{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3OCJKKNZO27CAQG7JOI2PQOOG5","short_pith_number":"pith:3OCJKKNZ","canonical_record":{"source":{"id":"1509.06231","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-09-21T14:13:19Z","cross_cats_sorted":["cs.SC","math.NA"],"title_canon_sha256":"fd9a36399540058106fbb13fb91c1c5f58b6e46a61b173fe02952af4bdd38424","abstract_canon_sha256":"1207f84a58c3326f3378dd09917c883edbdc1ef152f216f8f1fe1b1a4501eb9d"},"schema_version":"1.0"},"canonical_sha256":"db849529b976be2040df4b91a7c1ce3772f1b1dfe7308b534fc4f8a18796359b","source":{"kind":"arxiv","id":"1509.06231","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06231","created_at":"2026-05-18T00:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06231v4","created_at":"2026-05-18T00:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06231","created_at":"2026-05-18T00:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"3OCJKKNZO27C","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3OCJKKNZO27CAQG7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3OCJKKNZ","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3OCJKKNZO27CAQG7JOI2PQOOG5","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06231","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-09-21T14:13:19Z","cross_cats_sorted":["cs.SC","math.NA"],"title_canon_sha256":"fd9a36399540058106fbb13fb91c1c5f58b6e46a61b173fe02952af4bdd38424","abstract_canon_sha256":"1207f84a58c3326f3378dd09917c883edbdc1ef152f216f8f1fe1b1a4501eb9d"},"schema_version":"1.0"},"canonical_sha256":"db849529b976be2040df4b91a7c1ce3772f1b1dfe7308b534fc4f8a18796359b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:59.041689Z","signature_b64":"Vem9DlHQqhFwyzUnPxCxki5CbwYVXs/b7DYlpoT7VXVVXixfLJBc+murF5MUfYfOO6vnjpsB2weggYnEuuRpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db849529b976be2040df4b91a7c1ce3772f1b1dfe7308b534fc4f8a18796359b","last_reissued_at":"2026-05-18T00:59:59.041265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:59.041265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06231","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:59:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AsS/snRCTsHuTSa4wBUmzfn1B76kUl8qs1CASVCWpr3oCUjMmadfPW9QZRWwcNaDDwkdqJcvWs6iSqXYW7XSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:21:37.928331Z"},"content_sha256":"066e3c8e1a0accd76886f23b01f20ef223859810dc953300abe4fac4f740b3d8","schema_version":"1.0","event_id":"sha256:066e3c8e1a0accd76886f23b01f20ef223859810dc953300abe4fac4f740b3d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3OCJKKNZO27CAQG7JOI2PQOOG5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.NA"],"primary_cat":"cs.NA","authors_text":"Chee Yap, Michael Sagraloff, Ruben Becker, Vikram Sharma","submitted_at":"2015-09-21T14:13:19Z","abstract_excerpt":"We describe a subdivision algorithm for isolating the complex roots of a polynomial $F\\in\\mathbb{C}[x]$. Given an oracle that provides approximations of each of the coefficients of $F$ to any absolute error bound and given an arbitrary square $\\mathcal{B}$ in the complex plane containing only simple roots of $F$, our algorithm returns disjoint isolating disks for the roots of $F$ in $\\mathcal{B}$. Our complexity analysis bounds the absolute error to which the coefficients of $F$ have to be provided, the total number of iterations, and the overall bit complexity. It further shows that the compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06231","kind":"arxiv","version":4},"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":"2026-05-18T00:59:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GpH43rb9UJdLT/Hx0wSG92FkOKX9c+0EolSLTu+QPlDrBeA1afrSu8rKrt7RYtkZRrcUs3ZQDAIzC9MXbxzFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T20:21:37.928982Z"},"content_sha256":"90695c893d5a8328ef2386f6366a367af4bb7a351386f993ed55e4d30a5991a4","schema_version":"1.0","event_id":"sha256:90695c893d5a8328ef2386f6366a367af4bb7a351386f993ed55e4d30a5991a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3OCJKKNZO27CAQG7JOI2PQOOG5/bundle.json","state_url":"https://pith.science/pith/3OCJKKNZO27CAQG7JOI2PQOOG5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3OCJKKNZO27CAQG7JOI2PQOOG5/