{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PHPMGWWUW4QSWUU5JVSYP5GTYH","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":"ac576dc10e2b41e43d1a05350806503fe97751405ea19a3ba9b3fb23ec7027d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-04-21T23:28:59Z","title_canon_sha256":"cd7d733f395a5feff035d9f2b3834179ae2bc79e18a3a30bbeb111afb7e3029a"},"schema_version":"1.0","source":{"id":"1804.09035","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09035","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09035v3","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09035","created_at":"2026-05-18T00:15:49Z"},{"alias_kind":"pith_short_12","alias_value":"PHPMGWWUW4QS","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PHPMGWWUW4QSWUU5","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PHPMGWWU","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:2877f5e9916d60cb6eb56615542a60e58cbeb4da39737aeab0fb4db7bc9bb741","target":"graph","created_at":"2026-05-18T00:15:49Z","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 stability result, as stated, is incorrect. In particular, the 1-dimensional extended persistence diagrams of a finely-triangulated simplicial complex X equipped with a continuous real-valued function f, and its one-skeleton graph G (also equipped with f), need not be close. To take an example, let X be a finely-triangulated disc of radius r and let f be the distance-to -the-boundary function, which increases radially from the boundary circle of X and is maximized at the center. The extended persistence diagram of (X,f) contains a point in 1-dimensional persistence of the form (0,r), wherea","authors_text":"Elchanan Solomon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-04-21T23:28:59Z","title":"Stability of Extended Functional Persistence in Dimensions Zero and One"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09035","kind":"arxiv","version":3},"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":"sha256:2d39a6a202f360776554b963cc72d5645e5e1c8c250ba0be8c1cec39be66737d","target":"record","created_at":"2026-05-18T00:15:49Z","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":"ac576dc10e2b41e43d1a05350806503fe97751405ea19a3ba9b3fb23ec7027d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-04-21T23:28:59Z","title_canon_sha256":"cd7d733f395a5feff035d9f2b3834179ae2bc79e18a3a30bbeb111afb7e3029a"},"schema_version":"1.0","source":{"id":"1804.09035","kind":"arxiv","version":3}},"canonical_sha256":"79dec35ad4b7212b529d4d6587f4d3c1efaeeae30596f9131cde8949a487a40b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79dec35ad4b7212b529d4d6587f4d3c1efaeeae30596f9131cde8949a487a40b","first_computed_at":"2026-05-18T00:15:49.535339Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:49.535339Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DfeevlmXIf6Jg64FD5m4B+IHxABwI1kztTR6zk3VX7L/MOblk7HvOtIwMqksjsMkQK3nAbhaFowhhs5dsHwnDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:49.535894Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09035","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d39a6a202f360776554b963cc72d5645e5e1c8c250ba0be8c1cec39be66737d","sha256:2877f5e9916d60cb6eb56615542a60e58cbeb4da39737aeab0fb4db7bc9bb741"],"state_sha256":"b987abe47ea7c5b231952743c8d09e5fda572fe1d05eb150a23f87367ca0a145"}