{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RJOEDLNQNIWTRJAUX5SZSWHDU3","short_pith_number":"pith:RJOEDLNQ","canonical_record":{"source":{"id":"1904.07937","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-16T19:22:40Z","cross_cats_sorted":["cs.NA","math.AG"],"title_canon_sha256":"3cd62edeb5ee41553f63a6b624fe9589394376b419b03b94f3cd03501d148305","abstract_canon_sha256":"fe3e18cc884a174f70b8a6e44c0309db038e258f2eabdddab6d16281a73a64f0"},"schema_version":"1.0"},"canonical_sha256":"8a5c41adb06a2d38a414bf659958e3a6e2a088d236a4a8568f7bdb4d5ea36f17","source":{"kind":"arxiv","id":"1904.07937","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.07937","created_at":"2026-07-05T06:11:14Z"},{"alias_kind":"arxiv_version","alias_value":"1904.07937v4","created_at":"2026-07-05T06:11:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07937","created_at":"2026-07-05T06:11:14Z"},{"alias_kind":"pith_short_12","alias_value":"RJOEDLNQNIWT","created_at":"2026-07-05T06:11:14Z"},{"alias_kind":"pith_short_16","alias_value":"RJOEDLNQNIWTRJAU","created_at":"2026-07-05T06:11:14Z"},{"alias_kind":"pith_short_8","alias_value":"RJOEDLNQ","created_at":"2026-07-05T06:11:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RJOEDLNQNIWTRJAUX5SZSWHDU3","target":"record","payload":{"canonical_record":{"source":{"id":"1904.07937","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-16T19:22:40Z","cross_cats_sorted":["cs.NA","math.AG"],"title_canon_sha256":"3cd62edeb5ee41553f63a6b624fe9589394376b419b03b94f3cd03501d148305","abstract_canon_sha256":"fe3e18cc884a174f70b8a6e44c0309db038e258f2eabdddab6d16281a73a64f0"},"schema_version":"1.0"},"canonical_sha256":"8a5c41adb06a2d38a414bf659958e3a6e2a088d236a4a8568f7bdb4d5ea36f17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:11:14.444761Z","signature_b64":"dZ26sBzDZD8Hntia7z0PjhKS/4S5X3zpIH23XTRmSF5/6lNcWT57hjkJmqwcJV/8FwtQGm3EQ9azoipYolXFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a5c41adb06a2d38a414bf659958e3a6e2a088d236a4a8568f7bdb4d5ea36f17","last_reissued_at":"2026-07-05T06:11:14.444296Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:11:14.444296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.07937","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":"2026-07-05T06:11:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4AYliSmRJzdqXecCfCq+OpfPJ0mOYLNY48eXypdmJYX0FNslRAKQ6tGGSEUzt/WK9MW9jXyEliHGWBM9kJZ1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T09:07:21.971314Z"},"content_sha256":"56020d14d12ba845fb0b0218ac37fc235db523ddaffc4d741d33c832b276b350","schema_version":"1.0","event_id":"sha256:56020d14d12ba845fb0b0218ac37fc235db523ddaffc4d741d33c832b276b350"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RJOEDLNQNIWTRJAUX5SZSWHDU3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On isolation of singular zeros of multivariate analytic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AG"],"primary_cat":"math.NA","authors_text":"Kisun Lee, Lihong Zhi, Nan Li","submitted_at":"2019-04-16T19:22:40Z","abstract_excerpt":"We give a separation bound for an isolated multiple root $x$ of a square multivariate analytic system $f$ satisfying that an operator deduced by adding $Df(x)$ and a projection of $D^2f(x)$ in a direction of the kernel of $Df(x)$ is invertible. We prove that the deflation process applied on $f$ and this kind of roots terminates after only one iteration. When $x$ is only given approximately, we give a numerical criterion for isolating a cluster of zeros of $f$ near $x$. We also propose a lower bound of the number of roots in the cluster."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07937","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1904.07937/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T06:11:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f7o+T2PgIw7guqMAC1qw5sHogzhN2jJRk32bXNzaHqTzeHGjtaAlztq0j6jIZqIPFws1YEu/2PlJ93OU5sDzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T09:07:21.971811Z"},"content_sha256":"614468c76b8074feec97be8a2e9bad878b473b0c025b5bfa977a42e0c9afc629","schema_version":"1.0","event_id":"sha256:614468c76b8074feec97be8a2e9bad878b473b0c025b5bfa977a42e0c9afc629"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RJOEDLNQNIWTRJAUX5SZSWHDU3/bundle.json","state_url":"https://pith.science