{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TM2LYMYQKNP37KUOTBZTHN5GAM","short_pith_number":"pith:TM2LYMYQ","canonical_record":{"source":{"id":"1009.4777","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-24T07:28:54Z","cross_cats_sorted":[],"title_canon_sha256":"26d85044893aa42cea655156a74b74e65ab9bc6ae6b9e20d0389368588b3da5b","abstract_canon_sha256":"0459f2ef1cec9f79c43199719e234adf87b19b70bfee96bc9fd8f7df5e686515"},"schema_version":"1.0"},"canonical_sha256":"9b34bc3310535fbfaa8e987333b7a60324b83d8a2808cf63e6937422acf96bc0","source":{"kind":"arxiv","id":"1009.4777","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4777","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4777v1","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4777","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"TM2LYMYQKNP3","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TM2LYMYQKNP37KUO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TM2LYMYQ","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TM2LYMYQKNP37KUOTBZTHN5GAM","target":"record","payload":{"canonical_record":{"source":{"id":"1009.4777","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-24T07:28:54Z","cross_cats_sorted":[],"title_canon_sha256":"26d85044893aa42cea655156a74b74e65ab9bc6ae6b9e20d0389368588b3da5b","abstract_canon_sha256":"0459f2ef1cec9f79c43199719e234adf87b19b70bfee96bc9fd8f7df5e686515"},"schema_version":"1.0"},"canonical_sha256":"9b34bc3310535fbfaa8e987333b7a60324b83d8a2808cf63e6937422acf96bc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:21.201368Z","signature_b64":"Qf4HCo8rVTqip7ev+y1R4wBOjy9QKYNfMOAkhWr7IWy0EcniPM7LlNoPNsAuWMdvq92Y5Hel06mZLfypGBv+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b34bc3310535fbfaa8e987333b7a60324b83d8a2808cf63e6937422acf96bc0","last_reissued_at":"2026-05-18T04:40:21.200758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:21.200758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.4777","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":"2026-05-18T04:40:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJtFtBKmTlQXDY6fkVBjFW/DStosvObomV+KCyip3MVWXann4X6lIa5DAllNfHeqKszF7MwAP1NXoOjRFPwKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:08:10.910067Z"},"content_sha256":"2064a79f5c1bb4940456effcfb7cd32037bde079df32bf2acd66b8efcfed2fbd","schema_version":"1.0","event_id":"sha256:2064a79f5c1bb4940456effcfb7cd32037bde079df32bf2acd66b8efcfed2fbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TM2LYMYQKNP37KUOTBZTHN5GAM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contracting Convex Immersed Closed Plane Curves with Slow Speed of Curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chi-Cheung Poon, Dong-Ho Tsai, Yu-Chu Lin","submitted_at":"2010-09-24T07:28:54Z","abstract_excerpt":"We study the contraction of a convex immersed plane curve with speed (1/{\\alpha})k^{{\\alpha}}, where {\\alpha}in(0,1] is a constant and show that, if the blow-up rate of the curvature is of type one, it will converge to a homothetic self-similar solution. We also discuss a special symmetric case of type two blow-up and show that it converges to a translational self-similar solution. In the case of curve shortening flow (i.e., when {\\alpha}=1), this translational self-similar solution is the familiar \"Grim Reaper\" (a terminology due to M. Grayson [GR])."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4777","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":"2026-05-18T04:40:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63tdQFxZgiA0oHPVNEq3LLfO7yF19owO7wv3nvxV83pAwKk9BK6VzspLHCPgSHzKVcq+bvbFNtRyFzE/2HH1Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T22:08:10.910728Z"},"content_sha256":"6995eaad21743f9a2cf597e210fbadf3cec00e2a7f0d3038cfd48d930a3f2ac4","schema_version":"1.0","event_id":"sha256:6995eaad21743f9a2cf597e210fbadf3cec00e2a7f0d3038cfd48d930a3f2ac4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TM2LYMYQKNP37KUOTBZTHN5GAM/bundle.json","state_url":"https://pith.science/pith/TM2LYMYQKNP37KUOTBZTHN5GAM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TM2LYMYQKNP37KUOTBZTHN5GAM/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":"2026-06-07T22:08:10Z","links":{"resolver":"https://pith.science/pith/TM2LYMYQKNP37KUOTBZTHN5GAM","bundle":"https://pith.science/pith/TM2LYMYQKNP37KUOTBZTHN5GAM/bundle.json","state":"https://pith.science/pith/TM2LYMYQKNP37KUOTBZTHN5GAM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TM2LYMYQKNP37KUOTBZTHN5GAM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TM2LYMYQKNP37KUOTBZTHN5GAM","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":"0459f2ef1cec9f79c43199719e234adf87b19b70bfee96bc9fd8f7df5e686515","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-24T07:28:54Z","title_canon_sha256":"26d85044893aa42cea655156a74b74e65ab9bc6ae6b9e20d0389368588b3da5b"},"schema_version":"1.0","source":{"id":"1009.4777","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4777","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4777v1","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4777","created_at":"2026-05-18T04:40:21Z"},{"alias_kind":"pith_short_12","alias_value":"TM2LYMYQKNP3","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"TM2LYMYQKNP37KUO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"TM2LYMYQ","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:6995eaad21743f9a2cf597e210fbadf3cec00e2a7f0d3038cfd48d930a3f2ac4","target":"graph","created_at":"2026-05-18T04:40:21Z","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 study the contraction of a convex immersed plane curve with speed (1/{\\alpha})k^{{\\alpha}}, where {\\alpha}in(0,1] is a constant and show that, if the blow-up rate of the curvature is of type one, it will converge to a homothetic self-similar solution. We also discuss a special symmetric case of type two blow-up and show that it converges to a translational self-similar solution. In the case of curve shortening flow (i.e., when {\\alpha}=1), this translational self-similar solution is the familiar \"Grim Reaper\" (a terminology due to M. Grayson [GR]).","authors_text":"Chi-Cheung Poon, Dong-Ho Tsai, Yu-Chu Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-24T07:28:54Z","title":"Contracting Convex Immersed Closed Plane Curves with Slow Speed of Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4777","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":"sha256:2064a79f5c1bb4940456effcfb7cd32037bde079df32bf2acd66b8efcfed2fbd","target":"record","created_at":"2026-05-18T04:40:21Z","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":"0459f2ef1cec9f79c43199719e234adf87b19b70bfee96bc9fd8f7df5e686515","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-09-24T07:28:54Z","title_canon_sha256":"26d85044893aa42cea655156a74b74e65ab9bc6ae6b9e20d0389368588b3da5b"},"schema_version":"1.0","source":{"id":"1009.4777","kind":"arxiv","version":1}},"canonical_sha256":"9b34bc3310535fbfaa8e987333b7a60324b83d8a2808cf63e6937422acf96bc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b34bc3310535fbfaa8e987333b7a60324b83d8a2808cf63e6937422acf96bc0","first_computed_at":"2026-05-18T04:40:21.200758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:21.200758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qf4HCo8rVTqip7ev+y1R4wBOjy9QKYNfMOAkhWr7IWy0EcniPM7LlNoPNsAuWMdvq92Y5Hel06mZLfypGBv+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:21.201368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4777","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2064a79f5c1bb4940456effcfb7cd32037bde079df32bf2acd66b8efcfed2fbd","sha256:6995eaad21743f9a2cf597e210fbadf3cec00e2a7f0d3038cfd48d930a3f2ac4"],"state_sha256":"5cb70e9d8192809a378dcb23e77b70b3828377ae072e07053f478a1e71469ebf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tx/mbBuZTlPAEALZ3WGu/CiW6tjys8XcyLCPxU2cuuDTixAXgVm8L4yTS4ma5Gy7yYnuqvcaE8qzFMOqnPTjBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T22:08:10.914494Z","bundle_sha256":"88a34aedaf639e87476041242c96227976932a1e3058bc9af8d0451f29f01599"}}