{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:6LFTBQMQAUIYEA4OU34POPVKLJ","short_pith_number":"pith:6LFTBQMQ","canonical_record":{"source":{"id":"2208.01984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-03T11:27:59Z","cross_cats_sorted":[],"title_canon_sha256":"9c16f2d50b8ec5352c0be190df0cee13d3228d1171bc733df22b300ce8d07740","abstract_canon_sha256":"1edd158e4cc6b13f1fbfc5a7634af4c5cf601e8c86dc885bf006f6c7279a1471"},"schema_version":"1.0"},"canonical_sha256":"f2cb30c190051182038ea6f8f73eaa5a54236b088fbac8faceefa8c786785f00","source":{"kind":"arxiv","id":"2208.01984","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.01984","created_at":"2026-07-05T04:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"2208.01984v1","created_at":"2026-07-05T04:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.01984","created_at":"2026-07-05T04:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"6LFTBQMQAUIY","created_at":"2026-07-05T04:45:52Z"},{"alias_kind":"pith_short_16","alias_value":"6LFTBQMQAUIYEA4O","created_at":"2026-07-05T04:45:52Z"},{"alias_kind":"pith_short_8","alias_value":"6LFTBQMQ","created_at":"2026-07-05T04:45:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:6LFTBQMQAUIYEA4OU34POPVKLJ","target":"record","payload":{"canonical_record":{"source":{"id":"2208.01984","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-03T11:27:59Z","cross_cats_sorted":[],"title_canon_sha256":"9c16f2d50b8ec5352c0be190df0cee13d3228d1171bc733df22b300ce8d07740","abstract_canon_sha256":"1edd158e4cc6b13f1fbfc5a7634af4c5cf601e8c86dc885bf006f6c7279a1471"},"schema_version":"1.0"},"canonical_sha256":"f2cb30c190051182038ea6f8f73eaa5a54236b088fbac8faceefa8c786785f00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:45:52.261170Z","signature_b64":"Qy27XzY28RkINBKtqLSG841CoeY3TSm+50kYZFUqUNT3tymzE/nlL6EILFy49h9p2PftRjZuriApD+Y3nnisCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2cb30c190051182038ea6f8f73eaa5a54236b088fbac8faceefa8c786785f00","last_reissued_at":"2026-07-05T04:45:52.260769Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:45:52.260769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2208.01984","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":"2026-07-05T04:45:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JmYr93pZIZGXYWxhmzYhbiKuavlUvLp9eAuK9i1+BmCFVkM9AaJlBe9V0mkN6uWLtRxVGEo7Pg6vXiDhuIgyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T02:43:09.579762Z"},"content_sha256":"bff22f16cc9d964a887dc04687ab7511e04bd7b51fce4915e02063bbcc4853cf","schema_version":"1.0","event_id":"sha256:bff22f16cc9d964a887dc04687ab7511e04bd7b51fce4915e02063bbcc4853cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:6LFTBQMQAUIYEA4OU34POPVKLJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Disproof of a conjecture on the minimum Wiener index of signed trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chuanming Wang, Songlin Guo, Wei Wang","submitted_at":"2022-08-03T11:27:59Z","abstract_excerpt":"The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices. Sam Spiro [The Wiener index of signed graphs, Appl. Math. Comput., 416(2022)126755] recently introduced the Wiener index for a signed graph and conjectured that the path $P_n$ with alternating signs has the minimum Wiener index among all signed trees with $n$ vertices. By constructing an infinite family of counterexamples, we prove that the conjecture is false whenever $n$ is at least 30."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.01984","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/2208.01984/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":"2026-07-05T04:45:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Lxt4jXx8pYlqF9Wv+2XB/tmEhiM1SB6Ti9F1xdkrG9PXxl+F0fCcxI7MKbbAL0wdgoAxuuvLA+yC9xlF4G0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T02:43:09.580256Z"},"content_sha256":"c9d46cda17058178a9fee1d1c39d9ac512187d8e88d50dc438b322c318095a48","schema_version":"1.0","event_id":"sha256:c9d46cda17058178a9fee1d1c39d9ac512187d8e88d50dc438b322c318095a48"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6LFTBQMQAUIYEA4OU34POPVKLJ/bundle.json","state_url":"https://pith.science/pith/6LFTBQMQAUIYEA4OU34POPVKLJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6LFTBQMQAUIYEA4OU34POPVKLJ/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":"2026-08-22T02:43:09Z","links":{"resolver":"https://pith.science/pith/6LFTBQMQAUIYEA4OU34POPVKLJ","bundle":"https://pith.science/pith/6LFTBQMQAUIYEA4OU34POPVKLJ/bundle.json","state":"https://pith.science/pith/6LFTBQMQAUIYEA4OU34POPVKLJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6LFTBQMQAUIYEA4OU34POPVKLJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:6LFTBQMQAUIYEA4OU34POPVKLJ","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":"1edd158e4cc6b13f1fbfc5a7634af4c5cf601e8c86dc885bf006f6c7279a1471","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-03T11:27:59Z","title_canon_sha256":"9c16f2d50b8ec5352c0be190df0cee13d3228d1171bc733df22b300ce8d07740"},"schema_version":"1.0","source":{"id":"2208.01984","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.01984","created_at":"2026-07-05T04:45:52Z"},{"alias_kind":"arxiv_version","alias_value":"2208.01984v1","created_at":"2026-07-05T04:45:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.01984","created_at":"2026-07-05T04:45:52Z"},{"alias_kind":"pith_short_12","alias_value":"6LFTBQMQAUIY","created_at":"2026-07-05T04:45:52Z"},{"alias_kind":"pith_short_16","alias_value":"6LFTBQMQAUIYEA4O","created_at":"2026-07-05T04:45:52Z"},{"alias_kind":"pith_short_8","alias_value":"6LFTBQMQ","created_at":"2026-07-05T04:45:52Z"}],"graph_snapshots":[{"event_id":"sha256:c9d46cda17058178a9fee1d1c39d9ac512187d8e88d50dc438b322c318095a48","target":"graph","created_at":"2026-07-05T04:45:52Z","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/2208.01984/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Wiener index of a connected graph is the sum of distances between all unordered pairs of vertices. Sam Spiro [The Wiener index of signed graphs, Appl. Math. Comput., 416(2022)126755] recently introduced the Wiener index for a signed graph and conjectured that the path $P_n$ with alternating signs has the minimum Wiener index among all signed trees with $n$ vertices. By constructing an infinite family of counterexamples, we prove that the conjecture is false whenever $n$ is at least 30.","authors_text":"Chuanming Wang, Songlin Guo, Wei Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-03T11:27:59Z","title":"Disproof of a conjecture on the minimum Wiener index of signed trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.01984","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:bff22f16cc9d964a887dc04687ab7511e04bd7b51fce4915e02063bbcc4853cf","target":"record","created_at":"2026-07-05T04:45:52Z","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":"1edd158e4cc6b13f1fbfc5a7634af4c5cf601e8c86dc885bf006f6c7279a1471","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-08-03T11:27:59Z","title_canon_sha256":"9c16f2d50b8ec5352c0be190df0cee13d3228d1171bc733df22b300ce8d07740"},"schema_version":"1.0","source":{"id":"2208.01984","kind":"arxiv","version":1}},"canonical_sha256":"f2cb30c190051182038ea6f8f73eaa5a54236b088fbac8faceefa8c786785f00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2cb30c190051182038ea6f8f73eaa5a54236b088fbac8faceefa8c786785f00","first_computed_at":"2026-07-05T04:45:52.260769Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:45:52.260769Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qy27XzY28RkINBKtqLSG841CoeY3TSm+50kYZFUqUNT3tymzE/nlL6EILFy49h9p2PftRjZuriApD+Y3nnisCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:45:52.261170Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.01984","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bff22f16cc9d964a887dc04687ab7511e04bd7b51fce4915e02063bbcc4853cf","sha256:c9d46cda17058178a9fee1d1c39d9ac512187d8e88d50dc438b322c318095a48"],"state_sha256":"9b76b70506f3b6bab069f08b91361c2ffda5b0da3a4925de3e4414303472804e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o5Q6xWc/qOa8y/1xpE0prRLFRIyS1EubakkApOSJQgOy6wDu/Vb45HcTdKHA3bTdb11TJPPP/tGM0JELveSRAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T02:43:09.584919Z","bundle_sha256":"7ee1fc09553a23740c6ebbf33d1e9cd2fedef0bb618be47d0e05b71421de5330"}}