{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:TXP3O63HEOEUWCOAWTAXHPYALG","short_pith_number":"pith:TXP3O63H","canonical_record":{"source":{"id":"1308.2281","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-08-10T06:42:15Z","cross_cats_sorted":[],"title_canon_sha256":"670ac67e9db2e8cd717a5f5ff14446d52ad6929d5f3782a27bed84c2c359254e","abstract_canon_sha256":"5ee095ad6038501dc81b375e22b67bc4d5575d82c242e32dd47f8fcecf7d5d2a"},"schema_version":"1.0"},"canonical_sha256":"9ddfb77b6723894b09c0b4c173bf00598656985d5e57ef415182524347a7d273","source":{"kind":"arxiv","id":"1308.2281","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2281","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2281v1","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2281","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"TXP3O63HEOEU","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TXP3O63HEOEUWCOA","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TXP3O63H","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:TXP3O63HEOEUWCOAWTAXHPYALG","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2281","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-08-10T06:42:15Z","cross_cats_sorted":[],"title_canon_sha256":"670ac67e9db2e8cd717a5f5ff14446d52ad6929d5f3782a27bed84c2c359254e","abstract_canon_sha256":"5ee095ad6038501dc81b375e22b67bc4d5575d82c242e32dd47f8fcecf7d5d2a"},"schema_version":"1.0"},"canonical_sha256":"9ddfb77b6723894b09c0b4c173bf00598656985d5e57ef415182524347a7d273","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:16:07.938963Z","signature_b64":"QBKOceGrPjKUzarH6aba2CVGsMWpNW68gCgCTTTt0EWWsbEOiA53F3R4tN7MjuUTJeX24aghH+db4LQdcugKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ddfb77b6723894b09c0b4c173bf00598656985d5e57ef415182524347a7d273","last_reissued_at":"2026-05-18T03:16:07.938411Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:16:07.938411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2281","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QgJqffQPN3tT5zlJu1SKjRCNeF7JLpUoDSHodOY5sxX2eO3v34SaXifEn/pchfVH1Ym0bK+cQ0nsnXOFe31LAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:14:58.102859Z"},"content_sha256":"84f487f7152fe15ec9016e2d0cde6639c9e3a2d65d3a77cdbafec46336175f33","schema_version":"1.0","event_id":"sha256:84f487f7152fe15ec9016e2d0cde6639c9e3a2d65d3a77cdbafec46336175f33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:TXP3O63HEOEUWCOAWTAXHPYALG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the determinant of the distance matrix of a bicyclic graph","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guang-Hui Xu, Ju-Li Zhang, Shi-Cai Gong","submitted_at":"2013-08-10T06:42:15Z","abstract_excerpt":"Two cycles are referred as disjoint if they have no common edges. In this paper, we will investigate the determinant of the distance matrix of a graph, giving a formula for the determinant of the distance matrix of a bicyclic graph whose two cycles are disjoint, which extends the formula for the determinant of the distance matrix of a tree, as well as that of a unicyclic graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2281","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:16:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XAXIcss4rZuDul776erxkiy4y1/a7gStX/3aTJZlpUpPWN9kyyW64g4g0X1vmA5kQMKZYNqgcfZ3+C8JvnpVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T08:14:58.103203Z"},"content_sha256":"228bbe8bab81869c5c3ec50a33900e36a6a79435111733f55610b8a4ade65ad0","schema_version":"1.0","event_id":"sha256:228bbe8bab81869c5c3ec50a33900e36a6a79435111733f55610b8a4ade65ad0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TXP3O63HEOEUWCOAWTAXHPYALG/bundle.json","state_url":"https://pith.science/pith/TXP3O63HEOEUWCOAWTAXHPYALG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TXP3O63HEOEUWCOAWTAXHPYALG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T08:14:58Z","links":{"resolver":"https://pith.science/pith/TXP3O63HEOEUWCOAWTAXHPYALG","bundle":"https://pith.science/pith/TXP3O63HEOEUWCOAWTAXHPYALG/bundle.json","state":"https://pith.science/pith/TXP3O63HEOEUWCOAWTAXHPYALG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TXP3O63HEOEUWCOAWTAXHPYALG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TXP3O63HEOEUWCOAWTAXHPYALG","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":"5ee095ad6038501dc81b375e22b67bc4d5575d82c242e32dd47f8fcecf7d5d2a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-08-10T06:42:15Z","title_canon_sha256":"670ac67e9db2e8cd717a5f5ff14446d52ad6929d5f3782a27bed84c2c359254e"},"schema_version":"1.0","source":{"id":"1308.2281","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2281","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2281v1","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2281","created_at":"2026-05-18T03:16:07Z"},{"alias_kind":"pith_short_12","alias_value":"TXP3O63HEOEU","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TXP3O63HEOEUWCOA","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TXP3O63H","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:228bbe8bab81869c5c3ec50a33900e36a6a79435111733f55610b8a4ade65ad0","target":"graph","created_at":"2026-05-18T03:16:07Z","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":"Two cycles are referred as disjoint if they have no common edges. In this paper, we will investigate the determinant of the distance matrix of a graph, giving a formula for the determinant of the distance matrix of a bicyclic graph whose two cycles are disjoint, which extends the formula for the determinant of the distance matrix of a tree, as well as that of a unicyclic graph.","authors_text":"Guang-Hui Xu, Ju-Li Zhang, Shi-Cai Gong","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-08-10T06:42:15Z","title":"On the determinant of the distance matrix of a bicyclic graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2281","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":"sha256:84f487f7152fe15ec9016e2d0cde6639c9e3a2d65d3a77cdbafec46336175f33","target":"record","created_at":"2026-05-18T03:16:07Z","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":"5ee095ad6038501dc81b375e22b67bc4d5575d82c242e32dd47f8fcecf7d5d2a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CO","submitted_at":"2013-08-10T06:42:15Z","title_canon_sha256":"670ac67e9db2e8cd717a5f5ff14446d52ad6929d5f3782a27bed84c2c359254e"},"schema_version":"1.0","source":{"id":"1308.2281","kind":"arxiv","version":1}},"canonical_sha256":"9ddfb77b6723894b09c0b4c173bf00598656985d5e57ef415182524347a7d273","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ddfb77b6723894b09c0b4c173bf00598656985d5e57ef415182524347a7d273","first_computed_at":"2026-05-18T03:16:07.938411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:07.938411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QBKOceGrPjKUzarH6aba2CVGsMWpNW68gCgCTTTt0EWWsbEOiA53F3R4tN7MjuUTJeX24aghH+db4LQdcugKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:07.938963Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2281","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:84f487f7152fe15ec9016e2d0cde6639c9e3a2d65d3a77cdbafec46336175f33","sha256:228bbe8bab81869c5c3ec50a33900e36a6a79435111733f55610b8a4ade65ad0"],"state_sha256":"c6959e3022dccce54407b787ad6e124aa6f789ef2cb72e617884604a598a9aab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qva3e0rzEcLhOtLvp9RtNMDmocETWgdd+BDUkKfRERqsSotHuPUzZ/9M+JiH10JII3yjxnwAVK7s6MRrFRyBAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T08:14:58.105210Z","bundle_sha256":"559b41aa2466add074acf7214f8dc2a6762532b7e42aa45485370203e4ffcd6e"}}