{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5OOF5FGWDEC6ZC4LOKM7NORJQZ","short_pith_number":"pith:5OOF5FGW","canonical_record":{"source":{"id":"1505.03432","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-13T15:40:22Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dc065f5026bfb36d1a7d7ef54f690e0b6f7684d4450161138277b0da348ff4b5","abstract_canon_sha256":"bc8fd1a1fef6e5427577ba2ea7a4eb6d9cbe8fc96680fae065b46fe517a41773"},"schema_version":"1.0"},"canonical_sha256":"eb9c5e94d61905ec8b8b7299f6ba29865e207a587c76b90b52a361b257ac6ada","source":{"kind":"arxiv","id":"1505.03432","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03432","created_at":"2026-05-18T01:15:52Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03432v2","created_at":"2026-05-18T01:15:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03432","created_at":"2026-05-18T01:15:52Z"},{"alias_kind":"pith_short_12","alias_value":"5OOF5FGWDEC6","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5OOF5FGWDEC6ZC4L","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5OOF5FGW","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5OOF5FGWDEC6ZC4LOKM7NORJQZ","target":"record","payload":{"canonical_record":{"source":{"id":"1505.03432","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-13T15:40:22Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"dc065f5026bfb36d1a7d7ef54f690e0b6f7684d4450161138277b0da348ff4b5","abstract_canon_sha256":"bc8fd1a1fef6e5427577ba2ea7a4eb6d9cbe8fc96680fae065b46fe517a41773"},"schema_version":"1.0"},"canonical_sha256":"eb9c5e94d61905ec8b8b7299f6ba29865e207a587c76b90b52a361b257ac6ada","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:52.911676Z","signature_b64":"epRJnlztfpfrjMdY36wvYpwLybbseVzqX+TmWwLuedu5aWN8E1J90IaKUFdSfsUIOS8WUV3cB5omKFIK649dBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb9c5e94d61905ec8b8b7299f6ba29865e207a587c76b90b52a361b257ac6ada","last_reissued_at":"2026-05-18T01:15:52.911260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:52.911260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.03432","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":"2026-05-18T01:15:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+vvOOWnu54LE3YPptnQjfSVS4kRkd87x+1sYv/AJ6ca0nDjM3I7K51RX1miaa+U5tI5h/F0yPZE5HmtT78eDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:54:03.930054Z"},"content_sha256":"06fe3c8bafc77bd145b6524a8bfc7b018653b133f02c6bfb120e80d7ce4f689b","schema_version":"1.0","event_id":"sha256:06fe3c8bafc77bd145b6524a8bfc7b018653b133f02c6bfb120e80d7ce4f689b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5OOF5FGWDEC6ZC4LOKM7NORJQZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An epsilon-delta bound for plane algebraic curves and its use for certified homotopy continuation of systems of plane algebraic curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Stefan Kranich","submitted_at":"2015-05-13T15:40:22Z","abstract_excerpt":"We explain how, given a plane algebraic curve $\\mathcal{C}\\colon f(x,y) = 0$, $x_1 \\in \\mathbb{C}$ not a singularity of $y$ w.r.t. $x$, and $\\varepsilon > 0$, we can compute $\\delta > 0$ such that $|y_j(x_1) - y_j(x_2)| < \\varepsilon$ for all holomorphic functions $y_j(x)$ which satisfy $f(x, y_j(x)) = 0$ in a neighbourhood of $x_1$ and for all $x_2$ with $|x_1 - x_2| < \\delta$. Consequently, we obtain an algorithm for reliable homotopy continuation of plane algebraic curves. As an example application, we study continuous deformation of closed discrete Darboux transforms.\n  Moreover, we discus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03432","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":"2026-05-18T01:15:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mGHpBdDNe2pnITwwkm9GrJcEQtK+r80HoLDD+lDtNA3Kli7CfubD65/AoBCSB78mwHRDEFq26hShOjtedP/9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T04:54:03.930416Z"},"content_sha256":"a83995fa02e3a4a963be703f8fdc0ef76b91df1223288f04cebd6f56c55b48e0","schema_version":"1.0","event_id":"sha256:a83995fa02e3a4a963be703f8fdc0ef76b91df1223288f04cebd6f56c55b48e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5OOF5FGWDEC6ZC4LOKM7NORJQZ/bundle.json","state_url":"https://pith.science