{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:BEU5UXX6JIK2G5OYPE5II3KYOP","short_pith_number":"pith:BEU5UXX6","canonical_record":{"source":{"id":"0907.1430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-09T07:37:00Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9c5e551b788b62370862fc21e610d88e4b3f91bde4458b23ca052f0df6c155cf","abstract_canon_sha256":"e36a92e4449e52147882506876099c8ebeb635dfe72fb0df2dba1bbf6862ddeb"},"schema_version":"1.0"},"canonical_sha256":"0929da5efe4a15a375d8793a846d5873dd1000420fbee01f2f35dddc50a602d6","source":{"kind":"arxiv","id":"0907.1430","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.1430","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"0907.1430v2","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.1430","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"BEU5UXX6JIK2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BEU5UXX6JIK2G5OY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BEU5UXX6","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:BEU5UXX6JIK2G5OYPE5II3KYOP","target":"record","payload":{"canonical_record":{"source":{"id":"0907.1430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-09T07:37:00Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"9c5e551b788b62370862fc21e610d88e4b3f91bde4458b23ca052f0df6c155cf","abstract_canon_sha256":"e36a92e4449e52147882506876099c8ebeb635dfe72fb0df2dba1bbf6862ddeb"},"schema_version":"1.0"},"canonical_sha256":"0929da5efe4a15a375d8793a846d5873dd1000420fbee01f2f35dddc50a602d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:51.231530Z","signature_b64":"qdyKWUiKATVhSQwTiY1DIcTkkJqsCK9Z177cpfZWerj3vGc3G/GPpR9+ySkv7GWnJ7mK3CwWeDVHJhKUAUHwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0929da5efe4a15a375d8793a846d5873dd1000420fbee01f2f35dddc50a602d6","last_reissued_at":"2026-05-18T03:39:51.231084Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:51.231084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.1430","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WOiqeJ8l4i54Y9uW2IXLgZyw8YWZ+o24Jr8w4nAflJqrImDy7A4v1DFXxwP3fZJOqrBeH5rSQw2SFF4SVcYpDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:39:45.372277Z"},"content_sha256":"d5f12416c9532b1f08655472b09b0f7c0ca93d8c7bcff499c3b97806590a91ea","schema_version":"1.0","event_id":"sha256:d5f12416c9532b1f08655472b09b0f7c0ca93d8c7bcff499c3b97806590a91ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:BEU5UXX6JIK2G5OYPE5II3KYOP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A non-local area preserving curve flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Liang Cheng, Li Ma","submitted_at":"2009-07-09T07:37:00Z","abstract_excerpt":"In this paper, we consider a kind of area preserving non-local flow for convex curves in the plane. We show that the flow exists globally, the length of evolving curve is non-increasing, and the curve converges to a circle in C^{\\infty} sense as time goes into infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1430","kind":"arxiv","version":2},"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":"2026-05-18T03:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"veuIwGR1Milce1yFKGsBY0WxVzrvg3W6HmIsYtkpYBf8xdi9umaaxKm5/v7cnzAbgxMzQXTqyDblOk1rFnjPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:39:45.372636Z"},"content_sha256":"afb320a05f2e9afb6b30be527e73a99408c1a4edb1af8f0af92457a3085d5e68","schema_version":"1.0","event_id":"sha256:afb320a05f2e9afb6b30be527e73a99408c1a4edb1af8f0af92457a3085d5e68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BEU5UXX6JIK2G5OYPE5II3KYOP/bundle.json","state_url":"https://pith.science/pith/BEU5UXX6JIK2G5OYPE5II3KYOP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BEU5UXX6JIK2G5OYPE5II3KYOP/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":"2026-06-01T22:39:45Z","links":{"resolver":"https://pith.science/pith/BEU5UXX6JIK2G5OYPE5II3KYOP","bundle":"https://pith.science/pith/BEU5UXX6JIK2G5OYPE5II3KYOP/bundle.json","state":"https://pith.science/pith/BEU5UXX6JIK2G5OYPE5II3KYOP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BEU5UXX6JIK2G5OYPE5II3KYOP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BEU5UXX6JIK2G5OYPE5II3KYOP","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":"e36a92e4449e52147882506876099c8ebeb635dfe72fb0df2dba1bbf6862ddeb","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-09T07:37:00Z","title_canon_sha256":"9c5e551b788b62370862fc21e610d88e4b3f91bde4458b23ca052f0df6c155cf"},"schema_version":"1.0","source":{"id":"0907.1430","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.1430","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"0907.1430v2","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.1430","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"BEU5UXX6JIK2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BEU5UXX6JIK2G5OY","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BEU5UXX6","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:afb320a05f2e9afb6b30be527e73a99408c1a4edb1af8f0af92457a3085d5e68","target":"graph","created_at":"2026-05-18T03:39:51Z","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 consider a kind of area preserving non-local flow for convex curves in the plane. We show that the flow exists globally, the length of evolving curve is non-increasing, and the curve converges to a circle in C^{\\infty} sense as time goes into infinity.","authors_text":"Liang Cheng, Li Ma","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-09T07:37:00Z","title":"A non-local area preserving curve flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1430","kind":"arxiv","version":2},"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:d5f12416c9532b1f08655472b09b0f7c0ca93d8c7bcff499c3b97806590a91ea","target":"record","created_at":"2026-05-18T03:39:51Z","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":"e36a92e4449e52147882506876099c8ebeb635dfe72fb0df2dba1bbf6862ddeb","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-07-09T07:37:00Z","title_canon_sha256":"9c5e551b788b62370862fc21e610d88e4b3f91bde4458b23ca052f0df6c155cf"},"schema_version":"1.0","source":{"id":"0907.1430","kind":"arxiv","version":2}},"canonical_sha256":"0929da5efe4a15a375d8793a846d5873dd1000420fbee01f2f35dddc50a602d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0929da5efe4a15a375d8793a846d5873dd1000420fbee01f2f35dddc50a602d6","first_computed_at":"2026-05-18T03:39:51.231084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:51.231084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qdyKWUiKATVhSQwTiY1DIcTkkJqsCK9Z177cpfZWerj3vGc3G/GPpR9+ySkv7GWnJ7mK3CwWeDVHJhKUAUHwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:51.231530Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.1430","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5f12416c9532b1f08655472b09b0f7c0ca93d8c7bcff499c3b97806590a91ea","sha256:afb320a05f2e9afb6b30be527e73a99408c1a4edb1af8f0af92457a3085d5e68"],"state_sha256":"aff5b37624cb35e9cfe9bf1ec059480a54ea862aa3fe9e85865ea8933b90c224"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rVH5bbVZsfZJ9IyYJwRZyAj97LW4zFoFHXVyUoBe+P/mrr3RkmaFqQ7g66iyKHPBEaVUtNHplk+Ilzq4nJs3AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:39:45.374581Z","bundle_sha256":"5e079b78c5523e9f40367cff0e31bf59e05b5ab8b0046d63992f121abf767ea0"}}