{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QYCAATZNCYVOIG3XUYSYGENV5Y","short_pith_number":"pith:QYCAATZN","canonical_record":{"source":{"id":"1508.01186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-05T19:21:58Z","cross_cats_sorted":[],"title_canon_sha256":"b51b6f9cea02431f1f55b7f6b4527d2c7e55c44f8c5cf9e043fc8f30677ef14f","abstract_canon_sha256":"b1a0bb0716a6734a52e116a0f2a44a7df906f124aee17b0baa4e5fe355e13867"},"schema_version":"1.0"},"canonical_sha256":"8604004f2d162ae41b77a6258311b5ee062dbad78c59baa2ff046777a86bd1dd","source":{"kind":"arxiv","id":"1508.01186","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01186","created_at":"2026-05-18T01:35:43Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01186v1","created_at":"2026-05-18T01:35:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01186","created_at":"2026-05-18T01:35:43Z"},{"alias_kind":"pith_short_12","alias_value":"QYCAATZNCYVO","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QYCAATZNCYVOIG3X","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QYCAATZN","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QYCAATZNCYVOIG3XUYSYGENV5Y","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01186","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-05T19:21:58Z","cross_cats_sorted":[],"title_canon_sha256":"b51b6f9cea02431f1f55b7f6b4527d2c7e55c44f8c5cf9e043fc8f30677ef14f","abstract_canon_sha256":"b1a0bb0716a6734a52e116a0f2a44a7df906f124aee17b0baa4e5fe355e13867"},"schema_version":"1.0"},"canonical_sha256":"8604004f2d162ae41b77a6258311b5ee062dbad78c59baa2ff046777a86bd1dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:43.896634Z","signature_b64":"RRLeFukeHl+kqSgd4QJeflA0jI0v6VTnv8jqzMV1mEp3X0GauQE4Em/YvlPpJcZ23xc9vySQOnxA8752unUZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8604004f2d162ae41b77a6258311b5ee062dbad78c59baa2ff046777a86bd1dd","last_reissued_at":"2026-05-18T01:35:43.896237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:43.896237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01186","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":"2026-05-18T01:35:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qWZBmLnOgaI6LLxyN8HVA0gBZfdKkMAc21x0L3DT04s1LHhcA09Rq9evViiLndHquD6jpfYBQpwUUtW4O4yrAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:02:21.781010Z"},"content_sha256":"1ca67eef4b580f5d061dbc42c0b0978e66eabd303cd2315ff25ae9031e585663","schema_version":"1.0","event_id":"sha256:1ca67eef4b580f5d061dbc42c0b0978e66eabd303cd2315ff25ae9031e585663"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QYCAATZNCYVOIG3XUYSYGENV5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Legendrian curve shortening flow in $\\mathbb{R}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gregory Drugan, Micah W. Warren, Weiyong He","submitted_at":"2015-08-05T19:21:58Z","abstract_excerpt":"Motivated by Legendrian curve shortening flows in $\\mathbb{R}^{3}$, we study the curve shortening flow of figure-eight curves in the plane. We show that, under some symmetry and curvature conditions, a figure-eight curve will shrink to a point at the first singular time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01186","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":"2026-05-18T01:35:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"75GomliOmkc2w6bgzHpZn7xDf2qDyVFdjiflYOhdaJooFrZHfmyXsFhc7RLhUGO8gT/EUz5EQAd/LWtni74uCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:02:21.781375Z"},"content_sha256":"48fda119d03d09e4f648f3dc1b87c5c7144d731e7ad99e61c23c137a21c36899","schema_version":"1.0","event_id":"sha256:48fda119d03d09e4f648f3dc1b87c5c7144d731e7ad99e61c23c137a21c36899"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/bundle.json","state_url":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/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":"2026-06-09T03:02:21Z","links":{"resolver":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y","bundle":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/bundle.json","state":"https://pith.science/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QYCAATZNCYVOIG3XUYSYGENV5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QYCAATZNCYVOIG3XUYSYGENV5Y","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":"b1a0bb0716a6734a52e116a0f2a44a7df906f124aee17b0baa4e5fe355e13867","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-05T19:21:58Z","title_canon_sha256":"b51b6f9cea02431f1f55b7f6b4527d2c7e55c44f8c5cf9e043fc8f30677ef14f"},"schema_version":"1.0","source":{"id":"1508.01186","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01186","created_at":"2026-05-18T01:35:43Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01186v1","created_at":"2026-05-18T01:35:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01186","created_at":"2026-05-18T01:35:43Z"},{"alias_kind":"pith_short_12","alias_value":"QYCAATZNCYVO","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QYCAATZNCYVOIG3X","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QYCAATZN","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:48fda119d03d09e4f648f3dc1b87c5c7144d731e7ad99e61c23c137a21c36899","target":"graph","created_at":"2026-05-18T01:35:43Z","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":"Motivated by Legendrian curve shortening flows in $\\mathbb{R}^{3}$, we study the curve shortening flow of figure-eight curves in the plane. We show that, under some symmetry and curvature conditions, a figure-eight curve will shrink to a point at the first singular time.","authors_text":"Gregory Drugan, Micah W. Warren, Weiyong He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-05T19:21:58Z","title":"Legendrian curve shortening flow in $\\mathbb{R}^{3}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01186","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":"sha256:1ca67eef4b580f5d061dbc42c0b0978e66eabd303cd2315ff25ae9031e585663","target":"record","created_at":"2026-05-18T01:35:43Z","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":"b1a0bb0716a6734a52e116a0f2a44a7df906f124aee17b0baa4e5fe355e13867","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-05T19:21:58Z","title_canon_sha256":"b51b6f9cea02431f1f55b7f6b4527d2c7e55c44f8c5cf9e043fc8f30677ef14f"},"schema_version":"1.0","source":{"id":"1508.01186","kind":"arxiv","version":1}},"canonical_sha256":"8604004f2d162ae41b77a6258311b5ee062dbad78c59baa2ff046777a86bd1dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8604004f2d162ae41b77a6258311b5ee062dbad78c59baa2ff046777a86bd1dd","first_computed_at":"2026-05-18T01:35:43.896237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:43.896237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RRLeFukeHl+kqSgd4QJeflA0jI0v6VTnv8jqzMV1mEp3X0GauQE4Em/YvlPpJcZ23xc9vySQOnxA8752unUZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:43.896634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01186","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ca67eef4b580f5d061dbc42c0b0978e66eabd303cd2315ff25ae9031e585663","sha256:48fda119d03d09e4f648f3dc1b87c5c7144d731e7ad99e61c23c137a21c36899"],"state_sha256":"36cdc178f2afbc517befb2a0324f37b4033e9a0c1ea9947af6f1e468e692cc9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+1T9DH5LlPLEUxgKxd5ooJwD8TL8W9etxqftT7U1HkpGaxVD1yJboC+EkIvA8YrZzX1xkLbTMcaosnqiNCtUBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:02:21.786095Z","bundle_sha256":"361808d90442fc6b5297dd197f15cde7eb2b808a3dd8517619d7bfd920dbaabd"}}