{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:C6PF2NP2TAOQZYWEYQU5PTFQMK","short_pith_number":"pith:C6PF2NP2","schema_version":"1.0","canonical_sha256":"179e5d35fa981d0ce2c4c429d7ccb062bef8ebfd284725bd6a7c10b0a9295a9f","source":{"kind":"arxiv","id":"1712.04244","version":4},"attestation_state":"computed","paper":{"title":"On the notion of a basis of a finite dimensional vector space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Alexander Gamkrelidze, Grigori Giorgadze","submitted_at":"2017-12-12T11:27:17Z","abstract_excerpt":"In this Note we show that the notion of a basis of a finite-dimensional vector space could be introduced by an argument much weaker than Gauss' reduction method. Our aim is to give a short proof of a simply formulated lemma, which in fact is equivalent to the theorem on frame extension, using only a simple notion of the kernel of a linear mapping, without any reference to special results, and derive the notions of basis and dimension in a quite intuitive and logically appropriate way, as well as obtain their basic properties, including a lucid proof of Steinitz's theorem."},"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":"1712.04244","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2017-12-12T11:27:17Z","cross_cats_sorted":[],"title_canon_sha256":"743c5fc5fcfc8202da967a2de7cca668e281ebcab34a66283caf6428f87b67d7","abstract_canon_sha256":"638bdb53e5e0f6374a6b99905ed8ba83d5ab520adba4d14001f84548a9149ed6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:41.901484Z","signature_b64":"4OOHCxdsjpncediM+qdqv3TxIIq6AgtNLRS/ZXTM/tskkOUUt9c7KaSBlcr2ONRwjE2ITZFGEGjXzeaNMXN1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"179e5d35fa981d0ce2c4c429d7ccb062bef8ebfd284725bd6a7c10b0a9295a9f","last_reissued_at":"2026-05-18T00:15:41.900754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:41.900754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the notion of a basis of a finite dimensional vector space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Alexander Gamkrelidze, Grigori Giorgadze","submitted_at":"2017-12-12T11:27:17Z","abstract_excerpt":"In this Note we show that the notion of a basis of a finite-dimensional vector space could be introduced by an argument much weaker than Gauss' reduction method. Our aim is to give a short proof of a simply formulated lemma, which in fact is equivalent to the theorem on frame extension, using only a simple notion of the kernel of a linear mapping, without any reference to special results, and derive the notions of basis and dimension in a quite intuitive and logically appropriate way, as well as obtain their basic properties, including a lucid proof of Steinitz's theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04244","kind":"arxiv","version":4},"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":"1712.04244","created_at":"2026-05-18T00:15:41.900862+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.04244v4","created_at":"2026-05-18T00:15:41.900862+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04244","created_at":"2026-05-18T00:15:41.900862+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6PF2NP2TAOQ","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6PF2NP2TAOQZYWE","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6PF2NP2","created_at":"2026-05-18T12:31:08.081275+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/C6PF2NP2TAOQZYWEYQU5PTFQMK","json":"https://pith.science/pith/C6PF2NP2TAOQZYWEYQU5PTFQMK.json","graph_json":"https://pith.science/api/pith-number/C6PF2NP2TAOQZYWEYQU5PTFQMK/graph.json","events_json":"https://pith.science/api/pith-number/C6PF2NP2TAOQZYWEYQU5PTFQMK/events.json","paper":"https://pith.science/paper/C6PF2NP2"},"agent_actions":{"view_html":"https://pith.science/pith/C6PF2NP2TAOQZYWEYQU5PTFQMK","download_json":"https://pith.science/pith/C6PF2NP2TAOQZYWEYQU5PTFQMK.json","view_paper":"https://pith.science/paper/C6PF2NP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.04244&json=true","fetch_graph":"https://pith.science/api/pith-number/C6PF2NP2TAOQZYWEYQU5PTFQMK/graph.json","fetch_events":"https://pith.science/api/pith-number/C6PF2NP2TAOQZYWEYQU5PTFQMK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6PF2NP2TAOQZYWEYQU5PTFQMK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6PF2NP2TAOQZYWEYQU5PTFQMK/action/storage_attestation","attest_author":"https://pith.science/pith/C6PF2NP2TAOQZYWEYQU5PTFQMK/action/author_attestation","sign_citation":"https://pith.science/pith/C6PF2NP2TAOQZYWEYQU5PTFQMK/action/citation_signature","submit_replication":"https://pith.science/pith/C6PF2NP2TAOQZYWEYQU5PTFQMK/action/replication_record"}},"created_at":"2026-05-18T00:15:41.900862+00:00","updated_at":"2026-05-18T00:15:41.900862+00:00"}