{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XAABH4QMTIPIWASMRT6TCXQOGK","short_pith_number":"pith:XAABH4QM","canonical_record":{"source":{"id":"1511.04704","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-15T14:27:18Z","cross_cats_sorted":[],"title_canon_sha256":"442b98c4f80b74bb59d8ee10cef91a0e5a61bcc95ffa389e54e317ec6b9cef01","abstract_canon_sha256":"59a4799f1041683f1bc53f2c12a86c4813a248febb7d7d9b1c7b10e844265857"},"schema_version":"1.0"},"canonical_sha256":"b80013f20c9a1e8b024c8cfd315e0e329b08f31ba69ec6af5dc8ee71ebd959b8","source":{"kind":"arxiv","id":"1511.04704","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04704","created_at":"2026-05-18T01:17:00Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04704v2","created_at":"2026-05-18T01:17:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04704","created_at":"2026-05-18T01:17:00Z"},{"alias_kind":"pith_short_12","alias_value":"XAABH4QMTIPI","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XAABH4QMTIPIWASM","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XAABH4QM","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XAABH4QMTIPIWASMRT6TCXQOGK","target":"record","payload":{"canonical_record":{"source":{"id":"1511.04704","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-15T14:27:18Z","cross_cats_sorted":[],"title_canon_sha256":"442b98c4f80b74bb59d8ee10cef91a0e5a61bcc95ffa389e54e317ec6b9cef01","abstract_canon_sha256":"59a4799f1041683f1bc53f2c12a86c4813a248febb7d7d9b1c7b10e844265857"},"schema_version":"1.0"},"canonical_sha256":"b80013f20c9a1e8b024c8cfd315e0e329b08f31ba69ec6af5dc8ee71ebd959b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:00.047819Z","signature_b64":"fFNlYQJr4WJIl6rYnWmIn5xbW3tuwdXVYsy6tY3JHDULf0+1Lz3aR9/MqoKkQumwygHb8yMEkwzvgldEaJAhDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b80013f20c9a1e8b024c8cfd315e0e329b08f31ba69ec6af5dc8ee71ebd959b8","last_reissued_at":"2026-05-18T01:17:00.047102Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:00.047102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.04704","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ASme1BhygLpJ3KyTFHsm6zdTnk1LZgkcW27OMva0Kom1TwGq70GiOMKdPkY03Gya15C6hDL3RFKtqhXCWK4/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:27:39.620993Z"},"content_sha256":"1c51eb37b0ceff99361ed9847f596dfb3272d8785d5a9a7241dce4efc87f3d64","schema_version":"1.0","event_id":"sha256:1c51eb37b0ceff99361ed9847f596dfb3272d8785d5a9a7241dce4efc87f3d64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XAABH4QMTIPIWASMRT6TCXQOGK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The maximum degree resistance distance of cacti","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jia-Bao Liu, Xiang-Feng Pan","submitted_at":"2015-11-15T14:27:18Z","abstract_excerpt":"Various topological indices, based on the distances between the vertices of a graph, are widely used in theoretical chemistry. The degree resistance distance of a graph $G$ is defined as ${D_R}(G) = \\sum\\limits_{\\{u,v\\} \\subseteq V(G)} {[d(u) + d(v)]R(u,v)},$ where $d(u)$ is the degree of the vertex $u,$ and $R(u, v)$ the resistance distance between the vertices $u$ and $v.$\n  A graph $G$ is called a cactus if each block of $G$ is either an edge or a cycle. In this paper, we completely characterize the extremal cacti having the maximum degree resistance distance among all cacti with $n$ vertic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04704","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LMZtlJ5BEJ5s/Zvk6SHHZ8zEt/oQUwWWI8EcieTm9D4wpffF2wof1yP3tfVDJU5QwvYiZlWKZEZNo7IswGGmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:27:39.621856Z"},"content_sha256":"6043acb072791ba172a839ed5dad232bd5f3061edb44725b9e2f8224c7d85f22","schema_version":"1.0","event_id":"sha256:6043acb072791ba172a839ed5dad232bd5f3061edb44725b9e2f8224c7d85f22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAABH4QMTIPIWASMRT6TCXQOGK/bundle.json","state_url":"https://pith.science/pith/XAABH4QMTIPIWASMRT6TCXQOGK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAABH4QMTIPIWASMRT6TCXQOGK/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":"2026-06-07T17:27:39Z","links":{"resolver":"https://pith.science/pith/XAABH4QMTIPIWASMRT6TCXQOGK","bundle":"https://pith.science/pith/XAABH4QMTIPIWASMRT6TCXQOGK/bundle.json","state":"https://pith.science/pith/XAABH4QMTIPIWASMRT6TCXQOGK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAABH4QMTIPIWASMRT6TCXQOGK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XAABH4QMTIPIWASMRT6TCXQOGK","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":"59a4799f1041683f1bc53f2c12a86c4813a248febb7d7d9b1c7b10e844265857","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-15T14:27:18Z","title_canon_sha256":"442b98c4f80b74bb59d8ee10cef91a0e5a61bcc95ffa389e54e317ec6b9cef01"},"schema_version":"1.0","source":{"id":"1511.04704","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04704","created_at":"2026-05-18T01:17:00Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04704v2","created_at":"2026-05-18T01:17:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04704","created_at":"2026-05-18T01:17:00Z"},{"alias_kind":"pith_short_12","alias_value":"XAABH4QMTIPI","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XAABH4QMTIPIWASM","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XAABH4QM","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:6043acb072791ba172a839ed5dad232bd5f3061edb44725b9e2f8224c7d85f22","target":"graph","created_at":"2026-05-18T01:17:00Z","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":"Various topological indices, based on the distances between the vertices of a graph, are widely used in theoretical chemistry. The degree resistance distance of a graph $G$ is defined as ${D_R}(G) = \\sum\\limits_{\\{u,v\\} \\subseteq V(G)} {[d(u) + d(v)]R(u,v)},$ where $d(u)$ is the degree of the vertex $u,$ and $R(u, v)$ the resistance distance between the vertices $u$ and $v.$\n  A graph $G$ is called a cactus if each block of $G$ is either an edge or a cycle. In this paper, we completely characterize the extremal cacti having the maximum degree resistance distance among all cacti with $n$ vertic","authors_text":"Jia-Bao Liu, Xiang-Feng Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-15T14:27:18Z","title":"The maximum degree resistance distance of cacti"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04704","kind":"arxiv","version":2},"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":"sha256:1c51eb37b0ceff99361ed9847f596dfb3272d8785d5a9a7241dce4efc87f3d64","target":"record","created_at":"2026-05-18T01:17:00Z","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":"59a4799f1041683f1bc53f2c12a86c4813a248febb7d7d9b1c7b10e844265857","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-15T14:27:18Z","title_canon_sha256":"442b98c4f80b74bb59d8ee10cef91a0e5a61bcc95ffa389e54e317ec6b9cef01"},"schema_version":"1.0","source":{"id":"1511.04704","kind":"arxiv","version":2}},"canonical_sha256":"b80013f20c9a1e8b024c8cfd315e0e329b08f31ba69ec6af5dc8ee71ebd959b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b80013f20c9a1e8b024c8cfd315e0e329b08f31ba69ec6af5dc8ee71ebd959b8","first_computed_at":"2026-05-18T01:17:00.047102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:00.047102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fFNlYQJr4WJIl6rYnWmIn5xbW3tuwdXVYsy6tY3JHDULf0+1Lz3aR9/MqoKkQumwygHb8yMEkwzvgldEaJAhDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:00.047819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.04704","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1c51eb37b0ceff99361ed9847f596dfb3272d8785d5a9a7241dce4efc87f3d64","sha256:6043acb072791ba172a839ed5dad232bd5f3061edb44725b9e2f8224c7d85f22"],"state_sha256":"6dc9df15de8b02e0597a3e218a2601eeb848c6e0ea4f5ed2ed08bc4ed0eb2393"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C3Mu1Hn3mSa+8KQkvplrMct6CeU5v3G0xhdzJJJAgI3g4vR6OxXvrdp+s6PRyCmag+mNuqg5CAsCynXMNK6hDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:27:39.625636Z","bundle_sha256":"f5ec0104517a168629d3536cbb9cf86c701fc7ab97a099c0b998ec86d9dfc3b8"}}