{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:V22OFJQFD53G6L2DQFVFHDFMJ2","short_pith_number":"pith:V22OFJQF","canonical_record":{"source":{"id":"1708.04827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-16T09:52:04Z","cross_cats_sorted":[],"title_canon_sha256":"005d865e4d5aa0bd49102d901a659fb613d2bb9d647e2061ceb97afb86285c0a","abstract_canon_sha256":"f49ae528f006563d8d93c32bef46a17534226f4878b1baa89e37ff4c56f92a83"},"schema_version":"1.0"},"canonical_sha256":"aeb4e2a6051f766f2f43816a538cac4e93b6b44a0918b81f8f66268af8d3856d","source":{"kind":"arxiv","id":"1708.04827","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04827","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04827v1","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04827","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"pith_short_12","alias_value":"V22OFJQFD53G","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V22OFJQFD53G6L2D","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V22OFJQF","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:V22OFJQFD53G6L2DQFVFHDFMJ2","target":"record","payload":{"canonical_record":{"source":{"id":"1708.04827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-16T09:52:04Z","cross_cats_sorted":[],"title_canon_sha256":"005d865e4d5aa0bd49102d901a659fb613d2bb9d647e2061ceb97afb86285c0a","abstract_canon_sha256":"f49ae528f006563d8d93c32bef46a17534226f4878b1baa89e37ff4c56f92a83"},"schema_version":"1.0"},"canonical_sha256":"aeb4e2a6051f766f2f43816a538cac4e93b6b44a0918b81f8f66268af8d3856d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:57.789259Z","signature_b64":"40dt2WO6ZAgTPqyXG66n5R0UuNMN8eX3b5pheJp/Drt3qS+gvqn+elZmvdZEpaWpfwn3dFT7d9jT99RvQL/VBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aeb4e2a6051f766f2f43816a538cac4e93b6b44a0918b81f8f66268af8d3856d","last_reissued_at":"2026-05-18T00:37:57.788814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:57.788814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.04827","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:37:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QT3/EPG6jd8aWVTiEaqDJtgb8LknasPtOQmhsj8B5lMjyPAVmxF3wrY2QeH5LxMBUUnTSaYua6rTAOpEZ6bjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:52:54.329606Z"},"content_sha256":"6c44d70f23718e9aa6de513920be145ac76d97e10d89a810d104fe0ce2931985","schema_version":"1.0","event_id":"sha256:6c44d70f23718e9aa6de513920be145ac76d97e10d89a810d104fe0ce2931985"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:V22OFJQFD53G6L2DQFVFHDFMJ2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evolution of Locally Convex Closed Curves in Nonlocal Curvature Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dong-Ho Tsai, Natasa Sesum, Xiao-Liu Wang","submitted_at":"2017-08-16T09:52:04Z","abstract_excerpt":"We provide sufficient conditions on an initial curve for the area preserving and the length preserving curvature flows of curves in a plane, to develop a singularity at some finite time or converge to an $m$-fold circle as time goes to infinity. For the area-preserving flow, the positivity of the enclosed algebraic area determines whether the curvature blows up in finite time or not, while for the length-preserving flow, it is the positivity of an energy associated with initial curve that plays such a role."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04827","kind":"arxiv","version":1},"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":"2026-05-18T00:37:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wteTI9b3Gj55rKt2IggIOhTLMGlUU6WlGvzt+uMJY38c5GCYe9gx2JA4AcE4RhFXakc5CHNaCs2os+hXeNGeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:52:54.329944Z"},"content_sha256":"6d3886f39a417c3ad75aa9a6bd7b9ce3d9bde93b92fa425ed1770765bfe2a0c5","schema_version":"1.0","event_id":"sha256:6d3886f39a417c3ad75aa9a6bd7b9ce3d9bde93b92fa425ed1770765bfe2a0c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V22OFJQFD53G6L2DQFVFHDFMJ2/bundle.json","state_url":"https://pith.science/pith/V22