{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NQML4TQZQKCBMV6MTARCRWQW2T","short_pith_number":"pith:NQML4TQZ","canonical_record":{"source":{"id":"2201.05539","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-01-14T16:19:01Z","cross_cats_sorted":[],"title_canon_sha256":"9a98436d13e14427403741ea4fb871a4efddc77248f9e72ceb2f685db69b99d5","abstract_canon_sha256":"8bd7996617f7a810f58086b8b9b1784ca52f73ea3395f3a28773f1282f424b82"},"schema_version":"1.0"},"canonical_sha256":"6c18be4e1982841657cc982228da16d4f588dfe2fc3f4e0ffd5daa044110305b","source":{"kind":"arxiv","id":"2201.05539","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.05539","created_at":"2026-07-05T03:48:33Z"},{"alias_kind":"arxiv_version","alias_value":"2201.05539v1","created_at":"2026-07-05T03:48:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.05539","created_at":"2026-07-05T03:48:33Z"},{"alias_kind":"pith_short_12","alias_value":"NQML4TQZQKCB","created_at":"2026-07-05T03:48:33Z"},{"alias_kind":"pith_short_16","alias_value":"NQML4TQZQKCBMV6M","created_at":"2026-07-05T03:48:33Z"},{"alias_kind":"pith_short_8","alias_value":"NQML4TQZ","created_at":"2026-07-05T03:48:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NQML4TQZQKCBMV6MTARCRWQW2T","target":"record","payload":{"canonical_record":{"source":{"id":"2201.05539","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-01-14T16:19:01Z","cross_cats_sorted":[],"title_canon_sha256":"9a98436d13e14427403741ea4fb871a4efddc77248f9e72ceb2f685db69b99d5","abstract_canon_sha256":"8bd7996617f7a810f58086b8b9b1784ca52f73ea3395f3a28773f1282f424b82"},"schema_version":"1.0"},"canonical_sha256":"6c18be4e1982841657cc982228da16d4f588dfe2fc3f4e0ffd5daa044110305b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:48:33.445850Z","signature_b64":"JDm14DGng3eTS3UJytUza8MCWdPMUPLQXc9jv8KiNtqeTzGYgypPqetGGD/I/6/eKpA9Bo5JqLkk0r4cAzzpCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c18be4e1982841657cc982228da16d4f588dfe2fc3f4e0ffd5daa044110305b","last_reissued_at":"2026-07-05T03:48:33.445504Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:48:33.445504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2201.05539","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":"2026-07-05T03:48:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Ob7tRcYx2sQ7b2vtoaGV39lUTjsmHa4lr5RgfL8qiAsF6i7JpblmpORKYkYbw4q5KUdCKvY38sdl7xWT3DTDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T07:30:09.645946Z"},"content_sha256":"b8c1168d6d3ede56786238fcbb14c72cd85f826bb9071fc650e41744e61052fd","schema_version":"1.0","event_id":"sha256:b8c1168d6d3ede56786238fcbb14c72cd85f826bb9071fc650e41744e61052fd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NQML4TQZQKCBMV6MTARCRWQW2T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper and Lower Bounds for Generalized Wiener Indices on unicyclic graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"\\'Alvaro Mart\\'inez-P\\'erez, os\\'e M. Rodr\\'iguez","submitted_at":"2022-01-14T16:19:01Z","abstract_excerpt":"The aim of this paper is to obtain new inequalities for a large family of generalizations of the Wiener Index and to characterize the set of extremal graphs with respect to them. Our main results provide upper and lower bounds for these topological indices on unicyclic graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.05539","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.05539/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":"2026-07-05T03:48:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Rxsqs6xu6mLyqOYujizPR/sR2NIDoI7qhaDx4ivU36sTPgZQEOvvYLGqAsTqhOMMVS23GJNZreMfPaC13wlBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T07:30:09.648991Z"},"content_sha256":"f298816734862a04aed7ff38a00daf96ff26ff0ee88af8d4a93efc81ffc85387","schema_version":"1.0","event_id":"sha256:f298816734862a04aed7ff38a00daf96ff26ff0ee88af8d4a93efc81ffc85387"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQML4TQZQKCBMV6MTARCRWQW2T/bundle.json","state_url":"https://pith.science/pith