{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QPXQHT2AMGICP3AZIG76LHO5KV","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":"baec367c6376b7b96e06f510e7d41c64f0097d7851fbff06bd206a4b0a7e2a84","cross_cats_sorted":["math.GT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-20T22:14:56Z","title_canon_sha256":"b96cb913725195875942f6acc36327ee46418ca768fad9e3564d9742e08d2ffc"},"schema_version":"1.0","source":{"id":"1509.06064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06064","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06064v1","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06064","created_at":"2026-05-18T00:32:36Z"},{"alias_kind":"pith_short_12","alias_value":"QPXQHT2AMGIC","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QPXQHT2AMGICP3AZ","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QPXQHT2A","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:7d39634e0f958c1674fbc4248259703fb682b2c95ad2f9a90d089b026fdb0e8d","target":"graph","created_at":"2026-05-18T00:32:36Z","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":"We present sufficient conditions for topological stability of continuous functions $f:\\mathbb{R}\\to\\mathbb{R}$ having finitely many local extrema with respect to averagings by discrete measures with finite supports.","authors_text":"Oksana Marunkevych, Sergiy Maksymenko","cross_cats":["math.GT","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-20T22:14:56Z","title":"Topological stability of continuous functions with respect to averagings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06064","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":"sha256:0543cec4cb53440d2e375432b05bf0e7318b487b4bf4475d2bfa2edd8d502ccc","target":"record","created_at":"2026-05-18T00:32:36Z","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":"baec367c6376b7b96e06f510e7d41c64f0097d7851fbff06bd206a4b0a7e2a84","cross_cats_sorted":["math.GT","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-09-20T22:14:56Z","title_canon_sha256":"b96cb913725195875942f6acc36327ee46418ca768fad9e3564d9742e08d2ffc"},"schema_version":"1.0","source":{"id":"1509.06064","kind":"arxiv","version":1}},"canonical_sha256":"83ef03cf40619027ec1941bfe59ddd5571f902c26b082444e3e6240036d85f8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83ef03cf40619027ec1941bfe59ddd5571f902c26b082444e3e6240036d85f8e","first_computed_at":"2026-05-18T00:32:36.602027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:36.602027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xcOgWWwcmwiOFyTsJ3ERK8jnL37OUWCeFdBkMrhh7GrQzE1h065OxIycas2T5Daboq4GeaROnWvm2gCrN+/XBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:36.602790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0543cec4cb53440d2e375432b05bf0e7318b487b4bf4475d2bfa2edd8d502ccc","sha256:7d39634e0f958c1674fbc4248259703fb682b2c95ad2f9a90d089b026fdb0e8d"],"state_sha256":"b674880775977555113d53604126ad09e8616fded001890f043ad4a719fa5651"}