{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:KQQKN2PVPFU4ZKVWP3ADCF7LTF","short_pith_number":"pith:KQQKN2PV","schema_version":"1.0","canonical_sha256":"5420a6e9f57969ccaab67ec03117eb9964793aa296d2a3ec497ca9145b73a0e7","source":{"kind":"arxiv","id":"1303.1421","version":3},"attestation_state":"computed","paper":{"title":"On the Distributional Hessian of the Distance Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.DG","authors_text":"Carlo Mantegazza, Gennady Uraltsev, Giovanni Mascellani","submitted_at":"2013-03-06T18:45:22Z","abstract_excerpt":"We describe the precise structure of the distributional Hessian of the distance function from a point of a Riemannian manifold. In doing this we also discuss some geometrical properties of the cutlocus of a point and we compare some different weak notions of Hessian and Laplacian."},"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":"1303.1421","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-06T18:45:22Z","cross_cats_sorted":["math.AP","math.FA"],"title_canon_sha256":"db96782a2507c5f5e657a164b38c835e021a549855c0b60ce4630f538efeeece","abstract_canon_sha256":"3f1db9df34234cf89bd2c8db6dfdd0dc2bc8e6742d61e6295af5fbfd929c4b5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:25.620606Z","signature_b64":"iHuUy2BB/qEoN5GPIjPi3fFC0ElBMnh/6f2qCX5og5C1uz6sYe2DpYcPhQmjwG5NSI6HLKDyRQ2Rnl744TxWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5420a6e9f57969ccaab67ec03117eb9964793aa296d2a3ec497ca9145b73a0e7","last_reissued_at":"2026-05-18T01:22:25.619885Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:25.619885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Distributional Hessian of the Distance Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA"],"primary_cat":"math.DG","authors_text":"Carlo Mantegazza, Gennady Uraltsev, Giovanni Mascellani","submitted_at":"2013-03-06T18:45:22Z","abstract_excerpt":"We describe the precise structure of the distributional Hessian of the distance function from a point of a Riemannian manifold. In doing this we also discuss some geometrical properties of the cutlocus of a point and we compare some different weak notions of Hessian and Laplacian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.1421","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1303.1421","created_at":"2026-05-18T01:22:25.619998+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.1421v3","created_at":"2026-05-18T01:22:25.619998+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.1421","created_at":"2026-05-18T01:22:25.619998+00:00"},{"alias_kind":"pith_short_12","alias_value":"KQQKN2PVPFU4","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_16","alias_value":"KQQKN2PVPFU4ZKVW","created_at":"2026-05-18T12:27:51.066281+00:00"},{"alias_kind":"pith_short_8","alias_value":"KQQKN2PV","created_at":"2026-05-18T12:27:51.066281+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/KQQKN2PVPFU4ZKVWP3ADCF7LTF","json":"https://pith.science/pith/KQQKN2PVPFU4ZKVWP3ADCF7LTF.json","graph_json":"https://pith.science/api/pith-number/KQQKN2PVPFU4ZKVWP3ADCF7LTF/graph.json","events_json":"https://pith.science/api/pith-number/KQQKN2PVPFU4ZKVWP3ADCF7LTF/events.json","paper":"https://pith.science/paper/KQQKN2PV"},"agent_actions":{"view_html":"https://pith.science/pith/KQQKN2PVPFU4ZKVWP3ADCF7LTF","download_json":"https://pith.science/pith/KQQKN2PVPFU4ZKVWP3ADCF7LTF.json","view_paper":"https://pith.science/paper/KQQKN2PV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.1421&json=true","fetch_graph":"https://pith.science/api/pith-number/KQQKN2PVPFU4ZKVWP3ADCF7LTF/graph.json","fetch_events":"https://pith.science/api/pith-number/KQQKN2PVPFU4ZKVWP3ADCF7LTF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KQQKN2PVPFU4ZKVWP3ADCF7LTF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KQQKN2PVPFU4ZKVWP3ADCF7LTF/action/storage_attestation","attest_author":"https://pith.science/pith/KQQKN2PVPFU4ZKVWP3ADCF7LTF/action/author_attestation","sign_citation":"https://pith.science/pith/KQQKN2PVPFU4ZKVWP3ADCF7LTF/action/citation_signature","submit_replication":"https://pith.science/pith/KQQKN2PVPFU4ZKVWP3ADCF7LTF/action/replication_record"}},"created_at":"2026-05-18T01:22:25.619998+00:00","updated_at":"2026-05-18T01:22:25.619998+00:00"}