{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:WIWPZP6UDZEHGSEQXKSEZYIRUJ","short_pith_number":"pith:WIWPZP6U","schema_version":"1.0","canonical_sha256":"b22cfcbfd41e48734890baa44ce111a2706d7a83f5d34aa849fc443c1d9fadb3","source":{"kind":"arxiv","id":"1205.5935","version":1},"attestation_state":"computed","paper":{"title":"Geometric Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Eric Chisolm","submitted_at":"2012-05-27T04:27:20Z","abstract_excerpt":"This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways:\n  1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension.\n  2. It defines a product that's strongly motivated by geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane.\n  This system was invented by William Clifford and is more commonly known as Clifford algebra. It's actually older than the vector algebra that we use today (due to Gibbs) "},"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":"1205.5935","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-05-27T04:27:20Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"da11ea079030e7f9fcf4863a2f1ab6f6abc743b0e8a29167793f0325f1198957","abstract_canon_sha256":"bb74a054b2870e95fcbf3507175226222427ec39f31a4e8d02c7bde4b5ea2ccb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:48.714104Z","signature_b64":"4zrOnrqH6siHC6fuYMeCZXLDQUb+ht3DgDZpIw28Q26SHiLW5h8/NqWQCQWzSMw651Cr90Ayr45yh4JoPiJJDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b22cfcbfd41e48734890baa44ce111a2706d7a83f5d34aa849fc443c1d9fadb3","last_reissued_at":"2026-05-18T03:54:48.713545Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:48.713545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Geometric Algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Eric Chisolm","submitted_at":"2012-05-27T04:27:20Z","abstract_excerpt":"This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways:\n  1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension.\n  2. It defines a product that's strongly motivated by geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane.\n  This system was invented by William Clifford and is more commonly known as Clifford algebra. It's actually older than the vector algebra that we use today (due to Gibbs) "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5935","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":"1205.5935","created_at":"2026-05-18T03:54:48.713632+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.5935v1","created_at":"2026-05-18T03:54:48.713632+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.5935","created_at":"2026-05-18T03:54:48.713632+00:00"},{"alias_kind":"pith_short_12","alias_value":"WIWPZP6UDZEH","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_16","alias_value":"WIWPZP6UDZEHGSEQ","created_at":"2026-05-18T12:27:25.539911+00:00"},{"alias_kind":"pith_short_8","alias_value":"WIWPZP6U","created_at":"2026-05-18T12:27:25.539911+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.26761","citing_title":"PhD thesis: Modes, States, and Symmetries in quantum Optics for quantum Information and Metrology","ref_index":114,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WIWPZP6UDZEHGSEQXKSEZYIRUJ","json":"https://pith.science/pith/WIWPZP6UDZEHGSEQXKSEZYIRUJ.json","graph_json":"https://pith.science/api/pith-number/WIWPZP6UDZEHGSEQXKSEZYIRUJ/graph.json","events_json":"https://pith.science/api/pith-number/WIWPZP6UDZEHGSEQXKSEZYIRUJ/events.json","paper":"https://pith.science/paper/WIWPZP6U"},"agent_actions":{"view_html":"https://pith.science/pith/WIWPZP6UDZEHGSEQXKSEZYIRUJ","download_json":"https://pith.science/pith/WIWPZP6UDZEHGSEQXKSEZYIRUJ.json","view_paper":"https://pith.science/paper/WIWPZP6U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.5935&json=true","fetch_graph":"https://pith.science/api/pith-number/WIWPZP6UDZEHGSEQXKSEZYIRUJ/graph.json","fetch_events":"https://pith.science/api/pith-number/WIWPZP6UDZEHGSEQXKSEZYIRUJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WIWPZP6UDZEHGSEQXKSEZYIRUJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WIWPZP6UDZEHGSEQXKSEZYIRUJ/action/storage_attestation","attest_author":"https://pith.science/pith/WIWPZP6UDZEHGSEQXKSEZYIRUJ/action/author_attestation","sign_citation":"https://pith.science/pith/WIWPZP6UDZEHGSEQXKSEZYIRUJ/action/citation_signature","submit_replication":"https://pith.science/pith/WIWPZP6UDZEHGSEQXKSEZYIRUJ/action/replication_record"}},"created_at":"2026-05-18T03:54:48.713632+00:00","updated_at":"2026-05-18T03:54:48.713632+00:00"}