{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:6N3JI7BCMO3PXQHH7JXTA6WYJZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"20b0fef2cd8e0fbe5beb51d0997c0d9c5542dc220e63311e948ab12730778a41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-25T02:53:05Z","title_canon_sha256":"96f7789500783e2e5aefe4472f0ceba915dbee60afa9f1b1aba8af764e9b283f"},"schema_version":"1.0","source":{"id":"1905.10503","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.10503","created_at":"2026-05-17T23:45:08Z"},{"alias_kind":"arxiv_version","alias_value":"1905.10503v1","created_at":"2026-05-17T23:45:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.10503","created_at":"2026-05-17T23:45:08Z"},{"alias_kind":"pith_short_12","alias_value":"6N3JI7BCMO3P","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"6N3JI7BCMO3PXQHH","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"6N3JI7BC","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:a3b7cd070e19c6e00d8259e7926f0eccee09090014f86ba177dcace94bf3ee71","target":"graph","created_at":"2026-05-17T23:45:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let Ln denote linear octagonal-quadrilateral networks. In this paper, we aim to firstly investigate the Laplacian spectrum on the basis of Laplacian polynomial of Ln. Then, by applying the relationship between the coefficients and roots of the polynomials, the Kirchhoff index and the complexity are determined.","authors_text":"Jia-Bao Liu, Jinde Cao, M. Abdel-Aty, Udai Al-Juboori, Ying-Hao Pan, Zhi-Yu Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-25T02:53:05Z","title":"Computing the Laplacian spectrum of linear octagonal-quadrilateral networks and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.10503","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:371316570908c47eb4ce2742bea185e7d0070fefac3c034de79cefdbf6f64885","target":"record","created_at":"2026-05-17T23:45:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"20b0fef2cd8e0fbe5beb51d0997c0d9c5542dc220e63311e948ab12730778a41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-25T02:53:05Z","title_canon_sha256":"96f7789500783e2e5aefe4472f0ceba915dbee60afa9f1b1aba8af764e9b283f"},"schema_version":"1.0","source":{"id":"1905.10503","kind":"arxiv","version":1}},"canonical_sha256":"f376947c2263b6fbc0e7fa6f307ad84e6d37be9a563589766079bee03225afd7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f376947c2263b6fbc0e7fa6f307ad84e6d37be9a563589766079bee03225afd7","first_computed_at":"2026-05-17T23:45:08.296107Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:08.296107Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5YHhD9UKcVMa7xMiKYwAQ/0DMgBg37s2racHAuDn4rC1EOK6FLM4vlaZAGkGkB3sDrAuggQwAmrUFZ0T55bRDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:08.296980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.10503","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:371316570908c47eb4ce2742bea185e7d0070fefac3c034de79cefdbf6f64885","sha256:a3b7cd070e19c6e00d8259e7926f0eccee09090014f86ba177dcace94bf3ee71"],"state_sha256":"e285704efa047e13e783674c92f62b01b18fc88b8d5f712ee081c35c5a7f2379"}