{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NJRKQRLAYQTCV3CZJEFKRHQ4B4","short_pith_number":"pith:NJRKQRLA","canonical_record":{"source":{"id":"1509.05578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-18T10:27:59Z","cross_cats_sorted":["math.MG","math.OC"],"title_canon_sha256":"537cda1b412ba97c555f38d848773541b89e4cfc5506a4c897a214a6964591dd","abstract_canon_sha256":"3e5b5133961b2bdce97a2c2ab24f14c354d92f0404ccc8d3493fd90c8c06fc87"},"schema_version":"1.0"},"canonical_sha256":"6a62a84560c4262aec59490aa89e1c0f3c40295449494f60821090006e3807dc","source":{"kind":"arxiv","id":"1509.05578","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05578","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05578v2","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05578","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"pith_short_12","alias_value":"NJRKQRLAYQTC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJRKQRLAYQTCV3CZ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJRKQRLA","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NJRKQRLAYQTCV3CZJEFKRHQ4B4","target":"record","payload":{"canonical_record":{"source":{"id":"1509.05578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-18T10:27:59Z","cross_cats_sorted":["math.MG","math.OC"],"title_canon_sha256":"537cda1b412ba97c555f38d848773541b89e4cfc5506a4c897a214a6964591dd","abstract_canon_sha256":"3e5b5133961b2bdce97a2c2ab24f14c354d92f0404ccc8d3493fd90c8c06fc87"},"schema_version":"1.0"},"canonical_sha256":"6a62a84560c4262aec59490aa89e1c0f3c40295449494f60821090006e3807dc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:41.377473Z","signature_b64":"8WswrK1UUYMJMkD2YPwQejSBSrNsd7buYwSXX55NjFvs2OIJ2EgU8QDR5vrG0QNMj2n/4+yPGd3oaLpK+y9iCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a62a84560c4262aec59490aa89e1c0f3c40295449494f60821090006e3807dc","last_reissued_at":"2026-05-18T00:54:41.377027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:41.377027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.05578","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:54:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"edo/zoQEBTw4O1EhuK04ukqTYxkgjVoy6xYw3FiErb7fHpuxpPMoO/fsD74mJt5MS34KW3zLJe2YwdUG8fLvBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T11:56:40.091140Z"},"content_sha256":"698599b22b1f414acb211301a6ca3fee6237fd06b8a871fc979216f2a8672e8c","schema_version":"1.0","event_id":"sha256:698599b22b1f414acb211301a6ca3fee6237fd06b8a871fc979216f2a8672e8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NJRKQRLAYQTCV3CZJEFKRHQ4B4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-minimality of corners in subriemannian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.OC"],"primary_cat":"math.DG","authors_text":"Eero Hakavuori, Enrico Le Donne","submitted_at":"2015-09-18T10:27:59Z","abstract_excerpt":"We give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result we solve Problem II of Agrachev's list, and provide the first general result toward the 30-year-old open problem of regularity of subriemannian geodesics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05578","kind":"arxiv","version":2},"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":"2026-05-18T00:54:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"79BhHR9GyhdEN7LA0kROrioSp/boR6rNUbYUJ62NjBizm4nDBlqYUj3blKagtRa9b3W9UoViTl/bQ4XoIthGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T11:56:40.091494Z"},"content_sha256":"79034ff17531b12c5e24715619b0f2dbf884c8ccce5dabd1317551410f3ec69e","schema_version":"1.0","event_id":"sha256:79034ff17531b12c5e24715619b0f2dbf884c8ccce5dabd1317551410f3ec69e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJRKQRLAYQTCV3CZJEFKRHQ4B4/bundle.json","state_url":"https://pith.science/pith/NJRKQRLAYQTCV3CZJEFKRHQ4B4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJRKQRLAYQTCV3CZJEFKRHQ4B4/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":"2026-07-03T11:56:40Z","links":{"resolver":"https://pith.science/pith/NJRKQRLAYQTCV3CZJEFKRHQ4B4","bundle":"https://pith.science/pith/NJRKQRLAYQTCV3CZJEFKRHQ4B4/bundle.json","state":"https://pith.science/pith/NJRKQRLAYQTCV3CZJEFKRHQ4B4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJRKQRLAYQTCV3CZJEFKRHQ4B4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NJRKQRLAYQTCV3CZJEFKRHQ4B4","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":"3e5b5133961b2bdce97a2c2ab24f14c354d92f0404ccc8d3493fd90c8c06fc87","cross_cats_sorted":["math.MG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-18T10:27:59Z","title_canon_sha256":"537cda1b412ba97c555f38d848773541b89e4cfc5506a4c897a214a6964591dd"},"schema_version":"1.0","source":{"id":"1509.05578","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.05578","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"arxiv_version","alias_value":"1509.05578v2","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05578","created_at":"2026-05-18T00:54:41Z"},{"alias_kind":"pith_short_12","alias_value":"NJRKQRLAYQTC","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NJRKQRLAYQTCV3CZ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NJRKQRLA","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:79034ff17531b12c5e24715619b0f2dbf884c8ccce5dabd1317551410f3ec69e","target":"graph","created_at":"2026-05-18T00:54:41Z","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 give a short solution to one of the main open problems in subriemannian geometry. Namely, we prove that length minimizers do not have corner-type singularities. With this result we solve Problem II of Agrachev's list, and provide the first general result toward the 30-year-old open problem of regularity of subriemannian geodesics.","authors_text":"Eero Hakavuori, Enrico Le Donne","cross_cats":["math.MG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-18T10:27:59Z","title":"Non-minimality of corners in subriemannian geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05578","kind":"arxiv","version":2},"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":"sha256:698599b22b1f414acb211301a6ca3fee6237fd06b8a871fc979216f2a8672e8c","target":"record","created_at":"2026-05-18T00:54:41Z","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":"3e5b5133961b2bdce97a2c2ab24f14c354d92f0404ccc8d3493fd90c8c06fc87","cross_cats_sorted":["math.MG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-09-18T10:27:59Z","title_canon_sha256":"537cda1b412ba97c555f38d848773541b89e4cfc5506a4c897a214a6964591dd"},"schema_version":"1.0","source":{"id":"1509.05578","kind":"arxiv","version":2}},"canonical_sha256":"6a62a84560c4262aec59490aa89e1c0f3c40295449494f60821090006e3807dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a62a84560c4262aec59490aa89e1c0f3c40295449494f60821090006e3807dc","first_computed_at":"2026-05-18T00:54:41.377027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:41.377027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8WswrK1UUYMJMkD2YPwQejSBSrNsd7buYwSXX55NjFvs2OIJ2EgU8QDR5vrG0QNMj2n/4+yPGd3oaLpK+y9iCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:41.377473Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.05578","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:698599b22b1f414acb211301a6ca3fee6237fd06b8a871fc979216f2a8672e8c","sha256:79034ff17531b12c5e24715619b0f2dbf884c8ccce5dabd1317551410f3ec69e"],"state_sha256":"b4ebaa34367af2dcda4dbe81fb0107ee528f7a59ce2ba0eba9ef42bf772b9e35"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sqwldsKRZduYGcEnokKWSfAsqjUTOH+HFEDCLUhnjbkDQPE7cbKWJ0IbtMNGboxOA9B3ApVN5I2P9O4+JocKCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T11:56:40.093423Z","bundle_sha256":"24ac6207ee77b9812f773ac0e8926abfb940e974519ec07a6497c8d8a596277a"}}