{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:KJOCR5LQ7XGP7Z6JQHQE6AUPQG","short_pith_number":"pith:KJOCR5LQ","canonical_record":{"source":{"id":"1003.4842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-03-25T10:28:58Z","cross_cats_sorted":[],"title_canon_sha256":"3f6e5a4de9b1500c039075e96e7e3b696045bba777f83d81b25f6518d2532139","abstract_canon_sha256":"7d364d055765950bb02b69488e1ac762eb519c3b221737812b97742b49546b71"},"schema_version":"1.0"},"canonical_sha256":"525c28f570fdccffe7c981e04f028f8187dca98d9a0b367f1e17828abcb71795","source":{"kind":"arxiv","id":"1003.4842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4842","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4842v1","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4842","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"pith_short_12","alias_value":"KJOCR5LQ7XGP","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KJOCR5LQ7XGP7Z6J","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KJOCR5LQ","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:KJOCR5LQ7XGP7Z6JQHQE6AUPQG","target":"record","payload":{"canonical_record":{"source":{"id":"1003.4842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-03-25T10:28:58Z","cross_cats_sorted":[],"title_canon_sha256":"3f6e5a4de9b1500c039075e96e7e3b696045bba777f83d81b25f6518d2532139","abstract_canon_sha256":"7d364d055765950bb02b69488e1ac762eb519c3b221737812b97742b49546b71"},"schema_version":"1.0"},"canonical_sha256":"525c28f570fdccffe7c981e04f028f8187dca98d9a0b367f1e17828abcb71795","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:22.252629Z","signature_b64":"RQecNojEfV3mN2WIChUGcYjxcMFdIm1OLsS/4KSaMpwObaexgzjIN9Yi4IMbE0DrcnBs2wchsngzIKNERiO+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"525c28f570fdccffe7c981e04f028f8187dca98d9a0b367f1e17828abcb71795","last_reissued_at":"2026-05-18T03:03:22.252110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:22.252110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.4842","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":"2026-05-18T03:03:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K2hluVr/F/Y1ti8lKEV3G8yinfgSngQjgMAKe2SRawO4KmiSLuKxjudMW37oc+a0uQDoiefM9PQg1c1ufH4UAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:18:20.892748Z"},"content_sha256":"b0bd1f16c21b9826a92a17c0f7b4f35fc2b506a59573f09a4f1fe19ff0e9df79","schema_version":"1.0","event_id":"sha256:b0bd1f16c21b9826a92a17c0f7b4f35fc2b506a59573f09a4f1fe19ff0e9df79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:KJOCR5LQ7XGP7Z6JQHQE6AUPQG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lipschitz classification of almost-Riemannian distances on compact oriented surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Gr\\'egoire Charlot (IF), Inria Lorraine / Iecn / Mmas), Mario Sigalotti (IECN, Roberta Ghezzi (SISSA), Ugo Boscain","submitted_at":"2010-03-25T10:28:58Z","abstract_excerpt":"Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot--Caratheodory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyse the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4842","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":"2026-05-18T03:03:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Stzz5wbnF9Vokyo2LCZHgpNEeTcyCNcZta7QvJRwr+6RriVmCVzofbJbb9pwMOJD2D9SBWnA7KUefK2/6Zc+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T22:18:20.893089Z"},"content_sha256":"664a09c7d5a2eafd177d4115d918968f07132bd1a4f2a2fbde11540f75d33f48","schema_version":"1.0","event_id":"sha256:664a09c7d5a2eafd177d4115d918968f07132bd1a4f2a2fbde11540f75d33f48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJOCR5LQ7XGP7Z6JQHQE6AUPQG/bundle.json","state_url":"https://pith.science/pith/KJOCR5LQ7XGP7Z6JQHQE6AUPQG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJOCR5LQ7XGP7Z6JQHQE6AUPQG/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":"2026-06-20T22:18:20Z","links":{"resolver":"https://pith.science/pith/KJOCR5LQ7XGP7Z6JQHQE6AUPQG","bundle":"https://pith.science/pith/KJOCR5LQ7XGP7Z6JQHQE6AUPQG/bundle.json","state":"https://pith.science/pith/KJOCR5LQ7XGP7Z6JQHQE6AUPQG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJOCR5LQ7XGP7Z6JQHQE6AUPQG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:KJOCR5LQ7XGP7Z6JQHQE6AUPQG","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":"7d364d055765950bb02b69488e1ac762eb519c3b221737812b97742b49546b71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-03-25T10:28:58Z","title_canon_sha256":"3f6e5a4de9b1500c039075e96e7e3b696045bba777f83d81b25f6518d2532139"},"schema_version":"1.0","source":{"id":"1003.4842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.4842","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"arxiv_version","alias_value":"1003.4842v1","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.4842","created_at":"2026-05-18T03:03:22Z"},{"alias_kind":"pith_short_12","alias_value":"KJOCR5LQ7XGP","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"KJOCR5LQ7XGP7Z6J","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"KJOCR5LQ","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:664a09c7d5a2eafd177d4115d918968f07132bd1a4f2a2fbde11540f75d33f48","target":"graph","created_at":"2026-05-18T03:03:22Z","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":"Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot--Caratheodory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyse the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket a","authors_text":"Gr\\'egoire Charlot (IF), Inria Lorraine / Iecn / Mmas), Mario Sigalotti (IECN, Roberta Ghezzi (SISSA), Ugo Boscain","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-03-25T10:28:58Z","title":"Lipschitz classification of almost-Riemannian distances on compact oriented surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4842","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:b0bd1f16c21b9826a92a17c0f7b4f35fc2b506a59573f09a4f1fe19ff0e9df79","target":"record","created_at":"2026-05-18T03:03:22Z","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":"7d364d055765950bb02b69488e1ac762eb519c3b221737812b97742b49546b71","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-03-25T10:28:58Z","title_canon_sha256":"3f6e5a4de9b1500c039075e96e7e3b696045bba777f83d81b25f6518d2532139"},"schema_version":"1.0","source":{"id":"1003.4842","kind":"arxiv","version":1}},"canonical_sha256":"525c28f570fdccffe7c981e04f028f8187dca98d9a0b367f1e17828abcb71795","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"525c28f570fdccffe7c981e04f028f8187dca98d9a0b367f1e17828abcb71795","first_computed_at":"2026-05-18T03:03:22.252110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:22.252110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RQecNojEfV3mN2WIChUGcYjxcMFdIm1OLsS/4KSaMpwObaexgzjIN9Yi4IMbE0DrcnBs2wchsngzIKNERiO+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:22.252629Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.4842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0bd1f16c21b9826a92a17c0f7b4f35fc2b506a59573f09a4f1fe19ff0e9df79","sha256:664a09c7d5a2eafd177d4115d918968f07132bd1a4f2a2fbde11540f75d33f48"],"state_sha256":"9b78c95f1294dfb8b9229d881fbcbf32fa6d2ce872df5262c77592e2447cfaad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TWYP0sZ54nHqDzEqQxpqi2d0oG/MdBcxWgWdNgQZ4byM7Ef8YxbgY/tn6tP2XIECiRTwDNQUITJt5c4KNHgCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T22:18:20.895056Z","bundle_sha256":"302970f111436108d97fefd7e9383f65105e39cbf8538a0cce0a913de8846c75"}}