{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KYJBUIP2VJCCROUMQP7LN7LJ7R","short_pith_number":"pith:KYJBUIP2","canonical_record":{"source":{"id":"1508.05690","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2015-08-24T03:32:37Z","cross_cats_sorted":[],"title_canon_sha256":"6b27c23b610088250ec2f1e05132b4b13799899ffa87572bdf2a3f1786cd1706","abstract_canon_sha256":"ee28db26f75835b63a5609f4bab39fa10f9825e24d4c8a39f2cf836ff1403df9"},"schema_version":"1.0"},"canonical_sha256":"56121a21faaa4428ba8c83feb6fd69fc659087eecb71cecb4445c4bba75ccbcc","source":{"kind":"arxiv","id":"1508.05690","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05690","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05690v1","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05690","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"KYJBUIP2VJCC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KYJBUIP2VJCCROUM","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KYJBUIP2","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KYJBUIP2VJCCROUMQP7LN7LJ7R","target":"record","payload":{"canonical_record":{"source":{"id":"1508.05690","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2015-08-24T03:32:37Z","cross_cats_sorted":[],"title_canon_sha256":"6b27c23b610088250ec2f1e05132b4b13799899ffa87572bdf2a3f1786cd1706","abstract_canon_sha256":"ee28db26f75835b63a5609f4bab39fa10f9825e24d4c8a39f2cf836ff1403df9"},"schema_version":"1.0"},"canonical_sha256":"56121a21faaa4428ba8c83feb6fd69fc659087eecb71cecb4445c4bba75ccbcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:51.892888Z","signature_b64":"mdDep3snP+rzL8Rmi8208VbJ5/+VQxsuRTfzMLaS+YZVqcnv/V/L1aOqPyTGiidELk1LeqMZmWZIcf+TXWT4BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56121a21faaa4428ba8c83feb6fd69fc659087eecb71cecb4445c4bba75ccbcc","last_reissued_at":"2026-05-18T01:34:51.892419Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:51.892419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.05690","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":"2026-05-18T01:34:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nh0Ix1by5GPGrS87boyZW1Xg739LQBmSDQfHWnm26ZFtWBpSC50iUCek6bPQxt55G9fN3TiX5DjXcxJ3TdmyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:06:06.724989Z"},"content_sha256":"76c37b83926c278ef516fc0b1ffdc9c6c30a094778340e2df97dbac30d0a1384","schema_version":"1.0","event_id":"sha256:76c37b83926c278ef516fc0b1ffdc9c6c30a094778340e2df97dbac30d0a1384"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KYJBUIP2VJCCROUMQP7LN7LJ7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the extremal total reciprocal edge-eccentricity of trees","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lifang Zhao, Shuchao Li","submitted_at":"2015-08-24T03:32:37Z","abstract_excerpt":"The total reciprocal edge-eccentricity is a novel graph invariant with vast potential in structure activity/property relationships. This graph invariant displays high discriminating power with respect to both biological activity and physical properties. If $G=(V_G,E_G)$ is a simple connected graph, then the total reciprocal edge-eccentricity (REE) of $G$ is defined as $\\xi^{ee}(G)=\\sum_{uv\\in E_G}(1/\\varepsilon_G(u)+1/\\varepsilon_G(v))$, where $\\varepsilon_G(v)$ is the eccentricity of the vertex $v$. In this paper we first introduced four edge-grafting transformations to study the mathematical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05690","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":"2026-05-18T01:34:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TXLCl5AOcM5CR1dqFrz2o4gvofIXeYTCGu8cLXxzDYtnmTzNIU9CrqyGCaoUostT7nXt6VJmKEO+t3bclRe2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:06:06.725682Z"},"content_sha256":"2b9ee5eb166cfadf286ee6114c14dc80ea29d6f775b2bb940fbace0a816483ce","schema_version":"1.0","event_id":"sha256:2b9ee5eb166cfadf286ee6114c14dc80ea29d6f775b2bb940fbace0a816483ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KYJBUIP2VJCCROUMQP7LN7LJ7R/bundle.json","state_url":"https://pith.science/pith/KYJBUIP2VJCCROUMQP7LN7LJ7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KYJBUIP2VJCCROUMQP7LN7LJ7R/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":"2026-06-08T19:06:06Z","links":{"resolver":"https://pith.science/pith/KYJBUIP2VJCCROUMQP7LN7LJ7R","bundle":"https://pith.science/pith/KYJBUIP2VJCCROUMQP7LN7LJ7R/bundle.json","state":"https://pith.science/pith/KYJBUIP2VJCCROUMQP7LN7LJ7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KYJBUIP2VJCCROUMQP7LN7LJ7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KYJBUIP2VJCCROUMQP7LN7LJ7R","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":"ee28db26f75835b63a5609f4bab39fa10f9825e24d4c8a39f2cf836ff1403df9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2015-08-24T03:32:37Z","title_canon_sha256":"6b27c23b610088250ec2f1e05132b4b13799899ffa87572bdf2a3f1786cd1706"},"schema_version":"1.0","source":{"id":"1508.05690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.05690","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1508.05690v1","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05690","created_at":"2026-05-18T01:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"KYJBUIP2VJCC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KYJBUIP2VJCCROUM","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KYJBUIP2","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:2b9ee5eb166cfadf286ee6114c14dc80ea29d6f775b2bb940fbace0a816483ce","target":"graph","created_at":"2026-05-18T01:34:51Z","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 total reciprocal edge-eccentricity is a novel graph invariant with vast potential in structure activity/property relationships. This graph invariant displays high discriminating power with respect to both biological activity and physical properties. If $G=(V_G,E_G)$ is a simple connected graph, then the total reciprocal edge-eccentricity (REE) of $G$ is defined as $\\xi^{ee}(G)=\\sum_{uv\\in E_G}(1/\\varepsilon_G(u)+1/\\varepsilon_G(v))$, where $\\varepsilon_G(v)$ is the eccentricity of the vertex $v$. In this paper we first introduced four edge-grafting transformations to study the mathematical","authors_text":"Lifang Zhao, Shuchao Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2015-08-24T03:32:37Z","title":"On the extremal total reciprocal edge-eccentricity of trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05690","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":"sha256:76c37b83926c278ef516fc0b1ffdc9c6c30a094778340e2df97dbac30d0a1384","target":"record","created_at":"2026-05-18T01:34:51Z","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":"ee28db26f75835b63a5609f4bab39fa10f9825e24d4c8a39f2cf836ff1403df9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.CO","submitted_at":"2015-08-24T03:32:37Z","title_canon_sha256":"6b27c23b610088250ec2f1e05132b4b13799899ffa87572bdf2a3f1786cd1706"},"schema_version":"1.0","source":{"id":"1508.05690","kind":"arxiv","version":1}},"canonical_sha256":"56121a21faaa4428ba8c83feb6fd69fc659087eecb71cecb4445c4bba75ccbcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56121a21faaa4428ba8c83feb6fd69fc659087eecb71cecb4445c4bba75ccbcc","first_computed_at":"2026-05-18T01:34:51.892419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:51.892419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mdDep3snP+rzL8Rmi8208VbJ5/+VQxsuRTfzMLaS+YZVqcnv/V/L1aOqPyTGiidELk1LeqMZmWZIcf+TXWT4BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:51.892888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.05690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76c37b83926c278ef516fc0b1ffdc9c6c30a094778340e2df97dbac30d0a1384","sha256:2b9ee5eb166cfadf286ee6114c14dc80ea29d6f775b2bb940fbace0a816483ce"],"state_sha256":"83888be8650a9ded14e131ab490c2ff82508ad7d14def4291478d08429575405"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4eX3f838mhk+OdXvcgZH35igzKDqh8rt62eVuC2Um7mR33xsvVN7unDRWimOCo7LS+ayPzkeJ7uONEbT9scoDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:06:06.729253Z","bundle_sha256":"59b59890d20106a6979d2a05479d3dfae8e1c151ac5cb7f709db5bde8baaa50d"}}