{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:XFFDHS54AQQZVB5HK2NBDPDFLL","short_pith_number":"pith:XFFDHS54","schema_version":"1.0","canonical_sha256":"b94a33cbbc04219a87a7569a11bc655ac654c9ee0248720f4624c939c02a23d9","source":{"kind":"arxiv","id":"1412.4565","version":1},"attestation_state":"computed","paper":{"title":"Some differential properties of $GL_n(\\mathbb{R})$ with the trace metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alberto Dolcetti, Donato Pertici","submitted_at":"2014-12-15T12:38:56Z","abstract_excerpt":"In this note we consider some properties of $GL_n(\\mathbb{R})$ with the Semi-Riemannian structure induced by the trace metric $g$. In particular we study geodesics and curvature tensors. Moreover we prove that $GL_n$ has a suitable foliation, whose leaves are isometric to $(SL_n(\\mathbb{R}), g)$, while its component of matrices with positive determinant is isometric to the Semi-Riemannian product manifold $SL_n \\times \\mathbb{R}$."},"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":"1412.4565","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-15T12:38:56Z","cross_cats_sorted":[],"title_canon_sha256":"0afbe445d68b24cda91364e82a596b490ca7da7551cb2e784d40aca34abb6390","abstract_canon_sha256":"70dc4dbd64ddb0a2ce80baae674538de431671f0b5b3d3019098c3b9dbc5d807"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:18.813989Z","signature_b64":"412eeVm5L5N59/rurzBzey+P8Wqr4VaX80bSHVc00Id+50z6lVc+bROg7CjXwlBZ3RSDGy3r1Shxpx601YmHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b94a33cbbc04219a87a7569a11bc655ac654c9ee0248720f4624c939c02a23d9","last_reissued_at":"2026-05-18T02:31:18.813407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:18.813407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some differential properties of $GL_n(\\mathbb{R})$ with the trace metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Alberto Dolcetti, Donato Pertici","submitted_at":"2014-12-15T12:38:56Z","abstract_excerpt":"In this note we consider some properties of $GL_n(\\mathbb{R})$ with the Semi-Riemannian structure induced by the trace metric $g$. In particular we study geodesics and curvature tensors. Moreover we prove that $GL_n$ has a suitable foliation, whose leaves are isometric to $(SL_n(\\mathbb{R}), g)$, while its component of matrices with positive determinant is isometric to the Semi-Riemannian product manifold $SL_n \\times \\mathbb{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4565","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":"1412.4565","created_at":"2026-05-18T02:31:18.813503+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.4565v1","created_at":"2026-05-18T02:31:18.813503+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4565","created_at":"2026-05-18T02:31:18.813503+00:00"},{"alias_kind":"pith_short_12","alias_value":"XFFDHS54AQQZ","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"XFFDHS54AQQZVB5H","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"XFFDHS54","created_at":"2026-05-18T12:28:57.508820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.12534","citing_title":"A data-based notion of quantiles on Hadamard spaces","ref_index":7,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XFFDHS54AQQZVB5HK2NBDPDFLL","json":"https://pith.science/pith/XFFDHS54AQQZVB5HK2NBDPDFLL.json","graph_json":"https://pith.science/api/pith-number/XFFDHS54AQQZVB5HK2NBDPDFLL/graph.json","events_json":"https://pith.science/api/pith-number/XFFDHS54AQQZVB5HK2NBDPDFLL/events.json","paper":"https://pith.science/paper/XFFDHS54"},"agent_actions":{"view_html":"https://pith.science/pith/XFFDHS54AQQZVB5HK2NBDPDFLL","download_json":"https://pith.science/pith/XFFDHS54AQQZVB5HK2NBDPDFLL.json","view_paper":"https://pith.science/paper/XFFDHS54","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.4565&json=true","fetch_graph":"https://pith.science/api/pith-number/XFFDHS54AQQZVB5HK2NBDPDFLL/graph.json","fetch_events":"https://pith.science/api/pith-number/XFFDHS54AQQZVB5HK2NBDPDFLL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XFFDHS54AQQZVB5HK2NBDPDFLL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XFFDHS54AQQZVB5HK2NBDPDFLL/action/storage_attestation","attest_author":"https://pith.science/pith/XFFDHS54AQQZVB5HK2NBDPDFLL/action/author_attestation","sign_citation":"https://pith.science/pith/XFFDHS54AQQZVB5HK2NBDPDFLL/action/citation_signature","submit_replication":"https://pith.science/pith/XFFDHS54AQQZVB5HK2NBDPDFLL/action/replication_record"}},"created_at":"2026-05-18T02:31:18.813503+00:00","updated_at":"2026-05-18T02:31:18.813503+00:00"}