OFJQFD53G6L2DQFVFHDFMJ2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V22OFJQFD53G6L2DQFVFHDFMJ2/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":"2026-06-08T09:52:54Z","links":{"resolver":"https://pith.science/pith/V22OFJQFD53G6L2DQFVFHDFMJ2","bundle":"https://pith.science/pith/V22OFJQFD53G6L2DQFVFHDFMJ2/bundle.json","state":"https://pith.science/pith/V22OFJQFD53G6L2DQFVFHDFMJ2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V22OFJQFD53G6L2DQFVFHDFMJ2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V22OFJQFD53G6L2DQFVFHDFMJ2","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":"f49ae528f006563d8d93c32bef46a17534226f4878b1baa89e37ff4c56f92a83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-16T09:52:04Z","title_canon_sha256":"005d865e4d5aa0bd49102d901a659fb613d2bb9d647e2061ceb97afb86285c0a"},"schema_version":"1.0","source":{"id":"1708.04827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.04827","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"arxiv_version","alias_value":"1708.04827v1","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.04827","created_at":"2026-05-18T00:37:57Z"},{"alias_kind":"pith_short_12","alias_value":"V22OFJQFD53G","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V22OFJQFD53G6L2D","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V22OFJQF","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:6d3886f39a417c3ad75aa9a6bd7b9ce3d9bde93b92fa425ed1770765bfe2a0c5","target":"graph","created_at":"2026-05-18T00:37:57Z","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 provide sufficient conditions on an initial curve for the area preserving and the length preserving curvature flows of curves in a plane, to develop a singularity at some finite time or converge to an $m$-fold circle as time goes to infinity. For the area-preserving flow, the positivity of the enclosed algebraic area determines whether the curvature blows up in finite time or not, while for the length-preserving flow, it is the positivity of an energy associated with initial curve that plays such a role.","authors_text":"Dong-Ho Tsai, Natasa Sesum, Xiao-Liu Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-16T09:52:04Z","title":"Evolution of Locally Convex Closed Curves in Nonlocal Curvature Flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04827","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":"sha256:6c44d70f23718e9aa6de513920be145ac76d97e10d89a810d104fe0ce2931985","target":"record","created_at":"2026-05-18T00:37:57Z","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":"f49ae528f006563d8d93c32bef46a17534226f4878b1baa89e37ff4c56f92a83","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-16T09:52:04Z","title_canon_sha256":"005d865e4d5aa0bd49102d901a659fb613d2bb9d647e2061ceb97afb86285c0a"},"schema_version":"1.0","source":{"id":"1708.04827","kind":"arxiv","version":1}},"canonical_sha256":"aeb4e2a6051f766f2f43816a538cac4e93b6b44a0918b81f8f66268af8d3856d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aeb4e2a6051f766f2f43816a538cac4e93b6b44a0918b81f8f66268af8d3856d","first_computed_at":"2026-05-18T00:37:57.788814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:57.788814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"40dt2WO6ZAgTPqyXG66n5R0UuNMN8eX3b5pheJp/Drt3qS+gvqn+elZmvdZEpaWpfwn3dFT7d9jT99RvQL/VBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:57.789259Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.04827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c44d70f23718e9aa6de513920be145ac76d97e10d89a810d104fe0ce2931985","sha256:6d3886f39a417c3ad75aa9a6bd7b9ce3d9bde93b92fa425ed1770765bfe2a0c5"],"state_sha256":"e1169c5ad0937917a9035e43810df96edc73e78a3288e749d134616b66c1109e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uAVXVAJFNP1s0wc3DHg9aZ2HmSbWXXAj+QCtbjZQO3jzuNlxN34Em4vGmK89gd361XsN+ay133zGt0YyjGmTDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:52:54.331832Z","bundle_sha256":"3bf0e776363d3f7b94363c7cf6f7953015b7be25539eaeea36cd7038e5d23779"}}