{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2567XQQ6KL3AGIZS4HLCLWSI4L","short_pith_number":"pith:2567XQQ6","schema_version":"1.0","canonical_sha256":"d77dfbc21e52f6032332e1d625da48e2d45f8747e5a717abc598d327334dbf31","source":{"kind":"arxiv","id":"1406.5870","version":1},"attestation_state":"computed","paper":{"title":"A lossless reduction of geodesics on supermanifolds to non-graded differential geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Matthias Kalus, St\\'ephane Garnier","submitted_at":"2014-06-23T11:29:46Z","abstract_excerpt":"Let $\\mathcal M= (M,\\mathcal O_\\mathcal M)$ be a smooth supermanifold with connection $\\nabla$ and Batchelor model $\\mathcal O_\\mathcal M\\cong\\Gamma_{\\Lambda E^\\ast}$. From $(\\mathcal M,\\nabla)$ we construct a connection on the total space of the vector bundle $E\\to{M}$. This reduction of $\\nabla$ is well-defined independently of the isomorphism $\\mathcal O_\\mathcal M \\cong \\Gamma_{\\Lambda E^\\ast}$. It erases information, but however it turns out that the natural identification of supercurves in $\\mathcal M$ (as maps from $ \\mathbb R^{1|1}$ to $\\mathcal M$) with curves in $E$ restricts to a 1 "},"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":"1406.5870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-06-23T11:29:46Z","cross_cats_sorted":[],"title_canon_sha256":"20d7362d32b99f098d54632b3fed03be7d8b1e0f4bbcd2933521bf9ceeed322e","abstract_canon_sha256":"0c5997267cceb940bce5cdfcf25c67156040c462feaa11a42200ad30686e80be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:31.579270Z","signature_b64":"a5EmO1FG0ZfdpSX7SxX9hHvd8xqDo9I3ADVhkWAuqA4/MOcMNR+usAGzFRQhCs7LTT+l1nRXcUrpNOISAVG5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d77dfbc21e52f6032332e1d625da48e2d45f8747e5a717abc598d327334dbf31","last_reissued_at":"2026-05-18T02:28:31.578373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:31.578373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A lossless reduction of geodesics on supermanifolds to non-graded differential geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Matthias Kalus, St\\'ephane Garnier","submitted_at":"2014-06-23T11:29:46Z","abstract_excerpt":"Let $\\mathcal M= (M,\\mathcal O_\\mathcal M)$ be a smooth supermanifold with connection $\\nabla$ and Batchelor model $\\mathcal O_\\mathcal M\\cong\\Gamma_{\\Lambda E^\\ast}$. From $(\\mathcal M,\\nabla)$ we construct a connection on the total space of the vector bundle $E\\to{M}$. This reduction of $\\nabla$ is well-defined independently of the isomorphism $\\mathcal O_\\mathcal M \\cong \\Gamma_{\\Lambda E^\\ast}$. It erases information, but however it turns out that the natural identification of supercurves in $\\mathcal M$ (as maps from $ \\mathbb R^{1|1}$ to $\\mathcal M$) with curves in $E$ restricts to a 1 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5870","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":"1406.5870","created_at":"2026-05-18T02:28:31.578536+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.5870v1","created_at":"2026-05-18T02:28:31.578536+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5870","created_at":"2026-05-18T02:28:31.578536+00:00"},{"alias_kind":"pith_short_12","alias_value":"2567XQQ6KL3A","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"2567XQQ6KL3AGIZS","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"2567XQQ6","created_at":"2026-05-18T12:28:09.283467+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/2567XQQ6KL3AGIZS4HLCLWSI4L","json":"https://pith.science/pith/2567XQQ6KL3AGIZS4HLCLWSI4L.json","graph_json":"https://pith.science/api/pith-number/2567XQQ6KL3AGIZS4HLCLWSI4L/graph.json","events_json":"https://pith.science/api/pith-number/2567XQQ6KL3AGIZS4HLCLWSI4L/events.json","paper":"https://pith.science/paper/2567XQQ6"},"agent_actions":{"view_html":"https://pith.science/pith/2567XQQ6KL3AGIZS4HLCLWSI4L","download_json":"https://pith.science/pith/2567XQQ6KL3AGIZS4HLCLWSI4L.json","view_paper":"https://pith.science/paper/2567XQQ6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.5870&json=true","fetch_graph":"https://pith.science/api/pith-number/2567XQQ6KL3AGIZS4HLCLWSI4L/graph.json","fetch_events":"https://pith.science/api/pith-number/2567XQQ6KL3AGIZS4HLCLWSI4L/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2567XQQ6KL3AGIZS4HLCLWSI4L/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2567XQQ6KL3AGIZS4HLCLWSI4L/action/storage_attestation","attest_author":"https://pith.science/pith/2567XQQ6KL3AGIZS4HLCLWSI4L/action/author_attestation","sign_citation":"https://pith.science/pith/2567XQQ6KL3AGIZS4HLCLWSI4L/action/citation_signature","submit_replication":"https://pith.science/pith/2567XQQ6KL3AGIZS4HLCLWSI4L/action/replication_record"}},"created_at":"2026-05-18T02:28:31.578536+00:00","updated_at":"2026-05-18T02:28:31.578536+00:00"}