{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BIX6XF7UYHOSP3LWBMSYSQFFMI","short_pith_number":"pith:BIX6XF7U","canonical_record":{"source":{"id":"1703.10986","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-31T17:10:49Z","cross_cats_sorted":[],"title_canon_sha256":"fc72f8e5d00ab2bfa50f9c191f6db9d7ca6c886197506fe07f97c23b5ca99e7b","abstract_canon_sha256":"c474c87748201df1340c99930a9095d530d47cfe04bbd944504fe780c4cf726b"},"schema_version":"1.0"},"canonical_sha256":"0a2feb97f4c1dd27ed760b258940a5620b4db4c3376e9365c16a1a170538e6f7","source":{"kind":"arxiv","id":"1703.10986","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10986","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10986v2","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10986","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"BIX6XF7UYHOS","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BIX6XF7UYHOSP3LW","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BIX6XF7U","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BIX6XF7UYHOSP3LWBMSYSQFFMI","target":"record","payload":{"canonical_record":{"source":{"id":"1703.10986","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-31T17:10:49Z","cross_cats_sorted":[],"title_canon_sha256":"fc72f8e5d00ab2bfa50f9c191f6db9d7ca6c886197506fe07f97c23b5ca99e7b","abstract_canon_sha256":"c474c87748201df1340c99930a9095d530d47cfe04bbd944504fe780c4cf726b"},"schema_version":"1.0"},"canonical_sha256":"0a2feb97f4c1dd27ed760b258940a5620b4db4c3376e9365c16a1a170538e6f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:09.041691Z","signature_b64":"h17DesgbrAruFVljklRr0xBkF1fFixZR3vGGbiJloi2eFFjVRlXRrq6W2C7ASq/MRtKwITmdbA89hv778WF3Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a2feb97f4c1dd27ed760b258940a5620b4db4c3376e9365c16a1a170538e6f7","last_reissued_at":"2026-05-18T00:23:09.041096Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:09.041096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.10986","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":"2026-05-18T00:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LvklLz12vHSnaM/u5jaLFIcqE+s4JXdub7Tic1G5G1n/+lNy+j5ctA1v8XMktarMZ2XE2BLTZUqARbkGBHheAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:31:49.379201Z"},"content_sha256":"a447e9275274810af275b7acefa7bbbed78ef1752847a1148fdf407232072bd6","schema_version":"1.0","event_id":"sha256:a447e9275274810af275b7acefa7bbbed78ef1752847a1148fdf407232072bd6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BIX6XF7UYHOSP3LWBMSYSQFFMI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Number of Zeros of Unilateral Polynomials over Coquaternions Revisited","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":"2017-03-31T17:10:49Z","abstract_excerpt":"The literature on quaternionic polynomials and, in particular, on methods for determining and classifying their zero-sets, is fast developing and reveals a growing interest on this subject. In contrast, polynomials defined over the algebra of coquaternions have received very little attention from researchers. One of the few exceptions is the very recent paper by Janovsk\\'a and Opfer [Electronic Transactions on Numerical Analysis, Volume 46, pp. 55-70, 2017], where, among other results, we can find a first attempt to prove that a unilateral coquaternionic polynomial of degree $n$ has, at most, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10986","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":"2026-05-18T00:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zhvMeSYraSE+dwgY/14XsuOUGHft6hEN32t6sMBPmUR8DV3xesLeFlTb5+7vl7rhc7aCIfGOwjgQvW0MRFTJAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:31:49.379557Z"},"content_sha256":"b8958e8f5b9794702eb8a7658aab5ac8bec0f30624b6f84a7f2eb64df3cb578b","schema_version":"1.0","event_id":"sha256:b8958e8f5b9794702eb8a7658aab5ac8bec0f30624b6f84a7f2eb64df3cb578b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BIX6XF7UYHOSP3LWBMSYSQFFMI/bundle.json","state_url":"https://pith.science/pith/BIX6XF7UYHOSP