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In this paper, we show that the characteristic polynomial of a bipartite signed digraph of order $n$ with each cycle of length $\\equiv 0\\pmod 4$ negative and each cycle of length $\\equiv 2\\pmod 4$ positive is of the form \\\\ $$\\phi_S(z)=z^n+\\sum\\limits_{j=1}^{\\lfloor{\\frac{n}{2}}\\rfloor}(-1)^j c_{2j}(S)z^{"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.00572","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-03T15:39:37Z","cross_cats_sorted":[],"title_canon_sha256":"24ce5bfb978cd440f9becca8dc313c3ec4221149b963cd52a5ca9f3ca96b7591","abstract_canon_sha256":"81fb0450819de41bf0980561a2736f444838c6df992d80de55c636b8477e524b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:07.226909Z","signature_b64":"15TEqSuQgBYKEeAVtt/wT+Xkmb76DjXizIbMVkBeMrOjxUQeLi3UXeC60awsoWn/wCAzXK3XktmfOAuRNjGsBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2149c67f22e9ba1bf72e541d74227f92dfe4fca37aae155d10234e76ca556f89","last_reissued_at":"2026-05-18T02:30:07.226018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:07.226018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectra and energy of bipartite signed digraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Mushtaq A. 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In this paper, we show that the characteristic polynomial of a bipartite signed digraph of order $n$ with each cycle of length $\\equiv 0\\pmod 4$ negative and each cycle of length $\\equiv 2\\pmod 4$ positive is of the form \\\\ $$\\phi_S(z)=z^n+\\sum\\limits_{j=1}^{\\lfloor{\\frac{n}{2}}\\rfloor}(-1)^j c_{2j}(S)z^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00572","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":"1501.00572","created_at":"2026-05-18T02:30:07.226184+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00572v1","created_at":"2026-05-18T02:30:07.226184+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00572","created_at":"2026-05-18T02:30:07.226184+00:00"},{"alias_kind":"pith_short_12","alias_value":"EFE4M7ZC5G5B","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"EFE4M7ZC5G5BX5ZO","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"EFE4M7ZC","created_at":"2026-05-18T12:29:19.899920+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/EFE4M7ZC5G5BX5ZOKQOXIIT7SL","json":"https://pith.science/pith/EFE4M7ZC5G5BX5ZOKQOXIIT7SL.json","graph_json":"https://pith.science/api/pith-number/EFE4M7ZC5G5BX5ZOKQOXIIT7SL/graph.json","events_json":"https://pith.science/api/pith-number/EFE4M7ZC5G5BX5ZOKQOXIIT7SL/events.json","paper":"https://pith.science/paper/EFE4M7ZC"},"agent_actions":{"view_html":"https://pith.science/pith/EFE4M7ZC5G5BX5ZOKQOXIIT7SL","download_json":"https://pith.science/pith/EFE4M7ZC5G5BX5ZOKQOXIIT7SL.json","view_paper":"https://pith.science/paper/EFE4M7ZC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00572&json=true","fetch_graph":"https://pith.science/api/pith-number/EFE4M7ZC5G5BX5ZOKQOXIIT7SL/graph.json","fetch_events":"https://pith.science/api/pith-number/EFE4M7ZC5G5BX5ZOKQOXIIT7SL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EFE4M7ZC5G5BX5ZOKQOXIIT7SL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EFE4M7ZC5G5BX5ZOKQOXIIT7SL/action/storage_attestation","attest_author":"https://pith.science/pith/EFE4M7ZC5G5BX5ZOKQOXIIT7SL/action/author_attestation","sign_citation":"https://pith.science/pith/EFE4M7ZC5G5BX5ZOKQOXIIT7SL/action/citation_signature","submit_replication":"https://pith.science/pith/EFE4M7ZC5G5BX5ZOKQOXIIT7SL/action/replication_record"}},"created_at":"2026-05-18T02:30:07.226184+00:00","updated_at":"2026-05-18T02:30:07.226184+00:00"}