{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OCKHFAF34MMHUEILEV27JQ74PU","short_pith_number":"pith:OCKHFAF3","schema_version":"1.0","canonical_sha256":"70947280bbe3187a110b2575f4c3fc7d174da46ad070dc0ff63c5e81c87b164f","source":{"kind":"arxiv","id":"1203.2432","version":1},"attestation_state":"computed","paper":{"title":"Roughness in Cayley Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"B. Davvaz, M. H. Shahzamanian, M. Shirmohammadi","submitted_at":"2012-03-12T09:25:11Z","abstract_excerpt":"In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs containing Cayley graphs is proposed. Rough approximation is expanded to pseudo-Cayley graphs. Also, rough vertex pseudo-Cayley graphs and rough pseudo-Cayley graphs are introduced. Some theorems are provided, form which some properties such as connectivity and optimal connectivity are derived. This approach opens a new research field in sciences such as data networks."},"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":"1203.2432","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2012-03-12T09:25:11Z","cross_cats_sorted":[],"title_canon_sha256":"3b09fd17c2bdf5e75cd317334fd2aa0ca519e9ac27f48ec8c8900af318db13f5","abstract_canon_sha256":"d780555b20b542a80d06d01f5ef63f59e2ccfdf43d8149d63e503f1b3343532e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:00:25.487585Z","signature_b64":"9H7RhvhRgskA2DHmOVwhF4hS2uaeICnHyYS15KAWjrHNDDPM3mCuCshERTDGhDT/qRmak354kta0EMbqsMBeCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70947280bbe3187a110b2575f4c3fc7d174da46ad070dc0ff63c5e81c87b164f","last_reissued_at":"2026-05-18T04:00:25.486883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:00:25.486883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Roughness in Cayley Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"B. Davvaz, M. H. Shahzamanian, M. Shirmohammadi","submitted_at":"2012-03-12T09:25:11Z","abstract_excerpt":"In this paper, rough approximations of Cayley graphs are studied and rough edge Cayley graphs are introduced. Furthermore, a new algebraic definition called pseudo-Cayley graphs containing Cayley graphs is proposed. Rough approximation is expanded to pseudo-Cayley graphs. Also, rough vertex pseudo-Cayley graphs and rough pseudo-Cayley graphs are introduced. Some theorems are provided, form which some properties such as connectivity and optimal connectivity are derived. This approach opens a new research field in sciences such as data networks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2432","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":"1203.2432","created_at":"2026-05-18T04:00:25.487005+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.2432v1","created_at":"2026-05-18T04:00:25.487005+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2432","created_at":"2026-05-18T04:00:25.487005+00:00"},{"alias_kind":"pith_short_12","alias_value":"OCKHFAF34MMH","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OCKHFAF34MMHUEIL","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OCKHFAF3","created_at":"2026-05-18T12:27:16.716162+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/OCKHFAF34MMHUEILEV27JQ74PU","json":"https://pith.science/pith/OCKHFAF34MMHUEILEV27JQ74PU.json","graph_json":"https://pith.science/api/pith-number/OCKHFAF34MMHUEILEV27JQ74PU/graph.json","events_json":"https://pith.science/api/pith-number/OCKHFAF34MMHUEILEV27JQ74PU/events.json","paper":"https://pith.science/paper/OCKHFAF3"},"agent_actions":{"view_html":"https://pith.science/pith/OCKHFAF34MMHUEILEV27JQ74PU","download_json":"https://pith.science/pith/OCKHFAF34MMHUEILEV27JQ74PU.json","view_paper":"https://pith.science/paper/OCKHFAF3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.2432&json=true","fetch_graph":"https://pith.science/api/pith-number/OCKHFAF34MMHUEILEV27JQ74PU/graph.json","fetch_events":"https://pith.science/api/pith-number/OCKHFAF34MMHUEILEV27JQ74PU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OCKHFAF34MMHUEILEV27JQ74PU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OCKHFAF34MMHUEILEV27JQ74PU/action/storage_attestation","attest_author":"https://pith.science/pith/OCKHFAF34MMHUEILEV27JQ74PU/action/author_attestation","sign_citation":"https://pith.science/pith/OCKHFAF34MMHUEILEV27JQ74PU/action/citation_signature","submit_replication":"https://pith.science/pith/OCKHFAF34MMHUEILEV27JQ74PU/action/replication_record"}},"created_at":"2026-05-18T04:00:25.487005+00:00","updated_at":"2026-05-18T04:00:25.487005+00:00"}