3LWBMSYSQFFMI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BIX6XF7UYHOSP3LWBMSYSQFFMI/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":"2026-06-26T11:31:49Z","links":{"resolver":"https://pith.science/pith/BIX6XF7UYHOSP3LWBMSYSQFFMI","bundle":"https://pith.science/pith/BIX6XF7UYHOSP3LWBMSYSQFFMI/bundle.json","state":"https://pith.science/pith/BIX6XF7UYHOSP3LWBMSYSQFFMI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BIX6XF7UYHOSP3LWBMSYSQFFMI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BIX6XF7UYHOSP3LWBMSYSQFFMI","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":"c474c87748201df1340c99930a9095d530d47cfe04bbd944504fe780c4cf726b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-31T17:10:49Z","title_canon_sha256":"fc72f8e5d00ab2bfa50f9c191f6db9d7ca6c886197506fe07f97c23b5ca99e7b"},"schema_version":"1.0","source":{"id":"1703.10986","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.10986","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1703.10986v2","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.10986","created_at":"2026-05-18T00:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"BIX6XF7UYHOS","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BIX6XF7UYHOSP3LW","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BIX6XF7U","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:b8958e8f5b9794702eb8a7658aab5ac8bec0f30624b6f84a7f2eb64df3cb578b","target":"graph","created_at":"2026-05-18T00:23:09Z","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":"The literature on quaternionic polynomials and, in particular, on methods for determining and classifying their zero-sets, is fast developing and reveals a growing interest on this subject. In contrast, polynomials defined over the algebra of coquaternions have received very little attention from researchers. One of the few exceptions is the very recent paper by Janovsk\\'a and Opfer [Electronic Transactions on Numerical Analysis, Volume 46, pp. 55-70, 2017], where, among other results, we can find a first attempt to prove that a unilateral coquaternionic polynomial of degree $n$ has, at most, ","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":"2017-03-31T17:10:49Z","title":"The Number of Zeros of Unilateral Polynomials over Coquaternions Revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10986","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:a447e9275274810af275b7acefa7bbbed78ef1752847a1148fdf407232072bd6","target":"record","created_at":"2026-05-18T00:23:09Z","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":"c474c87748201df1340c99930a9095d530d47cfe04bbd944504fe780c4cf726b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-03-31T17:10:49Z","title_canon_sha256":"fc72f8e5d00ab2bfa50f9c191f6db9d7ca6c886197506fe07f97c23b5ca99e7b"},"schema_version":"1.0","source":{"id":"1703.10986","kind":"arxiv","version":2}},"canonical_sha256":"0a2feb97f4c1dd27ed760b258940a5620b4db4c3376e9365c16a1a170538e6f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a2feb97f4c1dd27ed760b258940a5620b4db4c3376e9365c16a1a170538e6f7","first_computed_at":"2026-05-18T00:23:09.041096Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:09.041096Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h17DesgbrAruFVljklRr0xBkF1fFixZR3vGGbiJloi2eFFjVRlXRrq6W2C7ASq/MRtKwITmdbA89hv778WF3Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:09.041691Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.10986","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a447e9275274810af275b7acefa7bbbed78ef1752847a1148fdf407232072bd6","sha256:b8958e8f5b9794702eb8a7658aab5ac8bec0f30624b6f84a7f2eb64df3cb578b"],"state_sha256":"d90bbb35eec57d9b03233b0e8c23933105d666cc2d6c1b3dfbc664fbe447ec47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lXJtb5PDZtSELcqUTM35dnCYRzeY2kyqweVpX9e1squU5LfJXv5brdky8o8v5Fc4GlD0y6SOROmjLTMPA80iBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:31:49.381416Z","bundle_sha256":"a6bc866518a5af909d1dc496d2e1c3bf59b27395b38141085e48f9a5b58f1bf0"}}