyua8XTgpIyboIoKkWRjJ/0oUdR03oMRIDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:55:32.739070Z","bundle_sha256":"aea7034356bee39801ef45d87ec13bcf116af0263264d72ea86b6291104e69d8"}}