{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZVXPJBYPS4T2ZFEJTQGDAXTXV2","short_pith_number":"pith:ZVXPJBYP","schema_version":"1.0","canonical_sha256":"cd6ef4870f9727ac94899c0c305e77aea1977b61dc3a4d6291c2fc91a276625b","source":{"kind":"arxiv","id":"1706.08587","version":1},"attestation_state":"computed","paper":{"title":"On structural properties of trees with minimal atom-bond connectivity index IV: Solving a conjecture about the pendent paths of length three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Darko Dimitrov","submitted_at":"2017-06-26T20:47:53Z","abstract_excerpt":"The atom-bond connectivity (ABC) index is one of the most investigated degree-based molecular structure descriptors with a variety of chemical applications. It is known that among all connected graphs, the trees minimize the ABC index. However, a full characterization of trees with a minimal ABC index is still an open problem. By now, one of the proved properties is that a tree with a minimal ABC index may have, at most, one pendent path of length $3$, with the conjecture that it cannot be a case if the order of a tree is larger than $1178$. Here, we provide an affirmative answer of a strength"},"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":"1706.08587","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-06-26T20:47:53Z","cross_cats_sorted":[],"title_canon_sha256":"1e769e45d09b5809b097bb0fe3d02463735ec32b50ae53e81cf8e5c19deb1a73","abstract_canon_sha256":"7cbe1f2b0393c5bc902e17809df05de6ce57ccc12fa47b7b88f04b275cea35b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:31.642901Z","signature_b64":"FR7XkfFtFZxtCPadRDXesek40rE1YBTC/Qe6rBasrrYQRQaOz0S434W553zeFXuRvL++8sPSj9OSCzmGzMouAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd6ef4870f9727ac94899c0c305e77aea1977b61dc3a4d6291c2fc91a276625b","last_reissued_at":"2026-05-18T00:41:31.642221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:31.642221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On structural properties of trees with minimal atom-bond connectivity index IV: Solving a conjecture about the pendent paths of length three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Darko Dimitrov","submitted_at":"2017-06-26T20:47:53Z","abstract_excerpt":"The atom-bond connectivity (ABC) index is one of the most investigated degree-based molecular structure descriptors with a variety of chemical applications. It is known that among all connected graphs, the trees minimize the ABC index. However, a full characterization of trees with a minimal ABC index is still an open problem. By now, one of the proved properties is that a tree with a minimal ABC index may have, at most, one pendent path of length $3$, with the conjecture that it cannot be a case if the order of a tree is larger than $1178$. Here, we provide an affirmative answer of a strength"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08587","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":"1706.08587","created_at":"2026-05-18T00:41:31.642337+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.08587v1","created_at":"2026-05-18T00:41:31.642337+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.08587","created_at":"2026-05-18T00:41:31.642337+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZVXPJBYPS4T2","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZVXPJBYPS4T2ZFEJ","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZVXPJBYP","created_at":"2026-05-18T12:31:59.375834+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/ZVXPJBYPS4T2ZFEJTQGDAXTXV2","json":"https://pith.science/pith/ZVXPJBYPS4T2ZFEJTQGDAXTXV2.json","graph_json":"https://pith.science/api/pith-number/ZVXPJBYPS4T2ZFEJTQGDAXTXV2/graph.json","events_json":"https://pith.science/api/pith-number/ZVXPJBYPS4T2ZFEJTQGDAXTXV2/events.json","paper":"https://pith.science/paper/ZVXPJBYP"},"agent_actions":{"view_html":"https://pith.science/pith/ZVXPJBYPS4T2ZFEJTQGDAXTXV2","download_json":"https://pith.science/pith/ZVXPJBYPS4T2ZFEJTQGDAXTXV2.json","view_paper":"https://pith.science/paper/ZVXPJBYP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.08587&json=true","fetch_graph":"https://pith.science/api/pith-number/ZVXPJBYPS4T2ZFEJTQGDAXTXV2/graph.json","fetch_events":"https://pith.science/api/pith-number/ZVXPJBYPS4T2ZFEJTQGDAXTXV2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZVXPJBYPS4T2ZFEJTQGDAXTXV2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZVXPJBYPS4T2ZFEJTQGDAXTXV2/action/storage_attestation","attest_author":"https://pith.science/pith/ZVXPJBYPS4T2ZFEJTQGDAXTXV2/action/author_attestation","sign_citation":"https://pith.science/pith/ZVXPJBYPS4T2ZFEJTQGDAXTXV2/action/citation_signature","submit_replication":"https://pith.science/pith/ZVXPJBYPS4T2ZFEJTQGDAXTXV2/action/replication_record"}},"created_at":"2026-05-18T00:41:31.642337+00:00","updated_at":"2026-05-18T00:41:31.642337+00:00"}