{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WUPFCYRXKBDA7IZTD22A3K7IEW","short_pith_number":"pith:WUPFCYRX","canonical_record":{"source":{"id":"1508.03685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-15T01:18:44Z","cross_cats_sorted":[],"title_canon_sha256":"a8e417da75aa5e3dd094c0f587d9de0a1a49fc87048bffcc79f0c878f59a3e3a","abstract_canon_sha256":"ff57a966a54da12cbda128ea41488bf451a467cf95763608f5c7440fb6bffdd4"},"schema_version":"1.0"},"canonical_sha256":"b51e51623750460fa3331eb40dabe825a5fda461189a673062756f66477f40ed","source":{"kind":"arxiv","id":"1508.03685","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03685","created_at":"2026-05-18T00:46:09Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03685v1","created_at":"2026-05-18T00:46:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03685","created_at":"2026-05-18T00:46:09Z"},{"alias_kind":"pith_short_12","alias_value":"WUPFCYRXKBDA","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WUPFCYRXKBDA7IZT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WUPFCYRX","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WUPFCYRXKBDA7IZTD22A3K7IEW","target":"record","payload":{"canonical_record":{"source":{"id":"1508.03685","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-15T01:18:44Z","cross_cats_sorted":[],"title_canon_sha256":"a8e417da75aa5e3dd094c0f587d9de0a1a49fc87048bffcc79f0c878f59a3e3a","abstract_canon_sha256":"ff57a966a54da12cbda128ea41488bf451a467cf95763608f5c7440fb6bffdd4"},"schema_version":"1.0"},"canonical_sha256":"b51e51623750460fa3331eb40dabe825a5fda461189a673062756f66477f40ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:09.183982Z","signature_b64":"2lZvUSYCJmMfA586zW/LcTuAVUldYPq98H8Lh8PH8Oi93+JSpYiRbHfBBZThIbgv4D4YSyecYH91Uq0ri9QsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b51e51623750460fa3331eb40dabe825a5fda461189a673062756f66477f40ed","last_reissued_at":"2026-05-18T00:46:09.183559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:09.183559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.03685","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":"2026-05-18T00:46:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nGvK+NH9ybAz+8FAaEyyU4CfxjPgJCu+AtIBpZIOXh9M1J0OgUn3+K5zB9XcomgBEkWIf9CHDQ4Dp0fhM9C2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:31:43.689498Z"},"content_sha256":"33505ed80787426e4df1d3b4ed417669b3baa7001d7bd1711dc0c25f8e6b42bd","schema_version":"1.0","event_id":"sha256:33505ed80787426e4df1d3b4ed417669b3baa7001d7bd1711dc0c25f8e6b42bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WUPFCYRXKBDA7IZTD22A3K7IEW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"C^1-umbilics with arbitrarily high indices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Masaaki Umehara, Naoya Ando, Toshifumi Fujiyama","submitted_at":"2015-08-15T01:18:44Z","abstract_excerpt":"In this paper, the existence of C^1-umbilics with arbitrarily high indices is shown. This implies that more than C^1-regularity is required to prove Loewner's conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03685","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":"2026-05-18T00:46:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U7o/5PVpK7NN3XW6Hzu8TdA6kNm4VU6frStVE8SvcsTRNgIwl8TKOhBd2h77NRWxDCrFAA8Mek32pRsr6gUjBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:31:43.689833Z"},"content_sha256":"9a4f047e029124a33914acb3c12fff10918953e46a3df3cc4234d030f293e1a8","schema_version":"1.0","event_id":"sha256:9a4f047e029124a33914acb3c12fff10918953e46a3df3cc4234d030f293e1a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WUPFCYRXKBDA7IZTD22A3K7IEW/bundle.json","state_url":"https://pith.science/pith/WUPFCYRXKBDA7IZTD22A3K7IEW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WUPFCYRXKBDA7IZTD22A3K7IEW/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":"2026-06-28T12:31:43Z","links":{"resolver":"https://pith.science/pith/WUPFCYRXKBDA7IZTD22A3K7IEW","bundle":"https://pith.science/pith/WUPFCYRXKBDA7IZTD22A3K7IEW/bundle.json","state":"https://pith.science/pith/WUPFCYRXKBDA7IZTD22A3K7IEW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WUPFCYRXKBDA7IZTD22A3K7IEW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WUPFCYRXKBDA7IZTD22A3K7IEW","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":"ff57a966a54da12cbda128ea41488bf451a467cf95763608f5c7440fb6bffdd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-15T01:18:44Z","title_canon_sha256":"a8e417da75aa5e3dd094c0f587d9de0a1a49fc87048bffcc79f0c878f59a3e3a"},"schema_version":"1.0","source":{"id":"1508.03685","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03685","created_at":"2026-05-18T00:46:09Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03685v1","created_at":"2026-05-18T00:46:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03685","created_at":"2026-05-18T00:46:09Z"},{"alias_kind":"pith_short_12","alias_value":"WUPFCYRXKBDA","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WUPFCYRXKBDA7IZT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WUPFCYRX","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:9a4f047e029124a33914acb3c12fff10918953e46a3df3cc4234d030f293e1a8","target":"graph","created_at":"2026-05-18T00:46:09Z","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":"In this paper, the existence of C^1-umbilics with arbitrarily high indices is shown. This implies that more than C^1-regularity is required to prove Loewner's conjecture.","authors_text":"Masaaki Umehara, Naoya Ando, Toshifumi Fujiyama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-15T01:18:44Z","title":"C^1-umbilics with arbitrarily high indices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03685","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":"sha256:33505ed80787426e4df1d3b4ed417669b3baa7001d7bd1711dc0c25f8e6b42bd","target":"record","created_at":"2026-05-18T00:46:09Z","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":"ff57a966a54da12cbda128ea41488bf451a467cf95763608f5c7440fb6bffdd4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-15T01:18:44Z","title_canon_sha256":"a8e417da75aa5e3dd094c0f587d9de0a1a49fc87048bffcc79f0c878f59a3e3a"},"schema_version":"1.0","source":{"id":"1508.03685","kind":"arxiv","version":1}},"canonical_sha256":"b51e51623750460fa3331eb40dabe825a5fda461189a673062756f66477f40ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b51e51623750460fa3331eb40dabe825a5fda461189a673062756f66477f40ed","first_computed_at":"2026-05-18T00:46:09.183559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:09.183559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2lZvUSYCJmMfA586zW/LcTuAVUldYPq98H8Lh8PH8Oi93+JSpYiRbHfBBZThIbgv4D4YSyecYH91Uq0ri9QsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:09.183982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03685","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33505ed80787426e4df1d3b4ed417669b3baa7001d7bd1711dc0c25f8e6b42bd","sha256:9a4f047e029124a33914acb3c12fff10918953e46a3df3cc4234d030f293e1a8"],"state_sha256":"78fe57e7b3c5f9872b4c3d8583b46f9098d33b8b9a0fb8928a282e4de74751c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4icjKJWvr+5JRRwTbn+WMA40uEQW8xrYNg+e9GQ58YcMsW+YUem87jajUtR5v+aWhCLU3sQCUncujBN8VzRDBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T12:31:43.691697Z","bundle_sha256":"3e8db847eef06089d738c0a87ff814cae1970044106de48e8aa2a5cf182d6eb9"}}