{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:JKRHHNS2GHN2CDZFZHPA6BDZG7","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":"5e21ee2aa1179d3f04575b74a8c67a91ea6ccdf73c2d92a8649890a9aba40447","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2007-02-12T20:52:43Z","title_canon_sha256":"120a8bcdf34b069f45265b2987140a09d91beed6cf3165d7a637668d59579ece"},"schema_version":"1.0","source":{"id":"math/0702344","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702344","created_at":"2026-06-03T22:06:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702344v1","created_at":"2026-06-03T22:06:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702344","created_at":"2026-06-03T22:06:22Z"},{"alias_kind":"pith_short_12","alias_value":"JKRHHNS2GHN2","created_at":"2026-06-03T22:06:22Z"},{"alias_kind":"pith_short_16","alias_value":"JKRHHNS2GHN2CDZF","created_at":"2026-06-03T22:06:22Z"},{"alias_kind":"pith_short_8","alias_value":"JKRHHNS2","created_at":"2026-06-03T22:06:22Z"}],"graph_snapshots":[{"event_id":"sha256:9a044b21ee2850d7bea77f8ca4e4b0db6bdfaae72913226704bdd86bee704ce7","target":"graph","created_at":"2026-06-03T22:06:22Z","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/math/0702344/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a new complexity measure of a path of (problems, solutions) pairs in terms of the length of the path in the condition metric which we define in the article. The measure gives an upper bound for the number of Newton steps sufficient to approximate the path discretely starting from one end and thus produce an approximate zero for the endpoint. This motivates the study of short paths or geodesics in the condition metric.","authors_text":"Michael Shub","cross_cats":["cs.NA"],"headline":"","license":"","primary_cat":"math.NA","submitted_at":"2007-02-12T20:52:43Z","title":"Complexity of Bezout's Theorem VI: Geodesics in the Condition (Number) Metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702344","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":"sha256:0c5cb8fcfa1a1e34b38dcace834c602b5adf88582b916ab7b9b258851316676b","target":"record","created_at":"2026-06-03T22:06:22Z","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":"5e21ee2aa1179d3f04575b74a8c67a91ea6ccdf73c2d92a8649890a9aba40447","cross_cats_sorted":["cs.NA"],"license":"","primary_cat":"math.NA","submitted_at":"2007-02-12T20:52:43Z","title_canon_sha256":"120a8bcdf34b069f45265b2987140a09d91beed6cf3165d7a637668d59579ece"},"schema_version":"1.0","source":{"id":"math/0702344","kind":"arxiv","version":1}},"canonical_sha256":"4aa273b65a31dba10f25c9de0f047937c86952801f42eb6c2117405d242ece96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4aa273b65a31dba10f25c9de0f047937c86952801f42eb6c2117405d242ece96","first_computed_at":"2026-06-03T22:06:22.037786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:22.037786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jzNbxabl2mbfyzZ3dKF1yGJ4A7vLFrUhjrs3riwOhE94IN/zgRO2h26kV6VHAaRtTURtnPScWxG65/5CFDXYAw==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:22.038185Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702344","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c5cb8fcfa1a1e34b38dcace834c602b5adf88582b916ab7b9b258851316676b","sha256:9a044b21ee2850d7bea77f8ca4e4b0db6bdfaae72913226704bdd86bee704ce7"],"state_sha256":"aa70af290d1cbb2799e76c5a6a61d502c45bcb4ca1f292b6b74a1ec88234fae9"}