{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GB4D5VFZZYYUUKJ7JQBBA7QVTC","short_pith_number":"pith:GB4D5VFZ","canonical_record":{"source":{"id":"1702.05303","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-17T11:30:50Z","cross_cats_sorted":[],"title_canon_sha256":"2c1eaf252c63d616ed81d86ab5561970a42ea7fc8a7ffb3d0c700a51c63116db","abstract_canon_sha256":"053c5255bcc6a187578328168203f4f6a490dfd86b5d0de8b580070ecafe9e3e"},"schema_version":"1.0"},"canonical_sha256":"30783ed4b9ce314a293f4c02107e1598a1391a15cde52c316d6e055d64cc0dd2","source":{"kind":"arxiv","id":"1702.05303","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05303","created_at":"2026-05-18T00:50:32Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05303v1","created_at":"2026-05-18T00:50:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05303","created_at":"2026-05-18T00:50:32Z"},{"alias_kind":"pith_short_12","alias_value":"GB4D5VFZZYYU","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GB4D5VFZZYYUUKJ7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GB4D5VFZ","created_at":"2026-05-18T12:31:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GB4D5VFZZYYUUKJ7JQBBA7QVTC","target":"record","payload":{"canonical_record":{"source":{"id":"1702.05303","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-17T11:30:50Z","cross_cats_sorted":[],"title_canon_sha256":"2c1eaf252c63d616ed81d86ab5561970a42ea7fc8a7ffb3d0c700a51c63116db","abstract_canon_sha256":"053c5255bcc6a187578328168203f4f6a490dfd86b5d0de8b580070ecafe9e3e"},"schema_version":"1.0"},"canonical_sha256":"30783ed4b9ce314a293f4c02107e1598a1391a15cde52c316d6e055d64cc0dd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:32.076820Z","signature_b64":"6HFsBhiaUBI3MsbCVvfOFewJh2Cc7+PErEoesYyTC23vZ3umVPMW+DnCr+2W2UPR004iL0DcbZJ4cs91k1t6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30783ed4b9ce314a293f4c02107e1598a1391a15cde52c316d6e055d64cc0dd2","last_reissued_at":"2026-05-18T00:50:32.076114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:32.076114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.05303","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":"2026-05-18T00:50:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5LVxJPFCydtcOiXcGqTFdFLHhgwJJKjlYavKlgfqZyKiQ+AJSxPeot6GUhC0MdqTO2hgsYeFE1K/ki7eaTSwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:35:59.517062Z"},"content_sha256":"65ada5a4008f84e8bb9c4013a819e6a4f986917abae212ffd4fe3a064c5e9254","schema_version":"1.0","event_id":"sha256:65ada5a4008f84e8bb9c4013a819e6a4f986917abae212ffd4fe3a064c5e9254"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GB4D5VFZZYYUUKJ7JQBBA7QVTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Properties of the Hyper-Wiener index as a local function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xiao-Dong Zhang, Ya-Hong Chen Hua Wang","submitted_at":"2017-02-17T11:30:50Z","abstract_excerpt":"Hyper-Wiener index was introduced as one of the main generalizations of the well known Wiener index. Through the years properties of the Wiener index have been extensively studied in both Mathematics and Chemistry. The Hyper-Wiener index, although received much attention, is far from being thoroughly examined due to its complex definition. We consider the local version of the Hyper-Wiener index ($WW(G)$), defined as $ww_G(v)=\\sum\\limits_{u\\in V(G)}(d^2(u,v)+d(u,v))$ for a vertex $v$ in a graph $G$, in trees. For established results on the Wiener index ($W(.)$), we present analogous studies on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05303","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":"2026-05-18T00:50:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QoD5mrd+aHS1A5vknR3VNSI1LIikIcOosZB/3DLp8KW45ca6/qY4vESjCIxozG5pkY8TQA8n69zL4uNdUvhJDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T15:35:59.517464Z"},"content_sha256":"9cd1cdd8b013aca5da8c755dae41e67c3cf63444040e7418caa0b617f968b584","schema_version":"1.0","event_id":"sha256:9cd1cdd8b013aca5da8c755dae41e67c3cf63444040e7418caa0b617f968b584"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GB4D5VFZZYYUUKJ7JQBBA7QVTC/bundle.json","state_url":"https