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":"2026-05-29T20:21:37Z","links":{"resolver":"https://pith.science/pith/3OCJKKNZO27CAQG7JOI2PQOOG5","bundle":"https://pith.science/pith/3OCJKKNZO27CAQG7JOI2PQOOG5/bundle.json","state":"https://pith.science/pith/3OCJKKNZO27CAQG7JOI2PQOOG5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3OCJKKNZO27CAQG7JOI2PQOOG5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3OCJKKNZO27CAQG7JOI2PQOOG5","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":"1207f84a58c3326f3378dd09917c883edbdc1ef152f216f8f1fe1b1a4501eb9d","cross_cats_sorted":["cs.SC","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-09-21T14:13:19Z","title_canon_sha256":"fd9a36399540058106fbb13fb91c1c5f58b6e46a61b173fe02952af4bdd38424"},"schema_version":"1.0","source":{"id":"1509.06231","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06231","created_at":"2026-05-18T00:59:59Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06231v4","created_at":"2026-05-18T00:59:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06231","created_at":"2026-05-18T00:59:59Z"},{"alias_kind":"pith_short_12","alias_value":"3OCJKKNZO27C","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3OCJKKNZO27CAQG7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3OCJKKNZ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:90695c893d5a8328ef2386f6366a367af4bb7a351386f993ed55e4d30a5991a4","target":"graph","created_at":"2026-05-18T00:59:59Z","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 describe a subdivision algorithm for isolating the complex roots of a polynomial $F\\in\\mathbb{C}[x]$. Given an oracle that provides approximations of each of the coefficients of $F$ to any absolute error bound and given an arbitrary square $\\mathcal{B}$ in the complex plane containing only simple roots of $F$, our algorithm returns disjoint isolating disks for the roots of $F$ in $\\mathcal{B}$. Our complexity analysis bounds the absolute error to which the coefficients of $F$ have to be provided, the total number of iterations, and the overall bit complexity. It further shows that the compl","authors_text":"Chee Yap, Michael Sagraloff, Ruben Becker, Vikram Sharma","cross_cats":["cs.SC","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-09-21T14:13:19Z","title":"A Near-Optimal Subdivision Algorithm for Complex Root Isolation based on the Pellet Test and Newton Iteration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06231","kind":"arxiv","version":4},"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":"sha256:066e3c8e1a0accd76886f23b01f20ef223859810dc953300abe4fac4f740b3d8","target":"record","created_at":"2026-05-18T00:59:59Z","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":"1207f84a58c3326f3378dd09917c883edbdc1ef152f216f8f1fe1b1a4501eb9d","cross_cats_sorted":["cs.SC","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NA","submitted_at":"2015-09-21T14:13:19Z","title_canon_sha256":"fd9a36399540058106fbb13fb91c1c5f58b6e46a61b173fe02952af4bdd38424"},"schema_version":"1.0","source":{"id":"1509.06231","kind":"arxiv","version":4}},"canonical_sha256":"db849529b976be2040df4b91a7c1ce3772f1b1dfe7308b534fc4f8a18796359b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db849529b976be2040df4b91a7c1ce3772f1b1dfe7308b534fc4f8a18796359b","first_computed_at":"2026-05-18T00:59:59.041265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:59.041265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vem9DlHQqhFwyzUnPxCxki5CbwYVXs/b7DYlpoT7VXVVXixfLJBc+murF5MUfYfOO6vnjpsB2weggYnEuuRpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:59.041689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06231","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:066e3c8e1a0accd76886f23b01f20ef223859810dc953300abe4fac4f740b3d8","sha256:90695c893d5a8328ef2386f6366a367af4bb7a351386f993ed55e4d30a5991a4"],"state_sha256":"3bf6347018f41ba3cfd54d44447c54aee683637744c3be4825455a9b7948b044"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JuYr/YSoY9GiX9ynFGfy7dBRflTkFLrlkVmXyugB5foRlZNUnIh1fqzCZhe+LOs3qRfA3HtQCycAGCButC4bBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T20:21:37.932451Z","bundle_sha256":"6da7ce48c470b0f26750b9a47078250a048f4b26f550f75f41ebaefe9fd40a95"}}