{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZEEZWLYBHBI4E6462FMXIX4DMB","short_pith_number":"pith:ZEEZWLYB","canonical_record":{"source":{"id":"1810.09308","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-22T14:21:25Z","cross_cats_sorted":["math.DS","math.SG"],"title_canon_sha256":"6abeb6d1d005984ee6c791f289ae413e053a82fa25e6548d81a52a4e1ec46b74","abstract_canon_sha256":"8d6e87b31d8f834a42872f8898fd41b77d66c940ccc338b034137d564eaff625"},"schema_version":"1.0"},"canonical_sha256":"c9099b2f013851c27b9ed159745f83606c1f002521914982305180bdb4b22951","source":{"kind":"arxiv","id":"1810.09308","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09308","created_at":"2026-05-17T23:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09308v3","created_at":"2026-05-17T23:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09308","created_at":"2026-05-17T23:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"ZEEZWLYBHBI4","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZEEZWLYBHBI4E646","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZEEZWLYB","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZEEZWLYBHBI4E6462FMXIX4DMB","target":"record","payload":{"canonical_record":{"source":{"id":"1810.09308","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-22T14:21:25Z","cross_cats_sorted":["math.DS","math.SG"],"title_canon_sha256":"6abeb6d1d005984ee6c791f289ae413e053a82fa25e6548d81a52a4e1ec46b74","abstract_canon_sha256":"8d6e87b31d8f834a42872f8898fd41b77d66c940ccc338b034137d564eaff625"},"schema_version":"1.0"},"canonical_sha256":"c9099b2f013851c27b9ed159745f83606c1f002521914982305180bdb4b22951","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:28.813884Z","signature_b64":"ij2G/xg8PdgSoPx/X8FW8EIiCmpmXfraelYE4J3W0YYbQA8I28bTjzQu+QYs9G2h2c8bBxs9GSo7YfGugggmAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9099b2f013851c27b9ed159745f83606c1f002521914982305180bdb4b22951","last_reissued_at":"2026-05-17T23:55:28.813469Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:28.813469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.09308","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/GxkxIKGwRCTGaOVS/elgp5ZPx1QPc18JRxMoUgU3N2oGf8AFncla/SXKhKOqgUCx9YIspFRBdX+KA95cdfOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:30:47.645735Z"},"content_sha256":"11733109746cc859599dc680cc1dabc85809b9431a1eeefcff37e4a2c9a7449e","schema_version":"1.0","event_id":"sha256:11733109746cc859599dc680cc1dabc85809b9431a1eeefcff37e4a2c9a7449e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZEEZWLYBHBI4E6462FMXIX4DMB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of closed $C^{1,1}$ curves of constant curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.SG"],"primary_cat":"math.DG","authors_text":"Daniel Ketover, Yevgeny Liokumovich","submitted_at":"2018-10-22T14:21:25Z","abstract_excerpt":"We show that on any Riemannian surface for each $0<c<\\infty$ there exists an immersed $C^{1,1}$ curve that is smooth and with curvature equal to $\\pm c$ away from a point. We give examples showing that, in general, the regularity of the curve obtained by our procedure cannot be improved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09308","kind":"arxiv","version":3},"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":"2026-05-17T23:55:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PbGG1aoZTmti/c8jhnkZbpaSg2J8d9lswE7DsL9QwGD2xXU82utsLl+HaYUoa//ZpDCpsBkSf1USndqVsy95CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:30:47.646418Z"},"content_sha256":"c61d58d21b579b531e10d3067aa8a20909ac6df95d3fd9ac37a677a37c412573","schema_version":"1.0","event_id":"sha256:c61d58d21b579b531e10d3067aa8a20909ac6df95d3fd9ac37a677a37c412573"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZEEZWLYBHBI4E6462FMXIX4DMB/bundle.json","state_url":"https://pith.science/pith/ZEEZWLYBHBI4E6462FMXIX4DMB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZEEZWLYBHBI4E6462FMXIX4DMB/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":"2026-06-06T20:30:47Z","links":{"resolver":"https://pith.science/pith/ZEEZWLYBHBI4E6462FMXIX4DMB","bundle":"https://pith.science/pith/ZEEZWLYBHBI4E6462FMXIX4DMB/bundle.json","state":"https://pith.science/pith/ZEEZWLYBHBI4E6462FMXIX4DMB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZEEZWLYBHBI4E6462FMXIX4DMB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZEEZWLYBHBI4E6462FMXIX4DMB","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":"8d6e87b31d8f834a42872f8898fd41b77d66c940ccc338b034137d564eaff625","cross_cats_sorted":["math.DS","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-22T14:21:25Z","title_canon_sha256":"6abeb6d1d005984ee6c791f289ae413e053a82fa25e6548d81a52a4e1ec46b74"},"schema_version":"1.0","source":{"id":"1810.09308","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.09308","created_at":"2026-05-17T23:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"1810.09308v3","created_at":"2026-05-17T23:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09308","created_at":"2026-05-17T23:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"ZEEZWLYBHBI4","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"ZEEZWLYBHBI4E646","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"ZEEZWLYB","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:c61d58d21b579b531e10d3067aa8a20909ac6df95d3fd9ac37a677a37c412573","target":"graph","created_at":"2026-05-17T23:55:28Z","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 show that on any Riemannian surface for each $0<c<\\infty$ there exists an immersed $C^{1,1}$ curve that is smooth and with curvature equal to $\\pm c$ away from a point. We give examples showing that, in general, the regularity of the curve obtained by our procedure cannot be improved.","authors_text":"Daniel Ketover, Yevgeny Liokumovich","cross_cats":["math.DS","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-22T14:21:25Z","title":"On the existence of closed $C^{1,1}$ curves of constant curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09308","kind":"arxiv","version":3},"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":"sha256:11733109746cc859599dc680cc1dabc85809b9431a1eeefcff37e4a2c9a7449e","target":"record","created_at":"2026-05-17T23:55:28Z","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":"8d6e87b31d8f834a42872f8898fd41b77d66c940ccc338b034137d564eaff625","cross_cats_sorted":["math.DS","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-10-22T14:21:25Z","title_canon_sha256":"6abeb6d1d005984ee6c791f289ae413e053a82fa25e6548d81a52a4e1ec46b74"},"schema_version":"1.0","source":{"id":"1810.09308","kind":"arxiv","version":3}},"canonical_sha256":"c9099b2f013851c27b9ed159745f83606c1f002521914982305180bdb4b22951","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9099b2f013851c27b9ed159745f83606c1f002521914982305180bdb4b22951","first_computed_at":"2026-05-17T23:55:28.813469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:28.813469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ij2G/xg8PdgSoPx/X8FW8EIiCmpmXfraelYE4J3W0YYbQA8I28bTjzQu+QYs9G2h2c8bBxs9GSo7YfGugggmAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:28.813884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.09308","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11733109746cc859599dc680cc1dabc85809b9431a1eeefcff37e4a2c9a7449e","sha256:c61d58d21b579b531e10d3067aa8a20909ac6df95d3fd9ac37a677a37c412573"],"state_sha256":"bcf2694e6d68f6473e3bdbd7e1a0dcd1c85ce6c074c29037e548a943db08fb2c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3wJEO8b39QNUaY5DEDvE/IqVtvGSP6yIf8uEcBaKMFj0eMRtjpV6bCUXSS0aet73fGRA5KeYGhF17/ngdhxdCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:30:47.649797Z","bundle_sha256":"9234038ab8c2681ba22f96c32075a1f5b51166f4d2ae0ca6107d4e00ea3f33f2"}}