://pith.science/pith/GB4D5VFZZYYUUKJ7JQBBA7QVTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GB4D5VFZZYYUUKJ7JQBBA7QVTC/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":"2026-06-09T15:35:59Z","links":{"resolver":"https://pith.science/pith/GB4D5VFZZYYUUKJ7JQBBA7QVTC","bundle":"https://pith.science/pith/GB4D5VFZZYYUUKJ7JQBBA7QVTC/bundle.json","state":"https://pith.science/pith/GB4D5VFZZYYUUKJ7JQBBA7QVTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GB4D5VFZZYYUUKJ7JQBBA7QVTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GB4D5VFZZYYUUKJ7JQBBA7QVTC","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":"053c5255bcc6a187578328168203f4f6a490dfd86b5d0de8b580070ecafe9e3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-17T11:30:50Z","title_canon_sha256":"2c1eaf252c63d616ed81d86ab5561970a42ea7fc8a7ffb3d0c700a51c63116db"},"schema_version":"1.0","source":{"id":"1702.05303","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05303","created_at":"2026-05-18T00:50:32Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05303v1","created_at":"2026-05-18T00:50:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05303","created_at":"2026-05-18T00:50:32Z"},{"alias_kind":"pith_short_12","alias_value":"GB4D5VFZZYYU","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GB4D5VFZZYYUUKJ7","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GB4D5VFZ","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:9cd1cdd8b013aca5da8c755dae41e67c3cf63444040e7418caa0b617f968b584","target":"graph","created_at":"2026-05-18T00:50:32Z","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":"Hyper-Wiener index was introduced as one of the main generalizations of the well known Wiener index. Through the years properties of the Wiener index have been extensively studied in both Mathematics and Chemistry. The Hyper-Wiener index, although received much attention, is far from being thoroughly examined due to its complex definition. We consider the local version of the Hyper-Wiener index ($WW(G)$), defined as $ww_G(v)=\\sum\\limits_{u\\in V(G)}(d^2(u,v)+d(u,v))$ for a vertex $v$ in a graph $G$, in trees. For established results on the Wiener index ($W(.)$), we present analogous studies on ","authors_text":"Xiao-Dong Zhang, Ya-Hong Chen Hua Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-17T11:30:50Z","title":"Properties of the Hyper-Wiener index as a local function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05303","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":"sha256:65ada5a4008f84e8bb9c4013a819e6a4f986917abae212ffd4fe3a064c5e9254","target":"record","created_at":"2026-05-18T00:50:32Z","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":"053c5255bcc6a187578328168203f4f6a490dfd86b5d0de8b580070ecafe9e3e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-17T11:30:50Z","title_canon_sha256":"2c1eaf252c63d616ed81d86ab5561970a42ea7fc8a7ffb3d0c700a51c63116db"},"schema_version":"1.0","source":{"id":"1702.05303","kind":"arxiv","version":1}},"canonical_sha256":"30783ed4b9ce314a293f4c02107e1598a1391a15cde52c316d6e055d64cc0dd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30783ed4b9ce314a293f4c02107e1598a1391a15cde52c316d6e055d64cc0dd2","first_computed_at":"2026-05-18T00:50:32.076114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:32.076114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6HFsBhiaUBI3MsbCVvfOFewJh2Cc7+PErEoesYyTC23vZ3umVPMW+DnCr+2W2UPR004iL0DcbZJ4cs91k1t6Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:32.076820Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05303","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65ada5a4008f84e8bb9c4013a819e6a4f986917abae212ffd4fe3a064c5e9254","sha256:9cd1cdd8b013aca5da8c755dae41e67c3cf63444040e7418caa0b617f968b584"],"state_sha256":"8a52c8cc5b098dc6e25ef29e5df37440628183bbe6b58f8040dd29564fd860e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1mWWtGaWjIH+jwHowPbzt8lHKV+UzlM+koXjSBoyyTYvmW1hDp5jYwyTvHSg7mMwllQR0+1roiUzqT0yhCmjDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T15:35:59.519754Z","bundle_sha256":"a3350ea26297f2536f9cfddc32b27fcc8233e2616bd3e24c9a136e9016446d5c"}}