{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MN7EPL2CK6UNYAVHGR3OL4VVYJ","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":"15d828b4ad60337e49e63c4ef3cc1b2e378b7cae244a593a19feba636e06f2a1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2015-02-25T09:26:36Z","title_canon_sha256":"0dd35eb3637435393d8f82797b8f5d7a5cf63f301f20f29ba1bf41cfe112126d"},"schema_version":"1.0","source":{"id":"1502.07093","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07093","created_at":"2026-05-18T01:26:10Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07093v2","created_at":"2026-05-18T01:26:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07093","created_at":"2026-05-18T01:26:10Z"},{"alias_kind":"pith_short_12","alias_value":"MN7EPL2CK6UN","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MN7EPL2CK6UNYAVH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MN7EPL2C","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:4c9535ea7ce8b5709f319115534c13668fa20b53fb4953911d76c75df49cf5f9","target":"graph","created_at":"2026-05-18T01:26:10Z","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":"The concept of the \\emph{Gutman index}, denoted $Gut(G)$ was introduced for a connected undirected graph $G$. In this note we apply the concept to the underlying graphs of the family of Jaco graphs, (\\emph{directed graphs by definition}), and describe a recursive formula for the \\emph{Gutman index} $Gut(J^*_{n+1}(x)).$ We also determine the \\emph{Gutman index} for the trivial \\emph{edge-joint} between Jaco graphs.","authors_text":"Johan Kok, Sunny Joseph Kalayathankal, Susanth C","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2015-02-25T09:26:36Z","title":"A Note on the Gutman Index of Jaco Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07093","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":"sha256:1caaf9e786f5e8b518eaa31f0a535ddf3633c0064eb46bfaee2579dcfff6992d","target":"record","created_at":"2026-05-18T01:26:10Z","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":"15d828b4ad60337e49e63c4ef3cc1b2e378b7cae244a593a19feba636e06f2a1","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2015-02-25T09:26:36Z","title_canon_sha256":"0dd35eb3637435393d8f82797b8f5d7a5cf63f301f20f29ba1bf41cfe112126d"},"schema_version":"1.0","source":{"id":"1502.07093","kind":"arxiv","version":2}},"canonical_sha256":"637e47af4257a8dc02a73476e5f2b5c27591d87d1159c6f15b6caa4cb3e7f39e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"637e47af4257a8dc02a73476e5f2b5c27591d87d1159c6f15b6caa4cb3e7f39e","first_computed_at":"2026-05-18T01:26:10.597654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:10.597654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"haR7/IUdNeWc+YNHyD+9aVQDr4AUw9J45RX7pFXR+lra7gn9GbYqcR45OhVTVr9s+TCrhgEUx5ZjdLZEY64cDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:10.598235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07093","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1caaf9e786f5e8b518eaa31f0a535ddf3633c0064eb46bfaee2579dcfff6992d","sha256:4c9535ea7ce8b5709f319115534c13668fa20b53fb4953911d76c75df49cf5f9"],"state_sha256":"5b5bc331a85f63fd9e1b1badf42c533ea4240f85a7f4c0270937fa804dbadf65"}