{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DKYNMVYKIMSCJX2ZFS3MQA3LIF","short_pith_number":"pith:DKYNMVYK","canonical_record":{"source":{"id":"1901.10317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-01-28T10:38:46Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"1fc31b47f4f146f87c1bf4123c38d6418081d6cf8bec9a2dd0af394d3e4c855e","abstract_canon_sha256":"66d2ba7e4529252f6c276367344488bb58c26812580f05085f9d43c7db7c897b"},"schema_version":"1.0"},"canonical_sha256":"1ab0d6570a432424df592cb6c8036b4172e118fe319766a839faac1a0e8ee157","source":{"kind":"arxiv","id":"1901.10317","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10317","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10317v1","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10317","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"DKYNMVYKIMSC","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DKYNMVYKIMSCJX2Z","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DKYNMVYK","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DKYNMVYKIMSCJX2ZFS3MQA3LIF","target":"record","payload":{"canonical_record":{"source":{"id":"1901.10317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-01-28T10:38:46Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"1fc31b47f4f146f87c1bf4123c38d6418081d6cf8bec9a2dd0af394d3e4c855e","abstract_canon_sha256":"66d2ba7e4529252f6c276367344488bb58c26812580f05085f9d43c7db7c897b"},"schema_version":"1.0"},"canonical_sha256":"1ab0d6570a432424df592cb6c8036b4172e118fe319766a839faac1a0e8ee157","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:15.618742Z","signature_b64":"ap/FRePRYMWl02t44+YvvExozeCFIJ+XLetnO7ZtfUSFnzGIAlmT4hXiaJY+Wrks8zPZNLY67Bp8pCQZUT2IBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ab0d6570a432424df592cb6c8036b4172e118fe319766a839faac1a0e8ee157","last_reissued_at":"2026-05-17T23:55:15.618331Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:15.618331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.10317","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":"2026-05-17T23:55:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rT2BH9w9HgqhCJOcSkQ2Gzg3gTUeOBtprn7WmenD4J0KLybM+cgpujTD8Yi5XleyTEGfhgElLje5MKCsLXb3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:05:43.210261Z"},"content_sha256":"de8f29e587e4df9313973b22e1688c57ab77c7ae6d04c08e4149f43ddc168ef1","schema_version":"1.0","event_id":"sha256:de8f29e587e4df9313973b22e1688c57ab77c7ae6d04c08e4149f43ddc168ef1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DKYNMVYKIMSCJX2ZFS3MQA3LIF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Complexity of Computing the Topology of Real Algebraic Space Curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.SC","authors_text":"Jin-San Cheng, Kai Jin","submitted_at":"2019-01-28T10:38:46Z","abstract_excerpt":"In this paper, we present a deterministic algorithm to find a strong generic position for an algebraic space curve. We modify our existing algorithm for computing the topology of an algebraic space curve and analyze the bit complexity of the algorithm. It is $\\tilde{\\mathcal {O}} (N^{20})$, where $N=\\max\\{d,\\tau\\}$, $d, \\tau$ are the degree bound and the bit size bound of the coefficients of the defining polynomials of the algebraic space curve. To our knowledge, this is the best bound among the existing work. It gains the existing results at least $N^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10317","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":"2026-05-17T23:55:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Inbbf29BdMT20jiU9nktRQNEsKqjgTs+Tyg1QHAdFfMkGOQj613uOSt6k7o8cOhoJ4x4/8pHmicbQMqBz/YbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:05:43.211006Z"},"content_sha256":"0149b5f6d454e76ab816edd698737fc178ade2d0506233266405f6d4d5351f1b","schema_version":"1.0","event_id":"sha256:0149b5f6d454e76ab816edd698737fc178ade2d0506233266405f6d4d5351f1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKYNMVYKIMSCJX2ZFS3MQA3LIF/bundle.json","state_url":"https://pith.science/pith/DKYNMVYKIMSCJX2ZFS3MQA3LIF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKYNMVYKIMSCJX2ZFS3MQA3LIF/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":"2026-06-09T19:05:43Z","links":{"resolver":"https://pith.science/pith/DKYNMVYKIMSCJX2ZFS3MQA3LIF","bundle":"https://pith.science/pith/DKYNMVYKIMSCJX2ZFS3MQA3LIF/bundle.json","state":"https://pith.science/pith/DKYNMVYKIMSCJX2ZFS3MQA3LIF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKYNMVYKIMSCJX2ZFS3MQA3LIF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DKYNMVYKIMSCJX2ZFS3MQA3LIF","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":"66d2ba7e4529252f6c276367344488bb58c26812580f05085f9d43c7db7c897b","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-01-28T10:38:46Z","title_canon_sha256":"1fc31b47f4f146f87c1bf4123c38d6418081d6cf8bec9a2dd0af394d3e4c855e"},"schema_version":"1.0","source":{"id":"1901.10317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.10317","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"arxiv_version","alias_value":"1901.10317v1","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10317","created_at":"2026-05-17T23:55:15Z"},{"alias_kind":"pith_short_12","alias_value":"DKYNMVYKIMSC","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"DKYNMVYKIMSCJX2Z","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"DKYNMVYK","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:0149b5f6d454e76ab816edd698737fc178ade2d0506233266405f6d4d5351f1b","target":"graph","created_at":"2026-05-17T23:55:15Z","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 present a deterministic algorithm to find a strong generic position for an algebraic space curve. We modify our existing algorithm for computing the topology of an algebraic space curve and analyze the bit complexity of the algorithm. It is $\\tilde{\\mathcal {O}} (N^{20})$, where $N=\\max\\{d,\\tau\\}$, $d, \\tau$ are the degree bound and the bit size bound of the coefficients of the defining polynomials of the algebraic space curve. To our knowledge, this is the best bound among the existing work. It gains the existing results at least $N^2$.","authors_text":"Jin-San Cheng, Kai Jin","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-01-28T10:38:46Z","title":"On the Complexity of Computing the Topology of Real Algebraic Space Curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10317","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:de8f29e587e4df9313973b22e1688c57ab77c7ae6d04c08e4149f43ddc168ef1","target":"record","created_at":"2026-05-17T23:55:15Z","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":"66d2ba7e4529252f6c276367344488bb58c26812580f05085f9d43c7db7c897b","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-01-28T10:38:46Z","title_canon_sha256":"1fc31b47f4f146f87c1bf4123c38d6418081d6cf8bec9a2dd0af394d3e4c855e"},"schema_version":"1.0","source":{"id":"1901.10317","kind":"arxiv","version":1}},"canonical_sha256":"1ab0d6570a432424df592cb6c8036b4172e118fe319766a839faac1a0e8ee157","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ab0d6570a432424df592cb6c8036b4172e118fe319766a839faac1a0e8ee157","first_computed_at":"2026-05-17T23:55:15.618331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:15.618331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ap/FRePRYMWl02t44+YvvExozeCFIJ+XLetnO7ZtfUSFnzGIAlmT4hXiaJY+Wrks8zPZNLY67Bp8pCQZUT2IBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:15.618742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.10317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de8f29e587e4df9313973b22e1688c57ab77c7ae6d04c08e4149f43ddc168ef1","sha256:0149b5f6d454e76ab816edd698737fc178ade2d0506233266405f6d4d5351f1b"],"state_sha256":"ece2440e56b2dfba88fd353df2647b2d603be2efeafc76ce430a9c5f2e4b6c08"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tNNp3eBZHvTYVlHPC5FVudryPhIlq/5AM6s7FoC09nW3v6ahqZf5vMBEGFGH4pfdMv5sN7p/ZqqIYK1X2JU0AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:05:43.215207Z","bundle_sha256":"c8c446b310379be72c9b97c89efe98abe2fde028d0194544a96ffb77b2f87364"}}