{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FFDV5QOTE7ZJ2AVNRWSWQKNFFF","short_pith_number":"pith:FFDV5QOT","canonical_record":{"source":{"id":"1602.05184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-16T20:56:17Z","cross_cats_sorted":[],"title_canon_sha256":"725eb0e5fa3d4997516b0bedb8faa6dca89013c03842bdfe6e5efed7a4392f8d","abstract_canon_sha256":"53e100ff2cfafb03f2559d429d0fbad9250e60df877457caaa3c81173180c5ac"},"schema_version":"1.0"},"canonical_sha256":"29475ec1d327f29d02ad8da56829a5296cc8057dbe7976f4dd52ad50e6c9b0cd","source":{"kind":"arxiv","id":"1602.05184","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05184","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05184v1","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05184","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"FFDV5QOTE7ZJ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FFDV5QOTE7ZJ2AVN","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FFDV5QOT","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FFDV5QOTE7ZJ2AVNRWSWQKNFFF","target":"record","payload":{"canonical_record":{"source":{"id":"1602.05184","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-16T20:56:17Z","cross_cats_sorted":[],"title_canon_sha256":"725eb0e5fa3d4997516b0bedb8faa6dca89013c03842bdfe6e5efed7a4392f8d","abstract_canon_sha256":"53e100ff2cfafb03f2559d429d0fbad9250e60df877457caaa3c81173180c5ac"},"schema_version":"1.0"},"canonical_sha256":"29475ec1d327f29d02ad8da56829a5296cc8057dbe7976f4dd52ad50e6c9b0cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:11.627803Z","signature_b64":"SDlwDcFyyvRL3DaXc3em/loddzOndZq0mmUbN73LrdqqvvguZGfW9eQ/oFLOFG9GuKWgqh4MuJc+PWR/A4cjBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"29475ec1d327f29d02ad8da56829a5296cc8057dbe7976f4dd52ad50e6c9b0cd","last_reissued_at":"2026-05-18T00:12:11.627147Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:11.627147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.05184","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":"2026-05-18T00:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SAayS70LoRn8wdFgBi522Or8HgYoq7IMoLSQxyKZrH/+fA/ehKEJbcIzssj4SYgKQeLox+l14t1pfS6dcEuwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:00:07.015820Z"},"content_sha256":"7acd414aa484ecb0d659df40071668af9b96607c24f40dc570281fcb27b1a209","schema_version":"1.0","event_id":"sha256:7acd414aa484ecb0d659df40071668af9b96607c24f40dc570281fcb27b1a209"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FFDV5QOTE7ZJ2AVNRWSWQKNFFF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the difference between the Szeged and Wiener index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexandre Pinlou, Borut Lu\\v{z}ar, Marthe Bonamy, Martin Knor, Riste \\v{S}krekovski","submitted_at":"2016-02-16T20:56:17Z","abstract_excerpt":"We prove a conjecture of Nadjafi-Arani, Khodashenas and Ashrafi on the difference between the Szeged and Wiener index of a graph. Namely, if $G$ is a 2-connected non-complete graph on $n$ vertices, then $Sz(G)-W(G)\\ge 2n-6$. Furthermore, the equality is obtained if and only if $G$ is the complete graph $K_{n-1}$ with an extra vertex attached to either $2$ or $n-2$ vertices of $K_{n-1}$. We apply our method to strengthen some known results on the difference between the Szeged and Wiener index of bipartite graphs, graphs of girth at least five, and the difference between the revised Szeged and W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05184","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":"2026-05-18T00:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G96JB7RlFxlR1mA3KomjMRBHsbOUNopssVKF7QUz0kH6B9JJaiAzlDMNOvLxuKf//eCQP2L6gRnNBsADJ/Z0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T02:00:07.016158Z"},"content_sha256":"36d7a0a046248d53f200fd98efab33f28025e99e2517da7603b0b164b362fd32","schema_version":"1.0","event_id":"sha256:36d7a0a046248d53f200fd98efab33f28025e99e2517da7603b0b164b362fd32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFDV5QOTE7ZJ2AVNRWSWQKNFFF/bundle.json","state_url":"https://pith.science/pith/FFDV5QOTE7ZJ2AVNRWSWQKNFFF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFDV5QOTE7ZJ2AVNRWSWQKNFFF/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":"2026-06-20T02:00:07Z","links":{"resolver":"https://pith.science/pith/FFDV5QOTE7ZJ2AVNRWSWQKNFFF","bundle":"https://pith.science/pith/FFDV5QOTE7ZJ2AVNRWSWQKNFFF/bundle.json","state":"https://pith.science/pith/FFDV5QOTE7ZJ2AVNRWSWQKNFFF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFDV5QOTE7ZJ2AVNRWSWQKNFFF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FFDV5QOTE7ZJ2AVNRWSWQKNFFF","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":"53e100ff2cfafb03f2559d429d0fbad9250e60df877457caaa3c81173180c5ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-16T20:56:17Z","title_canon_sha256":"725eb0e5fa3d4997516b0bedb8faa6dca89013c03842bdfe6e5efed7a4392f8d"},"schema_version":"1.0","source":{"id":"1602.05184","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.05184","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1602.05184v1","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.05184","created_at":"2026-05-18T00:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"FFDV5QOTE7ZJ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FFDV5QOTE7ZJ2AVN","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FFDV5QOT","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:36d7a0a046248d53f200fd98efab33f28025e99e2517da7603b0b164b362fd32","target":"graph","created_at":"2026-05-18T00:12:11Z","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":"We prove a conjecture of Nadjafi-Arani, Khodashenas and Ashrafi on the difference between the Szeged and Wiener index of a graph. Namely, if $G$ is a 2-connected non-complete graph on $n$ vertices, then $Sz(G)-W(G)\\ge 2n-6$. Furthermore, the equality is obtained if and only if $G$ is the complete graph $K_{n-1}$ with an extra vertex attached to either $2$ or $n-2$ vertices of $K_{n-1}$. We apply our method to strengthen some known results on the difference between the Szeged and Wiener index of bipartite graphs, graphs of girth at least five, and the difference between the revised Szeged and W","authors_text":"Alexandre Pinlou, Borut Lu\\v{z}ar, Marthe Bonamy, Martin Knor, Riste \\v{S}krekovski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-16T20:56:17Z","title":"On the difference between the Szeged and Wiener index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.05184","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":"sha256:7acd414aa484ecb0d659df40071668af9b96607c24f40dc570281fcb27b1a209","target":"record","created_at":"2026-05-18T00:12:11Z","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":"53e100ff2cfafb03f2559d429d0fbad9250e60df877457caaa3c81173180c5ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-16T20:56:17Z","title_canon_sha256":"725eb0e5fa3d4997516b0bedb8faa6dca89013c03842bdfe6e5efed7a4392f8d"},"schema_version":"1.0","source":{"id":"1602.05184","kind":"arxiv","version":1}},"canonical_sha256":"29475ec1d327f29d02ad8da56829a5296cc8057dbe7976f4dd52ad50e6c9b0cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"29475ec1d327f29d02ad8da56829a5296cc8057dbe7976f4dd52ad50e6c9b0cd","first_computed_at":"2026-05-18T00:12:11.627147Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:11.627147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SDlwDcFyyvRL3DaXc3em/loddzOndZq0mmUbN73LrdqqvvguZGfW9eQ/oFLOFG9GuKWgqh4MuJc+PWR/A4cjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:11.627803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.05184","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7acd414aa484ecb0d659df40071668af9b96607c24f40dc570281fcb27b1a209","sha256:36d7a0a046248d53f200fd98efab33f28025e99e2517da7603b0b164b362fd32"],"state_sha256":"89b49e7ee65f94d70c673e27a70ecaad6be5c704b841ce6888f8bde07d999df3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nK+ZIus3YRFlh/haWPTRUkqIFk7lC5Za9z9hE5dIGKI8GySnTFOn58asQRkyTAunvTFZgBodwBEuUYnN6/J6Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T02:00:07.018057Z","bundle_sha256":"8d0f08d63f4b971b67752d4b8d01afb788e42307afe08e6df739740de47cb9fe"}}