{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TWSI4UCFQLYEF6HS6W762QT6OS","short_pith_number":"pith:TWSI4UCF","schema_version":"1.0","canonical_sha256":"9da48e504582f042f8f2f5bfed427e74a833c3e5ff1724d08f5b9b07f28a3ee9","source":{"kind":"arxiv","id":"1707.04414","version":2},"attestation_state":"computed","paper":{"title":"A formula for the $g$-angle between two subspaces of a normed space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hendra Gunawan, Muhammad Nur, Oki Neswan","submitted_at":"2017-07-14T08:38:08Z","abstract_excerpt":"We develop the notion of $g$-angle between two subspaces of a normed space. In particular, we discuss the $g$-angle between a $1$-dimensional subspace and a $t$-dimensional subspace for $t\\geq 1$ and the $g$-angle between a $2$-dimensional subspace and a $t$-dimensional subspace for $t\\geq 2$. Moreover, we present an explicit formula for the $g$-angle between two subspaces of $\\ell^{p}$ spaces."},"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":"1707.04414","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-07-14T08:38:08Z","cross_cats_sorted":[],"title_canon_sha256":"52df80a7673e5993380a81ff50416f29ec07d5623e8e385177d149915e867f89","abstract_canon_sha256":"94a4ed6e5d4dd0ff2943d94e021d612e1a5ad9d081434e159808044aa0275881"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:08.712650Z","signature_b64":"tjpDhRRpIYcdDhLiB9VC4ob17gaY8NVUhhkmks/hnDxeUtlF/7tAyGCpPUvogJ0STS3fje2iVfMDThmVf3JECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9da48e504582f042f8f2f5bfed427e74a833c3e5ff1724d08f5b9b07f28a3ee9","last_reissued_at":"2026-05-18T00:23:08.711948Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:08.711948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A formula for the $g$-angle between two subspaces of a normed space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Hendra Gunawan, Muhammad Nur, Oki Neswan","submitted_at":"2017-07-14T08:38:08Z","abstract_excerpt":"We develop the notion of $g$-angle between two subspaces of a normed space. In particular, we discuss the $g$-angle between a $1$-dimensional subspace and a $t$-dimensional subspace for $t\\geq 1$ and the $g$-angle between a $2$-dimensional subspace and a $t$-dimensional subspace for $t\\geq 2$. Moreover, we present an explicit formula for the $g$-angle between two subspaces of $\\ell^{p}$ spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04414","kind":"arxiv","version":2},"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":"1707.04414","created_at":"2026-05-18T00:23:08.712073+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.04414v2","created_at":"2026-05-18T00:23:08.712073+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04414","created_at":"2026-05-18T00:23:08.712073+00:00"},{"alias_kind":"pith_short_12","alias_value":"TWSI4UCFQLYE","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TWSI4UCFQLYEF6HS","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TWSI4UCF","created_at":"2026-05-18T12:31:46.661854+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/TWSI4UCFQLYEF6HS6W762QT6OS","json":"https://pith.science/pith/TWSI4UCFQLYEF6HS6W762QT6OS.json","graph_json":"https://pith.science/api/pith-number/TWSI4UCFQLYEF6HS6W762QT6OS/graph.json","events_json":"https://pith.science/api/pith-number/TWSI4UCFQLYEF6HS6W762QT6OS/events.json","paper":"https://pith.science/paper/TWSI4UCF"},"agent_actions":{"view_html":"https://pith.science/pith/TWSI4UCFQLYEF6HS6W762QT6OS","download_json":"https://pith.science/pith/TWSI4UCFQLYEF6HS6W762QT6OS.json","view_paper":"https://pith.science/paper/TWSI4UCF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.04414&json=true","fetch_graph":"https://pith.science/api/pith-number/TWSI4UCFQLYEF6HS6W762QT6OS/graph.json","fetch_events":"https://pith.science/api/pith-number/TWSI4UCFQLYEF6HS6W762QT6OS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TWSI4UCFQLYEF6HS6W762QT6OS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TWSI4UCFQLYEF6HS6W762QT6OS/action/storage_attestation","attest_author":"https://pith.science/pith/TWSI4UCFQLYEF6HS6W762QT6OS/action/author_attestation","sign_citation":"https://pith.science/pith/TWSI4UCFQLYEF6HS6W762QT6OS/action/citation_signature","submit_replication":"https://pith.science/pith/TWSI4UCFQLYEF6HS6W762QT6OS/action/replication_record"}},"created_at":"2026-05-18T00:23:08.712073+00:00","updated_at":"2026-05-18T00:23:08.712073+00:00"}