{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ZBUGF3YHOCOBZHTE7QN3CXYR6Z","short_pith_number":"pith:ZBUGF3YH","schema_version":"1.0","canonical_sha256":"c86862ef07709c1c9e64fc1bb15f11f65bced55994d43576821dd92508b29d6d","source":{"kind":"arxiv","id":"1009.2612","version":1},"attestation_state":"computed","paper":{"title":"The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bernard Bonnard (IMB), Gabriel Janin (IMB), Gr\\'egoire Charlot (IF), Roberta Ghezzi (SISSA/ISAS)","submitted_at":"2010-09-14T10:07:22Z","abstract_excerpt":"We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Riemannian geometry. We compute estimations of the exponential map which allow us to describe the conjugate locus and the cut locus at a tangency point. We prove that this last one generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.2612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2010-09-14T10:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"e8e91794e167cbc74372045be142d34b68997af1c262ea30af2bb848dbaaed76","abstract_canon_sha256":"ce008d98356ca3bad39f55620334655d9bbfe403b7356301b7300a6e9927690b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:56.709853Z","signature_b64":"YqNOSJcQjfuwL8+jA3O6GHhaJG2tTLBk6kkz77mtLSgj8pJnB0mxprMSyxcEk4k9SKg/zMSn9lJQ4KgHsZPwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c86862ef07709c1c9e64fc1bb15f11f65bced55994d43576821dd92508b29d6d","last_reissued_at":"2026-05-18T04:40:56.709413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:56.709413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The sphere and the cut locus at a tangency point in two-dimensional almost-Riemannian geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bernard Bonnard (IMB), Gabriel Janin (IMB), Gr\\'egoire Charlot (IF), Roberta Ghezzi (SISSA/ISAS)","submitted_at":"2010-09-14T10:07:22Z","abstract_excerpt":"We study the tangential case in 2-dimensional almost-Riemannian geometry. We analyse the connection with the Martinet case in sub-Riemannian geometry. We compute estimations of the exponential map which allow us to describe the conjugate locus and the cut locus at a tangency point. We prove that this last one generically accumulates at the tangency point as an asymmetric cusp whose branches are separated by the singular set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2612","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.2612","created_at":"2026-05-18T04:40:56.709494+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.2612v1","created_at":"2026-05-18T04:40:56.709494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2612","created_at":"2026-05-18T04:40:56.709494+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZBUGF3YHOCOB","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZBUGF3YHOCOBZHTE","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZBUGF3YH","created_at":"2026-05-18T12:26:17.028572+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZBUGF3YHOCOBZHTE7QN3CXYR6Z","json":"https://pith.science/pith/ZBUGF3YHOCOBZHTE7QN3CXYR6Z.json","graph_json":"https://pith.science/api/pith-number/ZBUGF3YHOCOBZHTE7QN3CXYR6Z/graph.json","events_json":"https://pith.science/api/pith-number/ZBUGF3YHOCOBZHTE7QN3CXYR6Z/events.json","paper":"https://pith.science/paper/ZBUGF3YH"},"agent_actions":{"view_html":"https://pith.science/pith/ZBUGF3YHOCOBZHTE7QN3CXYR6Z","download_json":"https://pith.science/pith/ZBUGF3YHOCOBZHTE7QN3CXYR6Z.json","view_paper":"https://pith.science/paper/ZBUGF3YH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.2612&json=true","fetch_graph":"https://pith.science/api/pith-number/ZBUGF3YHOCOBZHTE7QN3CXYR6Z/graph.json","fetch_events":"https://pith.science/api/pith-number/ZBUGF3YHOCOBZHTE7QN3CXYR6Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZBUGF3YHOCOBZHTE7QN3CXYR6Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZBUGF3YHOCOBZHTE7QN3CXYR6Z/action/storage_attestation","attest_author":"https://pith.science/pith/ZBUGF3YHOCOBZHTE7QN3CXYR6Z/action/author_attestation","sign_citation":"https://pith.science/pith/ZBUGF3YHOCOBZHTE7QN3CXYR6Z/action/citation_signature","submit_replication":"https://pith.science/pith/ZBUGF3YHOCOBZHTE7QN3CXYR6Z/action/replication_record"}},"created_at":"2026-05-18T04:40:56.709494+00:00","updated_at":"2026-05-18T04:40:56.709494+00:00"}