{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AGBGBSPIQG5FS5IL63EEBW5JIB","short_pith_number":"pith:AGBGBSPI","canonical_record":{"source":{"id":"1612.03372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-11T05:04:53Z","cross_cats_sorted":[],"title_canon_sha256":"991c1e3ee97a8aec4c26a354706346a48f4d9a854b937b068a9608bbbde3e566","abstract_canon_sha256":"50c476fa88473a95a76f1ca2abbdb62e5cc1f6620a45ac1fe261594d4261b329"},"schema_version":"1.0"},"canonical_sha256":"018260c9e881ba59750bf6c840dba94075e9bc88b3eea4dd5e979676f385b22b","source":{"kind":"arxiv","id":"1612.03372","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03372","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03372v1","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03372","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"pith_short_12","alias_value":"AGBGBSPIQG5F","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AGBGBSPIQG5FS5IL","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AGBGBSPI","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AGBGBSPIQG5FS5IL63EEBW5JIB","target":"record","payload":{"canonical_record":{"source":{"id":"1612.03372","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-11T05:04:53Z","cross_cats_sorted":[],"title_canon_sha256":"991c1e3ee97a8aec4c26a354706346a48f4d9a854b937b068a9608bbbde3e566","abstract_canon_sha256":"50c476fa88473a95a76f1ca2abbdb62e5cc1f6620a45ac1fe261594d4261b329"},"schema_version":"1.0"},"canonical_sha256":"018260c9e881ba59750bf6c840dba94075e9bc88b3eea4dd5e979676f385b22b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:19.411297Z","signature_b64":"aqaXUCuSC39EfBDetKgID37NTqMjsMzpVR3g9SIJI+kXHxe6cgUi3XkoErbcPSnI8Y4IUXXyHwIwsZRhvUBkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"018260c9e881ba59750bf6c840dba94075e9bc88b3eea4dd5e979676f385b22b","last_reissued_at":"2026-05-18T00:55:19.410557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:19.410557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.03372","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":"2026-05-18T00:55:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYM4iaXlJk11saAp7EUAh2yKta6n5Os9sg2jc3wfMob8VMCGVVocpwtjdE8XdTCINoiXj0coTscSyuFSKwgmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:53:56.703210Z"},"content_sha256":"5ee1bbe116003d7be0adc379a24f35acaf377b7f4548499264389b2a8def5625","schema_version":"1.0","event_id":"sha256:5ee1bbe116003d7be0adc379a24f35acaf377b7f4548499264389b2a8def5625"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AGBGBSPIQG5FS5IL63EEBW5JIB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Jacobian group and complexity of the generalized Petersen graph GP(n,k) through Chebyshev polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"(2) Sobolev Institute of Mathematics, 3, (3) Novosibirsk State University, 4), 4) ((1) Yengnam University, (4) Siberian Federal University, A. D. Mednykh (2, I. A. Mednykh (2, Krasnoyarsk, Novosibirsk, Russia, Russia), South Korea, Yengnam, Y. S. Kwon (1)","submitted_at":"2016-12-11T05:04:53Z","abstract_excerpt":"In the present paper we find a simple algorithm for counting Jacobian group of the generalized Petersen graph GP(n,k). Also, we obtain a closed formula for the number of spanning trees of this graph in terms of Chebyshev polynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03372","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":"2026-05-18T00:55:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xst4bINjIoGGXd7avKTSpZ0gaZSiNaPcTO6C1TYDu30w4rWmZsjjmSJN4vSZjbUSbOBaX2W5zBE61lBtGIheAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T17:53:56.703592Z"},"content_sha256":"d7d7f035faa8ab0f8f8a924d0bdb54ab78ae17c979fbc390d2f50ab6f21aeecb","schema_version":"1.0","event_id":"sha256:d7d7f035faa8ab0f8f8a924d0bdb54ab78ae17c979fbc390d2f50ab6f21aeecb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AGBGBSPIQG5FS5IL63EEBW5JIB/bundle.json","state_url":"https://pith.science/pith