{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:EZRP6KBF5JMCDTL72A6LOGCDBJ","short_pith_number":"pith:EZRP6KBF","schema_version":"1.0","canonical_sha256":"2662ff2825ea5821cd7fd03cb718430a5a22517eb8594fabc5c9b6c94e13e3fc","source":{"kind":"arxiv","id":"1903.08332","version":1},"attestation_state":"computed","paper":{"title":"On Computing the Number of Short Cycles in Bipartite Graphs Using the Spectrum of the Directed Edge Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ali Dehghan, Amir H. Banihashemi","submitted_at":"2019-03-20T03:49:46Z","abstract_excerpt":"Counting short cycles in bipartite graphs is a fundamental problem of interest in many fields including the analysis and design of low-density parity-check (LDPC) codes. There are two computational approaches to count short cycles (with length smaller than $2g$, where $g$ is the girth of the graph) in bipartite graphs. The first approach is applicable to a general (irregular) bipartite graph, and uses the spectrum $\\{\\eta_i\\}$ of the directed edge matrix of the graph to compute the multiplicity $N_k$ of $k$-cycles with $k < 2g$ through the simple equation $N_k = \\sum_i \\eta_i^k/(2k)$. This app"},"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":"1903.08332","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-03-20T03:49:46Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"857f708d76ea432cc09bc1151139727ec523c7df63cd4c9ecdaf9a814c2fd170","abstract_canon_sha256":"527c3577ea9e27a3d8d54997ee2df5e7335ce8a14c3f87f2563e5f697c8673bf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:48.386194Z","signature_b64":"dFyPEOQzuPZgf/XE7IAB9TCnWApg2B9tjLyQ9T3HfcgwFvo7qGugMpB/T8FZYPbIH6RZJFbvGc/bfRbEDMtWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2662ff2825ea5821cd7fd03cb718430a5a22517eb8594fabc5c9b6c94e13e3fc","last_reissued_at":"2026-05-17T23:50:48.385607Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:48.385607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Computing the Number of Short Cycles in Bipartite Graphs Using the Spectrum of the Directed Edge Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ali Dehghan, Amir H. Banihashemi","submitted_at":"2019-03-20T03:49:46Z","abstract_excerpt":"Counting short cycles in bipartite graphs is a fundamental problem of interest in many fields including the analysis and design of low-density parity-check (LDPC) codes. There are two computational approaches to count short cycles (with length smaller than $2g$, where $g$ is the girth of the graph) in bipartite graphs. The first approach is applicable to a general (irregular) bipartite graph, and uses the spectrum $\\{\\eta_i\\}$ of the directed edge matrix of the graph to compute the multiplicity $N_k$ of $k$-cycles with $k < 2g$ through the simple equation $N_k = \\sum_i \\eta_i^k/(2k)$. This app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.08332","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":"1903.08332","created_at":"2026-05-17T23:50:48.385698+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.08332v1","created_at":"2026-05-17T23:50:48.385698+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.08332","created_at":"2026-05-17T23:50:48.385698+00:00"},{"alias_kind":"pith_short_12","alias_value":"EZRP6KBF5JMC","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"EZRP6KBF5JMCDTL7","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"EZRP6KBF","created_at":"2026-05-18T12:33:15.570797+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/EZRP6KBF5JMCDTL72A6LOGCDBJ","json":"https://pith.science/pith/EZRP6KBF5JMCDTL72A6LOGCDBJ.json","graph_json":"https://pith.science/api/pith-number/EZRP6KBF5JMCDTL72A6LOGCDBJ/graph.json","events_json":"https://pith.science/api/pith-number/EZRP6KBF5JMCDTL72A6LOGCDBJ/events.json","paper":"https://pith.science/paper/EZRP6KBF"},"agent_actions":{"view_html":"https://pith.science/pith/EZRP6KBF5JMCDTL72A6LOGCDBJ","download_json":"https://pith.science/pith/EZRP6KBF5JMCDTL72A6LOGCDBJ.json","view_paper":"https://pith.science/paper/EZRP6KBF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.08332&json=true","fetch_graph":"https://pith.science/api/pith-number/EZRP6KBF5JMCDTL72A6LOGCDBJ/graph.json","fetch_events":"https://pith.science/api/pith-number/EZRP6KBF5JMCDTL72A6LOGCDBJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EZRP6KBF5JMCDTL72A6LOGCDBJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EZRP6KBF5JMCDTL72A6LOGCDBJ/action/storage_attestation","attest_author":"https://pith.science/pith/EZRP6KBF5JMCDTL72A6LOGCDBJ/action/author_attestation","sign_citation":"https://pith.science/pith/EZRP6KBF5JMCDTL72A6LOGCDBJ/action/citation_signature","submit_replication":"https://pith.science/pith/EZRP6KBF5JMCDTL72A6LOGCDBJ/action/replication_record"}},"created_at":"2026-05-17T23:50:48.385698+00:00","updated_at":"2026-05-17T23:50:48.385698+00:00"}