{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:NNC4L7HKRYOP77QYZJHGBRUSC2","short_pith_number":"pith:NNC4L7HK","canonical_record":{"source":{"id":"1201.3443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T07:43:53Z","cross_cats_sorted":[],"title_canon_sha256":"02a6b44ed23df1075918d765dc61ef3dc65a3db370320066413024220cd64e2e","abstract_canon_sha256":"477f7066105f4445e3fafd2e5068601c17bf9208fa1bbf3f128e9a65fea209b9"},"schema_version":"1.0"},"canonical_sha256":"6b45c5fcea8e1cfffe18ca4e60c69216a093559989fd77c344cfd7cb7041f6fa","source":{"kind":"arxiv","id":"1201.3443","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3443","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3443v1","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3443","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"NNC4L7HKRYOP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NNC4L7HKRYOP77QY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NNC4L7HK","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:NNC4L7HKRYOP77QYZJHGBRUSC2","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T07:43:53Z","cross_cats_sorted":[],"title_canon_sha256":"02a6b44ed23df1075918d765dc61ef3dc65a3db370320066413024220cd64e2e","abstract_canon_sha256":"477f7066105f4445e3fafd2e5068601c17bf9208fa1bbf3f128e9a65fea209b9"},"schema_version":"1.0"},"canonical_sha256":"6b45c5fcea8e1cfffe18ca4e60c69216a093559989fd77c344cfd7cb7041f6fa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:12.682881Z","signature_b64":"Km84wKCfBKSxw61J8kgUMpTq5CMYFkuyey5e3gBAlYHArHVhpd2vlAx0vuBPaWwg09Jn9QDV+E2735HaaWWBAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b45c5fcea8e1cfffe18ca4e60c69216a093559989fd77c344cfd7cb7041f6fa","last_reissued_at":"2026-05-18T03:38:12.682442Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:12.682442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3443","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":"2026-05-18T03:38:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sAu1qsVhdyCTyTO1RN84wjnqvYxYeP/VSDTNFITt2ssqE0s4e7/GiZTKmfZqgt34Kl695FzjpKuRsovQ78KpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:59:18.679495Z"},"content_sha256":"92f67b1abb71b9ef441999842279c2faa17719bc3f5e8abebab08ab07da27478","schema_version":"1.0","event_id":"sha256:92f67b1abb71b9ef441999842279c2faa17719bc3f5e8abebab08ab07da27478"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:NNC4L7HKRYOP77QYZJHGBRUSC2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems: Case of Breadth One","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Lihong Zhi, Nan Li","submitted_at":"2012-01-17T07:43:53Z","abstract_excerpt":"In this paper we describe how to improve the performance of the symbolic-numeric method in (Li and Zhi,2009, 2011) for computing the multiplicity structure and refining approximate isolated singular solutions in the breadth one case. By introducing a parameterized and deflated system with smoothing parameters, we generalize the algorithm in (Rump and Graillat, 2009) to compute verified error bounds such that a slightly perturbed polynomial system is guaranteed to have a breadth-one multiple root within the computed bounds."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3443","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":"2026-05-18T03:38:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8we3yQjgTUkYPUnT8ncgmex/DFZGAWFHW/8L+5vcPpYQWSFSE5qlO0z8Qbmfv0pFGG0BI/I/iwdw7xCRyCgzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:59:18.679835Z"},"content_sha256":"f0aa43456d664d39f11dc523cf92b72dd7d819b800c0010286845a728f48285d","schema_version":"1.0","event_id":"sha256:f0aa43456d664d39f11dc523cf92b72dd7d819b800c0010286845a728f48285d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NNC4L7HKRYOP77QYZJHGBRUSC2/bundle.json","state_url":"https://pith.science/pith/NNC4L7HKRYOP77QYZJHGBRUSC2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NNC4L7HKRYOP77QYZJHGBRUSC2/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":"2026-05-31T01:59:18Z","links":{"resolver":"https://pith.science/pith/NNC4L7HKRYOP77QYZJHGBRUSC2","bundle":"https://pith.science/pith/NNC4L7HKRYOP77QYZJHGBRUSC2/bundle.json","state":"https://pith.science/pith/NNC4L7HKRYOP77QYZJHGBRUSC2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NNC4L7HKRYOP77QYZJHGBRUSC2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NNC4L7HKRYOP77QYZJHGBRUSC2","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":"477f7066105f4445e3fafd2e5068601c17bf9208fa1bbf3f128e9a65fea209b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T07:43:53Z","title_canon_sha256":"02a6b44ed23df1075918d765dc61ef3dc65a3db370320066413024220cd64e2e"},"schema_version":"1.0","source":{"id":"1201.3443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3443","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3443v1","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3443","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"NNC4L7HKRYOP","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NNC4L7HKRYOP77QY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NNC4L7HK","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:f0aa43456d664d39f11dc523cf92b72dd7d819b800c0010286845a728f48285d","target":"graph","created_at":"2026-05-18T03:38:12Z","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 describe how to improve the performance of the symbolic-numeric method in (Li and Zhi,2009, 2011) for computing the multiplicity structure and refining approximate isolated singular solutions in the breadth one case. By introducing a parameterized and deflated system with smoothing parameters, we generalize the algorithm in (Rump and Graillat, 2009) to compute verified error bounds such that a slightly perturbed polynomial system is guaranteed to have a breadth-one multiple root within the computed bounds.","authors_text":"Lihong Zhi, Nan Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T07:43:53Z","title":"Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems: Case of Breadth One"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3443","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":"sha256:92f67b1abb71b9ef441999842279c2faa17719bc3f5e8abebab08ab07da27478","target":"record","created_at":"2026-05-18T03:38:12Z","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":"477f7066105f4445e3fafd2e5068601c17bf9208fa1bbf3f128e9a65fea209b9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2012-01-17T07:43:53Z","title_canon_sha256":"02a6b44ed23df1075918d765dc61ef3dc65a3db370320066413024220cd64e2e"},"schema_version":"1.0","source":{"id":"1201.3443","kind":"arxiv","version":1}},"canonical_sha256":"6b45c5fcea8e1cfffe18ca4e60c69216a093559989fd77c344cfd7cb7041f6fa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b45c5fcea8e1cfffe18ca4e60c69216a093559989fd77c344cfd7cb7041f6fa","first_computed_at":"2026-05-18T03:38:12.682442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:12.682442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Km84wKCfBKSxw61J8kgUMpTq5CMYFkuyey5e3gBAlYHArHVhpd2vlAx0vuBPaWwg09Jn9QDV+E2735HaaWWBAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:12.682881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92f67b1abb71b9ef441999842279c2faa17719bc3f5e8abebab08ab07da27478","sha256:f0aa43456d664d39f11dc523cf92b72dd7d819b800c0010286845a728f48285d"],"state_sha256":"1b4648d0d89d0b9fa11c2f079e0e542eeb437c7575aa51eb109a69cb33245f06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OCUBPUCwhpdsF+R919wyRSzFc8A5rgS9zuC6NvKv/kRtpQGK7yjW0rUTLPqOJNK68b0aBBLkeyCAK8T5CiY+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:59:18.681744Z","bundle_sha256":"ad3f51e6dabb0a7492a682d6ff15ae46ac2adba8d2bad9067ad1465679e49173"}}