/pith/5OOF5FGWDEC6ZC4LOKM7NORJQZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5OOF5FGWDEC6ZC4LOKM7NORJQZ/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":"2026-06-26T04:54:03Z","links":{"resolver":"https://pith.science/pith/5OOF5FGWDEC6ZC4LOKM7NORJQZ","bundle":"https://pith.science/pith/5OOF5FGWDEC6ZC4LOKM7NORJQZ/bundle.json","state":"https://pith.science/pith/5OOF5FGWDEC6ZC4LOKM7NORJQZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5OOF5FGWDEC6ZC4LOKM7NORJQZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5OOF5FGWDEC6ZC4LOKM7NORJQZ","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":"bc8fd1a1fef6e5427577ba2ea7a4eb6d9cbe8fc96680fae065b46fe517a41773","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-13T15:40:22Z","title_canon_sha256":"dc065f5026bfb36d1a7d7ef54f690e0b6f7684d4450161138277b0da348ff4b5"},"schema_version":"1.0","source":{"id":"1505.03432","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03432","created_at":"2026-05-18T01:15:52Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03432v2","created_at":"2026-05-18T01:15:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03432","created_at":"2026-05-18T01:15:52Z"},{"alias_kind":"pith_short_12","alias_value":"5OOF5FGWDEC6","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5OOF5FGWDEC6ZC4L","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5OOF5FGW","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:a83995fa02e3a4a963be703f8fdc0ef76b91df1223288f04cebd6f56c55b48e0","target":"graph","created_at":"2026-05-18T01:15:52Z","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 explain how, given a plane algebraic curve $\\mathcal{C}\\colon f(x,y) = 0$, $x_1 \\in \\mathbb{C}$ not a singularity of $y$ w.r.t. $x$, and $\\varepsilon > 0$, we can compute $\\delta > 0$ such that $|y_j(x_1) - y_j(x_2)| < \\varepsilon$ for all holomorphic functions $y_j(x)$ which satisfy $f(x, y_j(x)) = 0$ in a neighbourhood of $x_1$ and for all $x_2$ with $|x_1 - x_2| < \\delta$. Consequently, we obtain an algorithm for reliable homotopy continuation of plane algebraic curves. As an example application, we study continuous deformation of closed discrete Darboux transforms.\n  Moreover, we discus","authors_text":"Stefan Kranich","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-13T15:40:22Z","title":"An epsilon-delta bound for plane algebraic curves and its use for certified homotopy continuation of systems of plane algebraic curves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03432","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":"sha256:06fe3c8bafc77bd145b6524a8bfc7b018653b133f02c6bfb120e80d7ce4f689b","target":"record","created_at":"2026-05-18T01:15:52Z","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":"bc8fd1a1fef6e5427577ba2ea7a4eb6d9cbe8fc96680fae065b46fe517a41773","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-05-13T15:40:22Z","title_canon_sha256":"dc065f5026bfb36d1a7d7ef54f690e0b6f7684d4450161138277b0da348ff4b5"},"schema_version":"1.0","source":{"id":"1505.03432","kind":"arxiv","version":2}},"canonical_sha256":"eb9c5e94d61905ec8b8b7299f6ba29865e207a587c76b90b52a361b257ac6ada","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb9c5e94d61905ec8b8b7299f6ba29865e207a587c76b90b52a361b257ac6ada","first_computed_at":"2026-05-18T01:15:52.911260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:52.911260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"epRJnlztfpfrjMdY36wvYpwLybbseVzqX+TmWwLuedu5aWN8E1J90IaKUFdSfsUIOS8WUV3cB5omKFIK649dBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:52.911676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03432","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06fe3c8bafc77bd145b6524a8bfc7b018653b133f02c6bfb120e80d7ce4f689b","sha256:a83995fa02e3a4a963be703f8fdc0ef76b91df1223288f04cebd6f56c55b48e0"],"state_sha256":"7d5833869ed972f22672f3dc9bfa5640541cbf1a447f3d69fc387334dde17f63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a5Qjhqz8VVGXszoc1T+DbBodANCluroeLb20umEUB5CkcqR2xj9Pn4mB7RPb2j2Vf+F82E2j5w4gHIRY0asZAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T04:54:03.932363Z","bundle_sha256":"8abdac2eaef0df221e207e16b6f335032930d55d421c36f0e9585de14958b437"}}