{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JUER2FQQTRA5D6QZVYQNKAD2FS","short_pith_number":"pith:JUER2FQQ","schema_version":"1.0","canonical_sha256":"4d091d16109c41d1fa19ae20d5007a2cab5c1334f824ec95043f193ff019df3e","source":{"kind":"arxiv","id":"1305.6851","version":1},"attestation_state":"computed","paper":{"title":"Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Wolfgang Bertram (IECN)","submitted_at":"2013-05-27T19:21:43Z","abstract_excerpt":"By \"parallelogram geometry\" we mean the elementary, \"commutative\", geometry corresponding to vector addition, and by \"trapezoid geometry\" a certain \"non-commutative deformation\" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebra and elementary group theory), and (3) axiomatic geometry."},"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":"1305.6851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2013-05-27T19:21:43Z","cross_cats_sorted":[],"title_canon_sha256":"b722854d236d0e6cbdcbe91612801276bfa572b924c7203d1babe12e3ae93211","abstract_canon_sha256":"e747e9e4ba628b4162208391c8491946404699f0d4fb02c4780dedd617210ffd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:17.780441Z","signature_b64":"4VQeBRRLfhmcdSb23OrWlXowUZb7VNbAS9l9G2VHLz0FEQACaYjLd+Br2o9t3ynYeLqPNKOojtkkUYfNN/vyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d091d16109c41d1fa19ae20d5007a2cab5c1334f824ec95043f193ff019df3e","last_reissued_at":"2026-05-18T03:22:17.780066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:17.780066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.HO","authors_text":"Wolfgang Bertram (IECN)","submitted_at":"2013-05-27T19:21:43Z","abstract_excerpt":"By \"parallelogram geometry\" we mean the elementary, \"commutative\", geometry corresponding to vector addition, and by \"trapezoid geometry\" a certain \"non-commutative deformation\" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebra and elementary group theory), and (3) axiomatic geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6851","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":"1305.6851","created_at":"2026-05-18T03:22:17.780118+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.6851v1","created_at":"2026-05-18T03:22:17.780118+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6851","created_at":"2026-05-18T03:22:17.780118+00:00"},{"alias_kind":"pith_short_12","alias_value":"JUER2FQQTRA5","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JUER2FQQTRA5D6QZ","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JUER2FQQ","created_at":"2026-05-18T12:27:49.015174+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/JUER2FQQTRA5D6QZVYQNKAD2FS","json":"https://pith.science/pith/JUER2FQQTRA5D6QZVYQNKAD2FS.json","graph_json":"https://pith.science/api/pith-number/JUER2FQQTRA5D6QZVYQNKAD2FS/graph.json","events_json":"https://pith.science/api/pith-number/JUER2FQQTRA5D6QZVYQNKAD2FS/events.json","paper":"https://pith.science/paper/JUER2FQQ"},"agent_actions":{"view_html":"https://pith.science/pith/JUER2FQQTRA5D6QZVYQNKAD2FS","download_json":"https://pith.science/pith/JUER2FQQTRA5D6QZVYQNKAD2FS.json","view_paper":"https://pith.science/paper/JUER2FQQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.6851&json=true","fetch_graph":"https://pith.science/api/pith-number/JUER2FQQTRA5D6QZVYQNKAD2FS/graph.json","fetch_events":"https://pith.science/api/pith-number/JUER2FQQTRA5D6QZVYQNKAD2FS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JUER2FQQTRA5D6QZVYQNKAD2FS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JUER2FQQTRA5D6QZVYQNKAD2FS/action/storage_attestation","attest_author":"https://pith.science/pith/JUER2FQQTRA5D6QZVYQNKAD2FS/action/author_attestation","sign_citation":"https://pith.science/pith/JUER2FQQTRA5D6QZVYQNKAD2FS/action/citation_signature","submit_replication":"https://pith.science/pith/JUER2FQQTRA5D6QZVYQNKAD2FS/action/replication_record"}},"created_at":"2026-05-18T03:22:17.780118+00:00","updated_at":"2026-05-18T03:22:17.780118+00:00"}