{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:BYYH5R6ISPU6QMXF423VHEZVCY","short_pith_number":"pith:BYYH5R6I","schema_version":"1.0","canonical_sha256":"0e307ec7c893e9e832e5e6b7539335160c9c9152b76944b779424b68c270e36d","source":{"kind":"arxiv","id":"math/0504091","version":1},"attestation_state":"computed","paper":{"title":"Navigating in the Cayley graphs of SL_N(Z) and SL_N(F_p)","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"T. R. Riley","submitted_at":"2005-04-06T04:23:35Z","abstract_excerpt":"We give a non-deterministic algorithm that expresses elements of SL_N(Z), for N > 2, as words in a finite set of generators, with the length of these words at most a constant times the word metric. We show that the non-deterministic time-complexity of the subtractive version of Euclid's algorithm for finding the greatest common divisor of N > 2 integers a_1,..., a_N is at most a constant times N log n where n := max {|a_1|,..., |a_N|}. This leads to an elementary proof that for N > 2 the word metric in SL_N(Z) is biLipschitz equivalent to the logarithm of the matrix norm -- an instance of a th"},"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":"math/0504091","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GR","submitted_at":"2005-04-06T04:23:35Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fb59e225d91b96140f10ed752a035cab2e71bb7e5c86142d1ad3f1426e965808","abstract_canon_sha256":"81b2041b9e083559ecc766bb174148ccb7141372d1208e7698cb4a5da4695d0b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:22.449947Z","signature_b64":"sx0sNgKQdjrlzbE0uUyCAYVaXplvKK4TNVnEjE09L5/jziOaE1SBic7CEQrKO9cLIdeU0IBpH1DiYOqnYxTfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e307ec7c893e9e832e5e6b7539335160c9c9152b76944b779424b68c270e36d","last_reissued_at":"2026-05-18T04:42:22.449280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:22.449280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Navigating in the Cayley graphs of SL_N(Z) and SL_N(F_p)","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"T. R. Riley","submitted_at":"2005-04-06T04:23:35Z","abstract_excerpt":"We give a non-deterministic algorithm that expresses elements of SL_N(Z), for N > 2, as words in a finite set of generators, with the length of these words at most a constant times the word metric. We show that the non-deterministic time-complexity of the subtractive version of Euclid's algorithm for finding the greatest common divisor of N > 2 integers a_1,..., a_N is at most a constant times N log n where n := max {|a_1|,..., |a_N|}. This leads to an elementary proof that for N > 2 the word metric in SL_N(Z) is biLipschitz equivalent to the logarithm of the matrix norm -- an instance of a th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504091","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":"math/0504091","created_at":"2026-05-18T04:42:22.449374+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0504091v1","created_at":"2026-05-18T04:42:22.449374+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504091","created_at":"2026-05-18T04:42:22.449374+00:00"},{"alias_kind":"pith_short_12","alias_value":"BYYH5R6ISPU6","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"BYYH5R6ISPU6QMXF","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"BYYH5R6I","created_at":"2026-05-18T12:25:53.335082+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/BYYH5R6ISPU6QMXF423VHEZVCY","json":"https://pith.science/pith/BYYH5R6ISPU6QMXF423VHEZVCY.json","graph_json":"https://pith.science/api/pith-number/BYYH5R6ISPU6QMXF423VHEZVCY/graph.json","events_json":"https://pith.science/api/pith-number/BYYH5R6ISPU6QMXF423VHEZVCY/events.json","paper":"https://pith.science/paper/BYYH5R6I"},"agent_actions":{"view_html":"https://pith.science/pith/BYYH5R6ISPU6QMXF423VHEZVCY","download_json":"https://pith.science/pith/BYYH5R6ISPU6QMXF423VHEZVCY.json","view_paper":"https://pith.science/paper/BYYH5R6I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0504091&json=true","fetch_graph":"https://pith.science/api/pith-number/BYYH5R6ISPU6QMXF423VHEZVCY/graph.json","fetch_events":"https://pith.science/api/pith-number/BYYH5R6ISPU6QMXF423VHEZVCY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BYYH5R6ISPU6QMXF423VHEZVCY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BYYH5R6ISPU6QMXF423VHEZVCY/action/storage_attestation","attest_author":"https://pith.science/pith/BYYH5R6ISPU6QMXF423VHEZVCY/action/author_attestation","sign_citation":"https://pith.science/pith/BYYH5R6ISPU6QMXF423VHEZVCY/action/citation_signature","submit_replication":"https://pith.science/pith/BYYH5R6ISPU6QMXF423VHEZVCY/action/replication_record"}},"created_at":"2026-05-18T04:42:22.449374+00:00","updated_at":"2026-05-18T04:42:22.449374+00:00"}