{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:GNPCCDTIEOJ5FLQCCZMCPB5FSP","short_pith_number":"pith:GNPCCDTI","canonical_record":{"source":{"id":"1705.01199","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-02T23:13:28Z","cross_cats_sorted":[],"title_canon_sha256":"2b3484f733c82173a93621666165d6a760ceedeeb439792996825974f5954c8d","abstract_canon_sha256":"f7cf1f1ff86e9b962c349fddcce7b4043251efca6470e56030bb1ce3db10f155"},"schema_version":"1.0"},"canonical_sha256":"335e210e682393d2ae0216582787a593c861a61cf372aeb74c7421d911f48b98","source":{"kind":"arxiv","id":"1705.01199","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01199","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01199v3","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01199","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"pith_short_12","alias_value":"GNPCCDTIEOJ5","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GNPCCDTIEOJ5FLQC","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GNPCCDTI","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:GNPCCDTIEOJ5FLQCCZMCPB5FSP","target":"record","payload":{"canonical_record":{"source":{"id":"1705.01199","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-02T23:13:28Z","cross_cats_sorted":[],"title_canon_sha256":"2b3484f733c82173a93621666165d6a760ceedeeb439792996825974f5954c8d","abstract_canon_sha256":"f7cf1f1ff86e9b962c349fddcce7b4043251efca6470e56030bb1ce3db10f155"},"schema_version":"1.0"},"canonical_sha256":"335e210e682393d2ae0216582787a593c861a61cf372aeb74c7421d911f48b98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:51.671668Z","signature_b64":"kclOg+wHTbohgNbiZe/0VeDTXB9GLqmNAuzUvDphB/9CWKFPcrgn16bL8iOMwRAHEezKBsmJt5RL++GHcz1kDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"335e210e682393d2ae0216582787a593c861a61cf372aeb74c7421d911f48b98","last_reissued_at":"2026-05-18T00:29:51.671048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:51.671048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.01199","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:29:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gsfb1+je9X24HDh1J1lykCT8E5iXPQVVDLbxL5Q70XrzO4KT9Z56bsWBPX4vw61OHq3/h35q6N6/y58QyxQRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:20:17.198294Z"},"content_sha256":"b7a66803f7cb1575146721009e28ed5c25f4acbd22d67339786f1e0d8fc6869b","schema_version":"1.0","event_id":"sha256:b7a66803f7cb1575146721009e28ed5c25f4acbd22d67339786f1e0d8fc6869b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:GNPCCDTIEOJ5FLQCCZMCPB5FSP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Four Edge-Independent Spanning Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Hoyer, Robin Thomas","submitted_at":"2017-05-02T23:13:28Z","abstract_excerpt":"We prove an ear-decomposition theorem for $4$-edge-connected graphs and use it to prove that for every $4$-edge-connected graph $G$ and every $r\\in V(G)$, there is a set of four spanning trees of $G$ with the following property. For every vertex in $G$, the unique paths back to $r$ in each tree are edge-disjoint. Our proof implies a polynomial-time algorithm for constructing the trees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01199","kind":"arxiv","version":3},"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":"2026-05-18T00:29:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UpJoclfPVofJGVMzdMEZHIkxEK0SK61zUhjYFZ3w80dmXL4dP/Y65HT829HvxYw1xUh2uwraf7G1h5QbIW/CBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T02:20:17.198966Z"},"content_sha256":"7afaeb01f557466b30693f99c0e008d9a82abd2b2cd6c2f6989fc4418e97a268","schema_version":"1.0","event_id":"sha256:7afaeb01f557466b30693f99c0e008d9a82abd2b2cd6c2f6989fc4418e97a268"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GNPCCDTIEOJ5FLQCCZMCPB5FSP/bundle.json","state_url":"https://pith.science/pith/GNPCCDTIEOJ5FLQCCZMCPB5FSP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GNPCCDTIEOJ5FLQCCZMCPB5FSP/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":"2026-06-12T02:20:17Z","links":{"resolver":"https://pith.science/pith/GNPCCDTIEOJ5FLQCCZMCPB5FSP","bundle":"https://pith.science/pith/GNPCCDTIEOJ5FLQCCZMCPB5FSP/bundle.json","state":"https://pith.science/pith/GNPCCDTIEOJ5FLQCCZMCPB5FSP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GNPCCDTIEOJ5FLQCCZMCPB5FSP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GNPCCDTIEOJ5FLQCCZMCPB5FSP","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":"f7cf1f1ff86e9b962c349fddcce7b4043251efca6470e56030bb1ce3db10f155","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-02T23:13:28Z","title_canon_sha256":"2b3484f733c82173a93621666165d6a760ceedeeb439792996825974f5954c8d"},"schema_version":"1.0","source":{"id":"1705.01199","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01199","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01199v3","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01199","created_at":"2026-05-18T00:29:51Z"},{"alias_kind":"pith_short_12","alias_value":"GNPCCDTIEOJ5","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"GNPCCDTIEOJ5FLQC","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"GNPCCDTI","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:7afaeb01f557466b30693f99c0e008d9a82abd2b2cd6c2f6989fc4418e97a268","target":"graph","created_at":"2026-05-18T00:29:51Z","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 an ear-decomposition theorem for $4$-edge-connected graphs and use it to prove that for every $4$-edge-connected graph $G$ and every $r\\in V(G)$, there is a set of four spanning trees of $G$ with the following property. For every vertex in $G$, the unique paths back to $r$ in each tree are edge-disjoint. Our proof implies a polynomial-time algorithm for constructing the trees.","authors_text":"Alexander Hoyer, Robin Thomas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-02T23:13:28Z","title":"Four Edge-Independent Spanning Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01199","kind":"arxiv","version":3},"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:b7a66803f7cb1575146721009e28ed5c25f4acbd22d67339786f1e0d8fc6869b","target":"record","created_at":"2026-05-18T00:29:51Z","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":"f7cf1f1ff86e9b962c349fddcce7b4043251efca6470e56030bb1ce3db10f155","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-02T23:13:28Z","title_canon_sha256":"2b3484f733c82173a93621666165d6a760ceedeeb439792996825974f5954c8d"},"schema_version":"1.0","source":{"id":"1705.01199","kind":"arxiv","version":3}},"canonical_sha256":"335e210e682393d2ae0216582787a593c861a61cf372aeb74c7421d911f48b98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"335e210e682393d2ae0216582787a593c861a61cf372aeb74c7421d911f48b98","first_computed_at":"2026-05-18T00:29:51.671048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:51.671048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kclOg+wHTbohgNbiZe/0VeDTXB9GLqmNAuzUvDphB/9CWKFPcrgn16bL8iOMwRAHEezKBsmJt5RL++GHcz1kDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:51.671668Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01199","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7a66803f7cb1575146721009e28ed5c25f4acbd22d67339786f1e0d8fc6869b","sha256:7afaeb01f557466b30693f99c0e008d9a82abd2b2cd6c2f6989fc4418e97a268"],"state_sha256":"0b55c42bed083cd06182d890a0e81a399e41edf4eda7caa8ffb1a25374424ba7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1bTGCeNZ9MHFdxQuyy+xURMlLLOgSxOB/RdreIt43+6RUwdeajNVZhqc00sPFLtQQkjK/vH4q+0nvm2Jc4naDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T02:20:17.202513Z","bundle_sha256":"8aad0bdfb91d068ff3dabb55329e95d6b7a3477584316240db5c5df21eb0c62d"}}