{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:IFQ2DL23VXBC45J7JLHQUPJVEE","short_pith_number":"pith:IFQ2DL23","schema_version":"1.0","canonical_sha256":"4161a1af5badc22e753f4acf0a3d35210bbe721ed17adabc124f150b9a091c8d","source":{"kind":"arxiv","id":"1511.02084","version":1},"attestation_state":"computed","paper":{"title":"The trace as an average over the unit sphere of a normed space with a 1-symmetric basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Kent E. Morrison, Tomasz Kania","submitted_at":"2015-11-06T14:10:05Z","abstract_excerpt":"We generalise the formula expressing the matrix trace of a given square matrix as the integral of the numerical values of $A$ over the Euclidean sphere to the unit spheres of finite-dimensional normed spaces that have a 1-symmetric basis. Our result is new even in the case of $\\ell_p$-norms in $\\mathbb{R}^N$ for $p\\neq 2$."},"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":"1511.02084","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-11-06T14:10:05Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"80d69d609bfaf503c5236c562bd2daef38e7a580c59fb1ac09cb5d44a857d554","abstract_canon_sha256":"c807fa50ec82d3ff3abeee3dd8baaf956da4806dab16073edbbc820198a08307"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:10.018905Z","signature_b64":"p8s5zh/69i8DF+UMswe00VXDonJVUYaHsSK2PyCl8DPs+LsRJuvNTvQk86A/V+bCqqMXHKuToILhEW4tOmJXCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4161a1af5badc22e753f4acf0a3d35210bbe721ed17adabc124f150b9a091c8d","last_reissued_at":"2026-05-18T01:00:10.018203Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:10.018203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The trace as an average over the unit sphere of a normed space with a 1-symmetric basis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Kent E. Morrison, Tomasz Kania","submitted_at":"2015-11-06T14:10:05Z","abstract_excerpt":"We generalise the formula expressing the matrix trace of a given square matrix as the integral of the numerical values of $A$ over the Euclidean sphere to the unit spheres of finite-dimensional normed spaces that have a 1-symmetric basis. Our result is new even in the case of $\\ell_p$-norms in $\\mathbb{R}^N$ for $p\\neq 2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02084","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":"1511.02084","created_at":"2026-05-18T01:00:10.018324+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.02084v1","created_at":"2026-05-18T01:00:10.018324+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02084","created_at":"2026-05-18T01:00:10.018324+00:00"},{"alias_kind":"pith_short_12","alias_value":"IFQ2DL23VXBC","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"IFQ2DL23VXBC45J7","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"IFQ2DL23","created_at":"2026-05-18T12:29:25.134429+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/IFQ2DL23VXBC45J7JLHQUPJVEE","json":"https://pith.science/pith/IFQ2DL23VXBC45J7JLHQUPJVEE.json","graph_json":"https://pith.science/api/pith-number/IFQ2DL23VXBC45J7JLHQUPJVEE/graph.json","events_json":"https://pith.science/api/pith-number/IFQ2DL23VXBC45J7JLHQUPJVEE/events.json","paper":"https://pith.science/paper/IFQ2DL23"},"agent_actions":{"view_html":"https://pith.science/pith/IFQ2DL23VXBC45J7JLHQUPJVEE","download_json":"https://pith.science/pith/IFQ2DL23VXBC45J7JLHQUPJVEE.json","view_paper":"https://pith.science/paper/IFQ2DL23","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.02084&json=true","fetch_graph":"https://pith.science/api/pith-number/IFQ2DL23VXBC45J7JLHQUPJVEE/graph.json","fetch_events":"https://pith.science/api/pith-number/IFQ2DL23VXBC45J7JLHQUPJVEE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IFQ2DL23VXBC45J7JLHQUPJVEE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IFQ2DL23VXBC45J7JLHQUPJVEE/action/storage_attestation","attest_author":"https://pith.science/pith/IFQ2DL23VXBC45J7JLHQUPJVEE/action/author_attestation","sign_citation":"https://pith.science/pith/IFQ2DL23VXBC45J7JLHQUPJVEE/action/citation_signature","submit_replication":"https://pith.science/pith/IFQ2DL23VXBC45J7JLHQUPJVEE/action/replication_record"}},"created_at":"2026-05-18T01:00:10.018324+00:00","updated_at":"2026-05-18T01:00:10.018324+00:00"}