/AGBGBSPIQG5FS5IL63EEBW5JIB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AGBGBSPIQG5FS5IL63EEBW5JIB/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":"2026-05-29T17:53:56Z","links":{"resolver":"https://pith.science/pith/AGBGBSPIQG5FS5IL63EEBW5JIB","bundle":"https://pith.science/pith/AGBGBSPIQG5FS5IL63EEBW5JIB/bundle.json","state":"https://pith.science/pith/AGBGBSPIQG5FS5IL63EEBW5JIB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AGBGBSPIQG5FS5IL63EEBW5JIB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AGBGBSPIQG5FS5IL63EEBW5JIB","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":"50c476fa88473a95a76f1ca2abbdb62e5cc1f6620a45ac1fe261594d4261b329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-11T05:04:53Z","title_canon_sha256":"991c1e3ee97a8aec4c26a354706346a48f4d9a854b937b068a9608bbbde3e566"},"schema_version":"1.0","source":{"id":"1612.03372","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03372","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03372v1","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03372","created_at":"2026-05-18T00:55:19Z"},{"alias_kind":"pith_short_12","alias_value":"AGBGBSPIQG5F","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AGBGBSPIQG5FS5IL","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AGBGBSPI","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:d7d7f035faa8ab0f8f8a924d0bdb54ab78ae17c979fbc390d2f50ab6f21aeecb","target":"graph","created_at":"2026-05-18T00:55:19Z","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":"In the present paper we find a simple algorithm for counting Jacobian group of the generalized Petersen graph GP(n,k). Also, we obtain a closed formula for the number of spanning trees of this graph in terms of Chebyshev polynomials.","authors_text":"(2) Sobolev Institute of Mathematics, 3, (3) Novosibirsk State University, 4), 4) ((1) Yengnam University, (4) Siberian Federal University, A. D. Mednykh (2, I. A. Mednykh (2, Krasnoyarsk, Novosibirsk, Russia, Russia), South Korea, Yengnam, Y. S. Kwon (1)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-11T05:04:53Z","title":"On Jacobian group and complexity of the generalized Petersen graph GP(n,k) through Chebyshev polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03372","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":"sha256:5ee1bbe116003d7be0adc379a24f35acaf377b7f4548499264389b2a8def5625","target":"record","created_at":"2026-05-18T00:55:19Z","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":"50c476fa88473a95a76f1ca2abbdb62e5cc1f6620a45ac1fe261594d4261b329","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-11T05:04:53Z","title_canon_sha256":"991c1e3ee97a8aec4c26a354706346a48f4d9a854b937b068a9608bbbde3e566"},"schema_version":"1.0","source":{"id":"1612.03372","kind":"arxiv","version":1}},"canonical_sha256":"018260c9e881ba59750bf6c840dba94075e9bc88b3eea4dd5e979676f385b22b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"018260c9e881ba59750bf6c840dba94075e9bc88b3eea4dd5e979676f385b22b","first_computed_at":"2026-05-18T00:55:19.410557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:19.410557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aqaXUCuSC39EfBDetKgID37NTqMjsMzpVR3g9SIJI+kXHxe6cgUi3XkoErbcPSnI8Y4IUXXyHwIwsZRhvUBkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:19.411297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03372","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ee1bbe116003d7be0adc379a24f35acaf377b7f4548499264389b2a8def5625","sha256:d7d7f035faa8ab0f8f8a924d0bdb54ab78ae17c979fbc390d2f50ab6f21aeecb"],"state_sha256":"03a9338ad67d927c48b61f1a042a3e0d1acb6d880afef1ca698d4da9bfd459a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QYLJGJvOhwhVyn1TL7vtiA0tDVGiLCMoRPWykVZkwGLdFopWFDlLRs9p/2i3qhZFiSoIGa56SAYqSYksFDA9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T17:53:56.706092Z","bundle_sha256":"1fd165e45fcec0d183432ace12699c155a512347979daa50309c22daf2d8d3ef"}}