{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:6KYZJ3PSAYOKJJAUU23XGAF7ZX","short_pith_number":"pith:6KYZJ3PS","canonical_record":{"source":{"id":"1703.04120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-12T13:56:56Z","cross_cats_sorted":[],"title_canon_sha256":"72b69371bf50fde140f44080b1ed66735bef157bb965a0a6226974b1e9d3e633","abstract_canon_sha256":"1319d61d5f8adb5a7a750b919e9d95311d18bb1796ff352d1a38818f945143f3"},"schema_version":"1.0"},"canonical_sha256":"f2b194edf2061ca4a414a6b77300bfcddb5bf53fa3d6d17161863844383f5679","source":{"kind":"arxiv","id":"1703.04120","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04120","created_at":"2026-05-18T00:48:49Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04120v1","created_at":"2026-05-18T00:48:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04120","created_at":"2026-05-18T00:48:49Z"},{"alias_kind":"pith_short_12","alias_value":"6KYZJ3PSAYOK","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6KYZJ3PSAYOKJJAU","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6KYZJ3PS","created_at":"2026-05-18T12:31:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:6KYZJ3PSAYOKJJAUU23XGAF7ZX","target":"record","payload":{"canonical_record":{"source":{"id":"1703.04120","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-12T13:56:56Z","cross_cats_sorted":[],"title_canon_sha256":"72b69371bf50fde140f44080b1ed66735bef157bb965a0a6226974b1e9d3e633","abstract_canon_sha256":"1319d61d5f8adb5a7a750b919e9d95311d18bb1796ff352d1a38818f945143f3"},"schema_version":"1.0"},"canonical_sha256":"f2b194edf2061ca4a414a6b77300bfcddb5bf53fa3d6d17161863844383f5679","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:49.723483Z","signature_b64":"perPjoOWd3NEFjo5Jy7MD3FWK7tMxL7imkvALNAGbIdxy2V7WC7rT5RxZgib57JmayAToj3HW0FYidgCIx8vDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2b194edf2061ca4a414a6b77300bfcddb5bf53fa3d6d17161863844383f5679","last_reissued_at":"2026-05-18T00:48:49.722682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:49.722682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.04120","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":"2026-05-18T00:48:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UeH5ZxV4Gpf3ta7NvSauPDB1lcB4jtEFRXwxH4OYRhrMWdfJhRzxUy+VsIy3hkVxQbf96AuEkG8EV2C78yh0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:04:02.077611Z"},"content_sha256":"3cf676771f3b8ffa7298668f0606ac260f6d339a98817dc2cdc92768155f1737","schema_version":"1.0","event_id":"sha256:3cf676771f3b8ffa7298668f0606ac260f6d339a98817dc2cdc92768155f1737"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:6KYZJ3PSAYOKJJAUU23XGAF7ZX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Abstract matrix-tree theorem and Bernardi polynomial","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yurii Burman","submitted_at":"2017-03-12T13:56:56Z","abstract_excerpt":"This paper is a continuation of arXiv:1612.03873. We prove a three-parameter family of identities (Theorem 1.1) involving a version of the Tutte polynomial for directed graphs introduced by Awan and Bernardi in arXiv:1610.01839. A particular case of this family (Corollary 1.6) is the higher-degree generalization of the matrix-tree theorem proved in arXiv:1612.03873, which thus receives a new proof, shorter (and less direct) than the original one. The theory has a parallel version for undirected graphs (Theorem 1.2)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04120","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":"2026-05-18T00:48:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ua6o2/WSJl/q0xNZpSrNxRZD4KzT40vveVdEYs5fyvUZTVuJhod2d/nZZCIFYD2f8PSoiks3qAQA7HH/RNRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:04:02.078298Z"},"content_sha256":"8e219e705de130148c18cafe72c6b01c401ed0a4ebe7cba584737fe7d5d4b111","schema_version":"1.0","event_id":"sha256:8e219e705de130148c18cafe72c6b01c401ed0a4ebe7cba584737fe7d5d4b111"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6KYZJ3PSAYOKJJAUU23XGAF7ZX/bundle.json","state_url":"https://pith.science/pith/6KYZJ3PSAYOKJJAUU23XGAF7ZX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6KYZJ3PSAYOKJJAUU23XGAF7ZX/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":"2026-05-26T15:04:02Z","links":{"resolver":"https://pith.science/pith/6KYZJ3PSAYOKJJAUU23XGAF7ZX","bundle":"https://pith.science/pith/6KYZJ3PSAYOKJJAUU23XGAF7ZX/bundle.json","state":"https://pith.science/pith/6KYZJ3PSAYOKJJAUU23XGAF7ZX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6KYZJ3PSAYOKJJAUU23XGAF7ZX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6KYZJ3PSAYOKJJAUU23XGAF7ZX","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":"1319d61d5f8adb5a7a750b919e9d95311d18bb1796ff352d1a38818f945143f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-12T13:56:56Z","title_canon_sha256":"72b69371bf50fde140f44080b1ed66735bef157bb965a0a6226974b1e9d3e633"},"schema_version":"1.0","source":{"id":"1703.04120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04120","created_at":"2026-05-18T00:48:49Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04120v1","created_at":"2026-05-18T00:48:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04120","created_at":"2026-05-18T00:48:49Z"},{"alias_kind":"pith_short_12","alias_value":"6KYZJ3PSAYOK","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6KYZJ3PSAYOKJJAU","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6KYZJ3PS","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:8e219e705de130148c18cafe72c6b01c401ed0a4ebe7cba584737fe7d5d4b111","target":"graph","created_at":"2026-05-18T00:48:49Z","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":"This paper is a continuation of arXiv:1612.03873. We prove a three-parameter family of identities (Theorem 1.1) involving a version of the Tutte polynomial for directed graphs introduced by Awan and Bernardi in arXiv:1610.01839. A particular case of this family (Corollary 1.6) is the higher-degree generalization of the matrix-tree theorem proved in arXiv:1612.03873, which thus receives a new proof, shorter (and less direct) than the original one. The theory has a parallel version for undirected graphs (Theorem 1.2).","authors_text":"Yurii Burman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-12T13:56:56Z","title":"Abstract matrix-tree theorem and Bernardi polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04120","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":"sha256:3cf676771f3b8ffa7298668f0606ac260f6d339a98817dc2cdc92768155f1737","target":"record","created_at":"2026-05-18T00:48:49Z","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":"1319d61d5f8adb5a7a750b919e9d95311d18bb1796ff352d1a38818f945143f3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-12T13:56:56Z","title_canon_sha256":"72b69371bf50fde140f44080b1ed66735bef157bb965a0a6226974b1e9d3e633"},"schema_version":"1.0","source":{"id":"1703.04120","kind":"arxiv","version":1}},"canonical_sha256":"f2b194edf2061ca4a414a6b77300bfcddb5bf53fa3d6d17161863844383f5679","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2b194edf2061ca4a414a6b77300bfcddb5bf53fa3d6d17161863844383f5679","first_computed_at":"2026-05-18T00:48:49.722682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:49.722682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"perPjoOWd3NEFjo5Jy7MD3FWK7tMxL7imkvALNAGbIdxy2V7WC7rT5RxZgib57JmayAToj3HW0FYidgCIx8vDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:49.723483Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cf676771f3b8ffa7298668f0606ac260f6d339a98817dc2cdc92768155f1737","sha256:8e219e705de130148c18cafe72c6b01c401ed0a4ebe7cba584737fe7d5d4b111"],"state_sha256":"b25cee5146696d0febbf3a9b32ace59ed07b8eea20938188406fe5fdeb9efb6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DuUms6QKNAfxw43YsO9DCmKvcvyOc9ek/6P4slBGtiMDvLftsYr1NKKd7gMu6JXOzo/6aF0HxZBaolVrmV4BDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:04:02.081379Z","bundle_sha256":"958d32fde01a779e8506f9bfe8e7c2673d03c48f80ff6a3b4891af2f3e1d7a62"}}