{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AVD6SO2SG55753L3E2K6XGGKWY","short_pith_number":"pith:AVD6SO2S","schema_version":"1.0","canonical_sha256":"0547e93b52377bfeed7b2695eb98cab62fb18cae7bf488cab270b886ab567898","source":{"kind":"arxiv","id":"1612.08855","version":2},"attestation_state":"computed","paper":{"title":"An algebraic approach to lifts of digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Dalf\\'o, J. Ryan, J. \\v{S}ir\\'a\\v{n}, M.A. Fiol, M. Miller","submitted_at":"2016-12-28T11:27:16Z","abstract_excerpt":"We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift $\\Gamma^{\\alpha}$ of a base (voltage) digraph. These techniques contract or expand a given digraph in order to study its characteristics, or obtain more involved structures. This study is carried out by introducing a quotient-like matrix, with complex polynomial entries, which fully represents $\\Gamma^{\\alpha}$. In particular, such a matrix gives the quotient matrix of a regular partition of $\\Gamma^{\\alpha}$, and when the involved group is Abelian, it completely determines the sp"},"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":"1612.08855","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-28T11:27:16Z","cross_cats_sorted":[],"title_canon_sha256":"7f6beab1bfe457a37c19191f1376036a1b0b889632368ede3d3fa0793e2ec423","abstract_canon_sha256":"6d083537015dfad9121c578ea124e4df82e0e8cf5e039307fac33a9cc6451910"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:47.804798Z","signature_b64":"NPHeo39brQU1BA4DaDL34EDHsFf+Z2IqNbUcjT68b0Z34aPbffPnlpFAioKKrP0QPqdHd4KYPj3YhWo0VXvRBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0547e93b52377bfeed7b2695eb98cab62fb18cae7bf488cab270b886ab567898","last_reissued_at":"2026-05-18T00:41:47.804053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:47.804053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An algebraic approach to lifts of digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C. Dalf\\'o, J. Ryan, J. \\v{S}ir\\'a\\v{n}, M.A. Fiol, M. Miller","submitted_at":"2016-12-28T11:27:16Z","abstract_excerpt":"We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift $\\Gamma^{\\alpha}$ of a base (voltage) digraph. These techniques contract or expand a given digraph in order to study its characteristics, or obtain more involved structures. This study is carried out by introducing a quotient-like matrix, with complex polynomial entries, which fully represents $\\Gamma^{\\alpha}$. In particular, such a matrix gives the quotient matrix of a regular partition of $\\Gamma^{\\alpha}$, and when the involved group is Abelian, it completely determines the sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08855","kind":"arxiv","version":2},"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":"1612.08855","created_at":"2026-05-18T00:41:47.804190+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08855v2","created_at":"2026-05-18T00:41:47.804190+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08855","created_at":"2026-05-18T00:41:47.804190+00:00"},{"alias_kind":"pith_short_12","alias_value":"AVD6SO2SG557","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"AVD6SO2SG55753L3","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"AVD6SO2S","created_at":"2026-05-18T12:30:07.202191+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/AVD6SO2SG55753L3E2K6XGGKWY","json":"https://pith.science/pith/AVD6SO2SG55753L3E2K6XGGKWY.json","graph_json":"https://pith.science/api/pith-number/AVD6SO2SG55753L3E2K6XGGKWY/graph.json","events_json":"https://pith.science/api/pith-number/AVD6SO2SG55753L3E2K6XGGKWY/events.json","paper":"https://pith.science/paper/AVD6SO2S"},"agent_actions":{"view_html":"https://pith.science/pith/AVD6SO2SG55753L3E2K6XGGKWY","download_json":"https://pith.science/pith/AVD6SO2SG55753L3E2K6XGGKWY.json","view_paper":"https://pith.science/paper/AVD6SO2S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08855&json=true","fetch_graph":"https://pith.science/api/pith-number/AVD6SO2SG55753L3E2K6XGGKWY/graph.json","fetch_events":"https://pith.science/api/pith-number/AVD6SO2SG55753L3E2K6XGGKWY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AVD6SO2SG55753L3E2K6XGGKWY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AVD6SO2SG55753L3E2K6XGGKWY/action/storage_attestation","attest_author":"https://pith.science/pith/AVD6SO2SG55753L3E2K6XGGKWY/action/author_attestation","sign_citation":"https://pith.science/pith/AVD6SO2SG55753L3E2K6XGGKWY/action/citation_signature","submit_replication":"https://pith.science/pith/AVD6SO2SG55753L3E2K6XGGKWY/action/replication_record"}},"created_at":"2026-05-18T00:41:47.804190+00:00","updated_at":"2026-05-18T00:41:47.804190+00:00"}