{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YVIS5NXNR5TKDL4FQCGVBNBZTX","short_pith_number":"pith:YVIS5NXN","canonical_record":{"source":{"id":"1702.04935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-16T12:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"dcc206d62e849b950b8043892e583b4a32f197d801d6bf7e198b54b0bcdaf485","abstract_canon_sha256":"3bcd75d0a0e5d52cdb3a24a243191b67be31f9d1292fa94bbaf836f8255a40cf"},"schema_version":"1.0"},"canonical_sha256":"c5512eb6ed8f66a1af85808d50b4399dc4016938cf18cbb51b6ee3baae28bde0","source":{"kind":"arxiv","id":"1702.04935","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04935","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04935v1","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04935","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"YVIS5NXNR5TK","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YVIS5NXNR5TKDL4F","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YVIS5NXN","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YVIS5NXNR5TKDL4FQCGVBNBZTX","target":"record","payload":{"canonical_record":{"source":{"id":"1702.04935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-16T12:01:02Z","cross_cats_sorted":[],"title_canon_sha256":"dcc206d62e849b950b8043892e583b4a32f197d801d6bf7e198b54b0bcdaf485","abstract_canon_sha256":"3bcd75d0a0e5d52cdb3a24a243191b67be31f9d1292fa94bbaf836f8255a40cf"},"schema_version":"1.0"},"canonical_sha256":"c5512eb6ed8f66a1af85808d50b4399dc4016938cf18cbb51b6ee3baae28bde0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:45.938863Z","signature_b64":"SvLWWY0RRD6X73PcOCmQMFJeebKPzBT8lfIu65vDH/grzPQh7gaiJQKjV7dTe1DwuH1c8iqFywSI5kSDe/wNBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5512eb6ed8f66a1af85808d50b4399dc4016938cf18cbb51b6ee3baae28bde0","last_reissued_at":"2026-05-18T00:23:45.938380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:45.938380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.04935","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":"2026-05-18T00:23:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fbljQGzQKhznAEt8qkhPn59nMSHtPgD+RqRQYfV+mNxqiJw4Bc+f8wKhW3gvhZ9+sUgFYW6y+tZoLJTTIDG9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:08:06.109296Z"},"content_sha256":"bb2fe60ff46387987d567be7a7aa310519d129c235724cfdd7394e96da4c7e29","schema_version":"1.0","event_id":"sha256:bb2fe60ff46387987d567be7a7aa310519d129c235724cfdd7394e96da4c7e29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YVIS5NXNR5TKDL4FQCGVBNBZTX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weierstrass method for quaternionic polynomial root-finding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Fernando Miranda, M. Irene Falc\\~ao, M. Joana Soares, Ricardo Severino","submitted_at":"2017-02-16T12:01:02Z","abstract_excerpt":"Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas which motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper we propose a Weierstrass-like method for finding simultaneously {\\sl all} the zeros of unilateral quaternion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04935","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":"2026-05-18T00:23:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nYjinlaJr5NZ3hKBjTTUYONN1J7Xv1FItSrVbOcvJk0RohT/mu9z9JAUIUcePh8kmNP49sHaDv9XhKuLLDytDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T10:08:06.109679Z"},"content_sha256":"0cdc0ce9e1dc45f9367ab12eee4fd7d553fb1a53b3f35cd5bc4e7ac200247798","schema_version":"1.0","event_id":"sha256:0cdc0ce9e1dc45f9367ab12eee4fd7d553fb1a53b3f35cd5bc4e7ac200247798"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YVIS5NXNR5TKDL4FQCGVBNBZTX/bundle.json","state_url":"https://pith.science/pith/YVIS5NXNR5TKDL4FQCGVBNBZTX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YVIS5NXNR5TKDL4FQCGVBNBZTX/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":"2026-06-26T10:08:06Z","links":{"resolver":"https://pith.science/pith/YVIS5NXNR5TKDL4FQCGVBNBZTX","bundle":"https://pith.science/pith/YVIS5NXNR5TKDL4FQCGVBNBZTX/bundle.json","state":"https://pith.science/pith/YVIS5NXNR5TKDL4FQCGVBNBZTX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YVIS5NXNR5TKDL4FQCGVBNBZTX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YVIS5NXNR5TKDL4FQCGVBNBZTX","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":"3bcd75d0a0e5d52cdb3a24a243191b67be31f9d1292fa94bbaf836f8255a40cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-16T12:01:02Z","title_canon_sha256":"dcc206d62e849b950b8043892e583b4a32f197d801d6bf7e198b54b0bcdaf485"},"schema_version":"1.0","source":{"id":"1702.04935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.04935","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"1702.04935v1","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04935","created_at":"2026-05-18T00:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"YVIS5NXNR5TK","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YVIS5NXNR5TKDL4F","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YVIS5NXN","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:0cdc0ce9e1dc45f9367ab12eee4fd7d553fb1a53b3f35cd5bc4e7ac200247798","target":"graph","created_at":"2026-05-18T00:23:45Z","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":"Quaternions, introduced by Hamilton in 1843 as a generalization of complex numbers, have found, in more recent years, a wealth of applications in a number of different areas which motivated the design of efficient methods for numerically approximating the zeros of quaternionic polynomials. In fact, one can find in the literature recent contributions to this subject based on the use of complex techniques, but numerical methods relying on quaternion arithmetic remain scarce. In this paper we propose a Weierstrass-like method for finding simultaneously {\\sl all} the zeros of unilateral quaternion","authors_text":"Fernando Miranda, M. Irene Falc\\~ao, M. Joana Soares, Ricardo Severino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-16T12:01:02Z","title":"Weierstrass method for quaternionic polynomial root-finding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04935","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:bb2fe60ff46387987d567be7a7aa310519d129c235724cfdd7394e96da4c7e29","target":"record","created_at":"2026-05-18T00:23:45Z","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":"3bcd75d0a0e5d52cdb3a24a243191b67be31f9d1292fa94bbaf836f8255a40cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-16T12:01:02Z","title_canon_sha256":"dcc206d62e849b950b8043892e583b4a32f197d801d6bf7e198b54b0bcdaf485"},"schema_version":"1.0","source":{"id":"1702.04935","kind":"arxiv","version":1}},"canonical_sha256":"c5512eb6ed8f66a1af85808d50b4399dc4016938cf18cbb51b6ee3baae28bde0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5512eb6ed8f66a1af85808d50b4399dc4016938cf18cbb51b6ee3baae28bde0","first_computed_at":"2026-05-18T00:23:45.938380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:45.938380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SvLWWY0RRD6X73PcOCmQMFJeebKPzBT8lfIu65vDH/grzPQh7gaiJQKjV7dTe1DwuH1c8iqFywSI5kSDe/wNBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:45.938863Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.04935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb2fe60ff46387987d567be7a7aa310519d129c235724cfdd7394e96da4c7e29","sha256:0cdc0ce9e1dc45f9367ab12eee4fd7d553fb1a53b3f35cd5bc4e7ac200247798"],"state_sha256":"c0db393d810c5cd3290893dc88272d2a42f5fe5f22dd0f0a751a6cdc40d1bf05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f3BSGJy792dNo8bFIiSv53Gjh8VkgJHfPLZn7lM0/EZr6xjrSXEY4X4UPqCfpofr2j4HBHlddRVdndtHGTTsDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T10:08:06.111657Z","bundle_sha256":"c73c652abd2e2d3e44f5eed3965073af4867f3030f4aaa3cf32adf2dca8589e1"}}