{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:EPL27CEVIA7TGI7VVPVI66AZTY","short_pith_number":"pith:EPL27CEV","canonical_record":{"source":{"id":"2110.14712","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-10-27T18:59:39Z","cross_cats_sorted":[],"title_canon_sha256":"6b91e760027f1a7e5f709124526b890a15f1a2ef9ed3c7515a34fed7f20a97a2","abstract_canon_sha256":"4d1ca49711afe04f483f71f6c5e2d9eb4519078b8cf9f1deebaa8576cbfe12e0"},"schema_version":"1.0"},"canonical_sha256":"23d7af8895403f3323f5abea8f78199e1b29c3427a784fb648d9e4d1b2288a49","source":{"kind":"arxiv","id":"2110.14712","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.14712","created_at":"2026-07-05T03:50:02Z"},{"alias_kind":"arxiv_version","alias_value":"2110.14712v2","created_at":"2026-07-05T03:50:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14712","created_at":"2026-07-05T03:50:02Z"},{"alias_kind":"pith_short_12","alias_value":"EPL27CEVIA7T","created_at":"2026-07-05T03:50:02Z"},{"alias_kind":"pith_short_16","alias_value":"EPL27CEVIA7TGI7V","created_at":"2026-07-05T03:50:02Z"},{"alias_kind":"pith_short_8","alias_value":"EPL27CEV","created_at":"2026-07-05T03:50:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:EPL27CEVIA7TGI7VVPVI66AZTY","target":"record","payload":{"canonical_record":{"source":{"id":"2110.14712","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-10-27T18:59:39Z","cross_cats_sorted":[],"title_canon_sha256":"6b91e760027f1a7e5f709124526b890a15f1a2ef9ed3c7515a34fed7f20a97a2","abstract_canon_sha256":"4d1ca49711afe04f483f71f6c5e2d9eb4519078b8cf9f1deebaa8576cbfe12e0"},"schema_version":"1.0"},"canonical_sha256":"23d7af8895403f3323f5abea8f78199e1b29c3427a784fb648d9e4d1b2288a49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:50:02.957188Z","signature_b64":"PMfjlkja48MwoyLnK+begeFNRAMn/KAHWHOmkPCwPzqUvF27ltIgvpGYcZQk3UB5GhgpcZbD9ATQZRWHx+DgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23d7af8895403f3323f5abea8f78199e1b29c3427a784fb648d9e4d1b2288a49","last_reissued_at":"2026-07-05T03:50:02.956579Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:50:02.956579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.14712","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":"2026-07-05T03:50:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V9OWCQqd8aK770dCDWgZFF16ZM0+tFrXo8WyqQOyB81V+/47x6/QqME9bV3nq+d8wjLvlGxb89dwY0P/ZAKrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T13:30:48.157301Z"},"content_sha256":"a482caa860c1579ad45138f88e0a19503ebe77a60e018162b08f0351afdd1769","schema_version":"1.0","event_id":"sha256:a482caa860c1579ad45138f88e0a19503ebe77a60e018162b08f0351afdd1769"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:EPL27CEVIA7TGI7VVPVI66AZTY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complete characterization of the minimal-ABC trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Darko Dimitrov, Zhibin Du","submitted_at":"2021-10-27T18:59:39Z","abstract_excerpt":"The problem of characterizing trees with minimal atom-bond-connectivity index (minimal-ABC trees) has a reputation as one of the most demanding recent open optimization problems in mathematical chemistry. Here firstly, we give an affirmative answer to the conjecture, which states that enough large minimal-ABC trees are comprised solely of a root vertex and so-called $D_z$- and $D_{z+1}$-branches. Based on the presented theoretical results here and some already known results, we obtain enough constraints to reduce the search space and solve the optimization problem, and thus, determine exactly "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14712","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.14712/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:50:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQi1mvzkKnS0AuZX0NNu5/z9qbFmjmYIdn6wsui6+TrNrsUEdUPT6epKVNvr6gyFW/C6zWIEZjj9eCsamLAHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T13:30:48.157953Z"},"content_sha256":"24a0359ecc025b23cea19e83d293210d8c2301682a3126d460630463b70adf7b","schema_version":"1.0","event_id":"sha256:24a0359ecc025b23cea19e83d293210d8c2301682a3126d460630463b70adf7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EPL27CEVIA7TGI7VVPVI66AZTY/bundle.json","state_url":"https://pith.science/pith/EPL27CEVIA7TGI7VVPVI66AZTY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EPL27CEVIA7TGI7VVPVI66AZTY/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":"2026-07-05T13:30:48Z","links":{"resolver":"https://pith.science/pith/EPL27CEVIA7TGI7VVPVI66AZTY","bundle":"https://pith.science/pith/EPL27CEVIA7TGI7VVPVI66AZTY/bundle.json","state":"https://pith.science/pith/EPL27CEVIA7TGI7VVPVI66AZTY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EPL27CEVIA7TGI7VVPVI66AZTY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:EPL27CEVIA7TGI7VVPVI66AZTY","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":"4d1ca49711afe04f483f71f6c5e2d9eb4519078b8cf9f1deebaa8576cbfe12e0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-10-27T18:59:39Z","title_canon_sha256":"6b91e760027f1a7e5f709124526b890a15f1a2ef9ed3c7515a34fed7f20a97a2"},"schema_version":"1.0","source":{"id":"2110.14712","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.14712","created_at":"2026-07-05T03:50:02Z"},{"alias_kind":"arxiv_version","alias_value":"2110.14712v2","created_at":"2026-07-05T03:50:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.14712","created_at":"2026-07-05T03:50:02Z"},{"alias_kind":"pith_short_12","alias_value":"EPL27CEVIA7T","created_at":"2026-07-05T03:50:02Z"},{"alias_kind":"pith_short_16","alias_value":"EPL27CEVIA7TGI7V","created_at":"2026-07-05T03:50:02Z"},{"alias_kind":"pith_short_8","alias_value":"EPL27CEV","created_at":"2026-07-05T03:50:02Z"}],"graph_snapshots":[{"event_id":"sha256:24a0359ecc025b23cea19e83d293210d8c2301682a3126d460630463b70adf7b","target":"graph","created_at":"2026-07-05T03:50:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.14712/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The problem of characterizing trees with minimal atom-bond-connectivity index (minimal-ABC trees) has a reputation as one of the most demanding recent open optimization problems in mathematical chemistry. Here firstly, we give an affirmative answer to the conjecture, which states that enough large minimal-ABC trees are comprised solely of a root vertex and so-called $D_z$- and $D_{z+1}$-branches. Based on the presented theoretical results here and some already known results, we obtain enough constraints to reduce the search space and solve the optimization problem, and thus, determine exactly ","authors_text":"Darko Dimitrov, Zhibin Du","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-10-27T18:59:39Z","title":"Complete characterization of the minimal-ABC trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.14712","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:a482caa860c1579ad45138f88e0a19503ebe77a60e018162b08f0351afdd1769","target":"record","created_at":"2026-07-05T03:50:02Z","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":"4d1ca49711afe04f483f71f6c5e2d9eb4519078b8cf9f1deebaa8576cbfe12e0","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2021-10-27T18:59:39Z","title_canon_sha256":"6b91e760027f1a7e5f709124526b890a15f1a2ef9ed3c7515a34fed7f20a97a2"},"schema_version":"1.0","source":{"id":"2110.14712","kind":"arxiv","version":2}},"canonical_sha256":"23d7af8895403f3323f5abea8f78199e1b29c3427a784fb648d9e4d1b2288a49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23d7af8895403f3323f5abea8f78199e1b29c3427a784fb648d9e4d1b2288a49","first_computed_at":"2026-07-05T03:50:02.956579Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:50:02.956579Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PMfjlkja48MwoyLnK+begeFNRAMn/KAHWHOmkPCwPzqUvF27ltIgvpGYcZQk3UB5GhgpcZbD9ATQZRWHx+DgCA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:50:02.957188Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.14712","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a482caa860c1579ad45138f88e0a19503ebe77a60e018162b08f0351afdd1769","sha256:24a0359ecc025b23cea19e83d293210d8c2301682a3126d460630463b70adf7b"],"state_sha256":"44e4ed7edb489de29dd29e003d0cf28f9033446767ba482824c20b41d7fb3557"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NK7J21/ZBSxGD4B1nzWwNPlSvs7qc28FNCmiG1HCv77EoSsE1+d1nLUjdNg5a+AAQARLd16Cn2pgCu4xvvaFCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T13:30:48.161423Z","bundle_sha256":"400de5280f31024e57a4d0bcefded5ed876d8e16894cbfba34474fad09d6e479"}}