/pith/RJOEDLNQNIWTRJAUX5SZSWHDU3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RJOEDLNQNIWTRJAUX5SZSWHDU3/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":"2026-08-06T09:07:21Z","links":{"resolver":"https://pith.science/pith/RJOEDLNQNIWTRJAUX5SZSWHDU3","bundle":"https://pith.science/pith/RJOEDLNQNIWTRJAUX5SZSWHDU3/bundle.json","state":"https://pith.science/pith/RJOEDLNQNIWTRJAUX5SZSWHDU3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RJOEDLNQNIWTRJAUX5SZSWHDU3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RJOEDLNQNIWTRJAUX5SZSWHDU3","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":"fe3e18cc884a174f70b8a6e44c0309db038e258f2eabdddab6d16281a73a64f0","cross_cats_sorted":["cs.NA","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-16T19:22:40Z","title_canon_sha256":"3cd62edeb5ee41553f63a6b624fe9589394376b419b03b94f3cd03501d148305"},"schema_version":"1.0","source":{"id":"1904.07937","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.07937","created_at":"2026-07-05T06:11:14Z"},{"alias_kind":"arxiv_version","alias_value":"1904.07937v4","created_at":"2026-07-05T06:11:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07937","created_at":"2026-07-05T06:11:14Z"},{"alias_kind":"pith_short_12","alias_value":"RJOEDLNQNIWT","created_at":"2026-07-05T06:11:14Z"},{"alias_kind":"pith_short_16","alias_value":"RJOEDLNQNIWTRJAU","created_at":"2026-07-05T06:11:14Z"},{"alias_kind":"pith_short_8","alias_value":"RJOEDLNQ","created_at":"2026-07-05T06:11:14Z"}],"graph_snapshots":[{"event_id":"sha256:614468c76b8074feec97be8a2e9bad878b473b0c025b5bfa977a42e0c9afc629","target":"graph","created_at":"2026-07-05T06:11:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1904.07937/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a separation bound for an isolated multiple root $x$ of a square multivariate analytic system $f$ satisfying that an operator deduced by adding $Df(x)$ and a projection of $D^2f(x)$ in a direction of the kernel of $Df(x)$ is invertible. We prove that the deflation process applied on $f$ and this kind of roots terminates after only one iteration. When $x$ is only given approximately, we give a numerical criterion for isolating a cluster of zeros of $f$ near $x$. We also propose a lower bound of the number of roots in the cluster.","authors_text":"Kisun Lee, Lihong Zhi, Nan Li","cross_cats":["cs.NA","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-16T19:22:40Z","title":"On isolation of singular zeros of multivariate analytic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07937","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":"sha256:56020d14d12ba845fb0b0218ac37fc235db523ddaffc4d741d33c832b276b350","target":"record","created_at":"2026-07-05T06:11:14Z","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":"fe3e18cc884a174f70b8a6e44c0309db038e258f2eabdddab6d16281a73a64f0","cross_cats_sorted":["cs.NA","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-04-16T19:22:40Z","title_canon_sha256":"3cd62edeb5ee41553f63a6b624fe9589394376b419b03b94f3cd03501d148305"},"schema_version":"1.0","source":{"id":"1904.07937","kind":"arxiv","version":4}},"canonical_sha256":"8a5c41adb06a2d38a414bf659958e3a6e2a088d236a4a8568f7bdb4d5ea36f17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8a5c41adb06a2d38a414bf659958e3a6e2a088d236a4a8568f7bdb4d5ea36f17","first_computed_at":"2026-07-05T06:11:14.444296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:11:14.444296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dZ26sBzDZD8Hntia7z0PjhKS/4S5X3zpIH23XTRmSF5/6lNcWT57hjkJmqwcJV/8FwtQGm3EQ9azoipYolXFCg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:11:14.444761Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.07937","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56020d14d12ba845fb0b0218ac37fc235db523ddaffc4d741d33c832b276b350","sha256:614468c76b8074feec97be8a2e9bad878b473b0c025b5bfa977a42e0c9afc629"],"state_sha256":"6da19e1b946f1970f5a923c1d065b3ac74b7b05fc2ac258111771c5dfd1aee47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y2i4qvqzYNGTWd8bMHOWXl5iuuePZHbu+3sGJFBYfyXk8FHrEjQLUYb01pxhrWIdG291hJlClNQCFNMGTMsnAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T09:07:21.975650Z","bundle_sha256":"a6926d85ca88ed99953ea511b4a09d531e8a406eff35ca94b664c0330c9abb4f"}}