{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MGXSSM73UEJRSET2HHUEI4CNWV","short_pith_number":"pith:MGXSSM73","canonical_record":{"source":{"id":"1902.08079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-21T14:50:53Z","cross_cats_sorted":[],"title_canon_sha256":"d6570bfaef0bc677825608d63ee09d669788fdd5f09e72a65236eee865a38ee7","abstract_canon_sha256":"22d68a73c6824a5cd031fc417a279614586e74c3514637d5dc552829fde396f4"},"schema_version":"1.0"},"canonical_sha256":"61af2933fba11319127a39e844704db5584a1c3342edbb6d7c69265b359ea2ce","source":{"kind":"arxiv","id":"1902.08079","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08079","created_at":"2026-05-17T23:53:02Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08079v1","created_at":"2026-05-17T23:53:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08079","created_at":"2026-05-17T23:53:02Z"},{"alias_kind":"pith_short_12","alias_value":"MGXSSM73UEJR","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MGXSSM73UEJRSET2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MGXSSM73","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MGXSSM73UEJRSET2HHUEI4CNWV","target":"record","payload":{"canonical_record":{"source":{"id":"1902.08079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-21T14:50:53Z","cross_cats_sorted":[],"title_canon_sha256":"d6570bfaef0bc677825608d63ee09d669788fdd5f09e72a65236eee865a38ee7","abstract_canon_sha256":"22d68a73c6824a5cd031fc417a279614586e74c3514637d5dc552829fde396f4"},"schema_version":"1.0"},"canonical_sha256":"61af2933fba11319127a39e844704db5584a1c3342edbb6d7c69265b359ea2ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:02.138798Z","signature_b64":"K44VfdGh6HaNxR+3X7DzuW6ABfLJmfvg7VPy/wJD6uWtSti4D/6wO10MA+4xly+icGxB6W+jebxw5sdSH5QADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61af2933fba11319127a39e844704db5584a1c3342edbb6d7c69265b359ea2ce","last_reissued_at":"2026-05-17T23:53:02.137895Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:02.137895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.08079","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":"2026-05-17T23:53:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1sGTKwVr9+yRSm/o5Sz2xqs9F2r39pt3xidbXCK0+MiBVFiYwEKPUZZYxfFN7bSSdtWfo3f+zF2vaUd82QqnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:01:00.017884Z"},"content_sha256":"c0fdace745296b7d4c328c951cdb314d7604e7e593a0cc1c75779e11c17ea803","schema_version":"1.0","event_id":"sha256:c0fdace745296b7d4c328c951cdb314d7604e7e593a0cc1c75779e11c17ea803"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MGXSSM73UEJRSET2HHUEI4CNWV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curve-shortening flow of open, elastic curves in $\\mathbb{R}^2$ with repelling endpoints: A minimizing movement approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Rufat Badal","submitted_at":"2019-02-21T14:50:53Z","abstract_excerpt":"We study an $L^{2}$-type gradient flow of an immersed elastic curve in $\\mathbb{R}^{2}$ whose endpoints repel each other via a Coulomb potential. By De Giorgi's minimizing movements scheme we prove long-time existence of the flow. The work is complemented by several numerical experiments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08079","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":"2026-05-17T23:53:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r5jFp1YKMqDa7PSCp++IH5/275uc3qsbnkUHlqFugpUsGKCtRf/J4jsJ/ppYgYvcKIN+gTFHwwiygYI7GAkkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T14:01:00.018225Z"},"content_sha256":"03252fc9c084b6e92708f7d3d0274cd7bb50f1da31f2e705f2b7ba9e20e6d062","schema_version":"1.0","event_id":"sha256:03252fc9c084b6e92708f7d3d0274cd7bb50f1da31f2e705f2b7ba9e20e6d062"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MGXSSM73UEJRSET2HHUEI4CNWV/bundle.json","state_url":"https://pith.science/pith/MGXSSM73UEJRSET2HHUEI4CNWV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MGXSSM73UEJRSET2HHUEI4CNWV/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":"2026-06-01T14:01:00Z","links":{"resolver":"https://pith.science/pith/MGXSSM73UEJRSET2HHUEI4CNWV","bundle":"https://pith.science/pith/MGXSSM73UEJRSET2HHUEI4CNWV/bundle.json","state":"https://pith.science/pith/MGXSSM73UEJRSET2HHUEI4CNWV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MGXSSM73UEJRSET2HHUEI4CNWV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MGXSSM73UEJRSET2HHUEI4CNWV","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":"22d68a73c6824a5cd031fc417a279614586e74c3514637d5dc552829fde396f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-21T14:50:53Z","title_canon_sha256":"d6570bfaef0bc677825608d63ee09d669788fdd5f09e72a65236eee865a38ee7"},"schema_version":"1.0","source":{"id":"1902.08079","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.08079","created_at":"2026-05-17T23:53:02Z"},{"alias_kind":"arxiv_version","alias_value":"1902.08079v1","created_at":"2026-05-17T23:53:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.08079","created_at":"2026-05-17T23:53:02Z"},{"alias_kind":"pith_short_12","alias_value":"MGXSSM73UEJR","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MGXSSM73UEJRSET2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MGXSSM73","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:03252fc9c084b6e92708f7d3d0274cd7bb50f1da31f2e705f2b7ba9e20e6d062","target":"graph","created_at":"2026-05-17T23:53:02Z","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 an $L^{2}$-type gradient flow of an immersed elastic curve in $\\mathbb{R}^{2}$ whose endpoints repel each other via a Coulomb potential. By De Giorgi's minimizing movements scheme we prove long-time existence of the flow. The work is complemented by several numerical experiments.","authors_text":"Rufat Badal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-21T14:50:53Z","title":"Curve-shortening flow of open, elastic curves in $\\mathbb{R}^2$ with repelling endpoints: A minimizing movement approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.08079","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:c0fdace745296b7d4c328c951cdb314d7604e7e593a0cc1c75779e11c17ea803","target":"record","created_at":"2026-05-17T23:53:02Z","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":"22d68a73c6824a5cd031fc417a279614586e74c3514637d5dc552829fde396f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-21T14:50:53Z","title_canon_sha256":"d6570bfaef0bc677825608d63ee09d669788fdd5f09e72a65236eee865a38ee7"},"schema_version":"1.0","source":{"id":"1902.08079","kind":"arxiv","version":1}},"canonical_sha256":"61af2933fba11319127a39e844704db5584a1c3342edbb6d7c69265b359ea2ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61af2933fba11319127a39e844704db5584a1c3342edbb6d7c69265b359ea2ce","first_computed_at":"2026-05-17T23:53:02.137895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:02.137895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K44VfdGh6HaNxR+3X7DzuW6ABfLJmfvg7VPy/wJD6uWtSti4D/6wO10MA+4xly+icGxB6W+jebxw5sdSH5QADQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:02.138798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.08079","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0fdace745296b7d4c328c951cdb314d7604e7e593a0cc1c75779e11c17ea803","sha256:03252fc9c084b6e92708f7d3d0274cd7bb50f1da31f2e705f2b7ba9e20e6d062"],"state_sha256":"aeb99f32a31ee4731ac5c814253bba599c13f0ff8d0d1579227994d64f9ab78a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kM5tWPl+27B2iWjyc/ZQAjhXb6PTy8QORzdFd0LsPrEtoMUqc+bG7vravvW9xNfsfC7ZZtI2sjH5He2vAMBZCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T14:01:00.020138Z","bundle_sha256":"640dddd0025e2bbaacdbd2994f90f8e73f73d95a477184fa3689acb09bc3d36a"}}