/NQML4TQZQKCBMV6MTARCRWQW2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQML4TQZQKCBMV6MTARCRWQW2T/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":"2026-08-14T07:30:09Z","links":{"resolver":"https://pith.science/pith/NQML4TQZQKCBMV6MTARCRWQW2T","bundle":"https://pith.science/pith/NQML4TQZQKCBMV6MTARCRWQW2T/bundle.json","state":"https://pith.science/pith/NQML4TQZQKCBMV6MTARCRWQW2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQML4TQZQKCBMV6MTARCRWQW2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NQML4TQZQKCBMV6MTARCRWQW2T","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":"8bd7996617f7a810f58086b8b9b1784ca52f73ea3395f3a28773f1282f424b82","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-01-14T16:19:01Z","title_canon_sha256":"9a98436d13e14427403741ea4fb871a4efddc77248f9e72ceb2f685db69b99d5"},"schema_version":"1.0","source":{"id":"2201.05539","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2201.05539","created_at":"2026-07-05T03:48:33Z"},{"alias_kind":"arxiv_version","alias_value":"2201.05539v1","created_at":"2026-07-05T03:48:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2201.05539","created_at":"2026-07-05T03:48:33Z"},{"alias_kind":"pith_short_12","alias_value":"NQML4TQZQKCB","created_at":"2026-07-05T03:48:33Z"},{"alias_kind":"pith_short_16","alias_value":"NQML4TQZQKCBMV6M","created_at":"2026-07-05T03:48:33Z"},{"alias_kind":"pith_short_8","alias_value":"NQML4TQZ","created_at":"2026-07-05T03:48:33Z"}],"graph_snapshots":[{"event_id":"sha256:f298816734862a04aed7ff38a00daf96ff26ff0ee88af8d4a93efc81ffc85387","target":"graph","created_at":"2026-07-05T03:48:33Z","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/2201.05539/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The aim of this paper is to obtain new inequalities for a large family of generalizations of the Wiener Index and to characterize the set of extremal graphs with respect to them. Our main results provide upper and lower bounds for these topological indices on unicyclic graphs.","authors_text":"\\'Alvaro Mart\\'inez-P\\'erez, os\\'e M. Rodr\\'iguez","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-01-14T16:19:01Z","title":"Upper and Lower Bounds for Generalized Wiener Indices on unicyclic graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.05539","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:b8c1168d6d3ede56786238fcbb14c72cd85f826bb9071fc650e41744e61052fd","target":"record","created_at":"2026-07-05T03:48:33Z","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":"8bd7996617f7a810f58086b8b9b1784ca52f73ea3395f3a28773f1282f424b82","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2022-01-14T16:19:01Z","title_canon_sha256":"9a98436d13e14427403741ea4fb871a4efddc77248f9e72ceb2f685db69b99d5"},"schema_version":"1.0","source":{"id":"2201.05539","kind":"arxiv","version":1}},"canonical_sha256":"6c18be4e1982841657cc982228da16d4f588dfe2fc3f4e0ffd5daa044110305b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c18be4e1982841657cc982228da16d4f588dfe2fc3f4e0ffd5daa044110305b","first_computed_at":"2026-07-05T03:48:33.445504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:48:33.445504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JDm14DGng3eTS3UJytUza8MCWdPMUPLQXc9jv8KiNtqeTzGYgypPqetGGD/I/6/eKpA9Bo5JqLkk0r4cAzzpCg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:48:33.445850Z","signed_message":"canonical_sha256_bytes"},"source_id":"2201.05539","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8c1168d6d3ede56786238fcbb14c72cd85f826bb9071fc650e41744e61052fd","sha256:f298816734862a04aed7ff38a00daf96ff26ff0ee88af8d4a93efc81ffc85387"],"state_sha256":"1942e93db47f839f47f7a0f9fe748a79f8f2ee609f1b251f778983f4bcc360f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J5+EAo8RK8dZVglBxFMX/p/dGGbbfpq99gGaKmPqfCVKZPuLes985dKInMwzlgz7t0JV309S8teB+2eY1z7uBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T07:30:09.666364Z","bundle_sha256":"269defc77659fd7f81cb9850c411b53d8638d9937fce476c21d777f78cf2b1b5"}}