{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RUBAE4GN77G7M27R3CF2XUPE2R","short_pith_number":"pith:RUBAE4GN","canonical_record":{"source":{"id":"1707.05123","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-17T12:47:39Z","cross_cats_sorted":[],"title_canon_sha256":"8c5459c7098f33e3d20859c368887a604c5fdadc400286d95640adaf3417560c","abstract_canon_sha256":"aeb08e118c269d54754a738784365af2b80d05d0f8c1ced5da3ce722809ddb2c"},"schema_version":"1.0"},"canonical_sha256":"8d020270cdffcdf66bf1d88babd1e4d4793837a3717203565405e9bcd0ebf6bc","source":{"kind":"arxiv","id":"1707.05123","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05123","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05123v3","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05123","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"RUBAE4GN77G7","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RUBAE4GN77G7M27R","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RUBAE4GN","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RUBAE4GN77G7M27R3CF2XUPE2R","target":"record","payload":{"canonical_record":{"source":{"id":"1707.05123","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-17T12:47:39Z","cross_cats_sorted":[],"title_canon_sha256":"8c5459c7098f33e3d20859c368887a604c5fdadc400286d95640adaf3417560c","abstract_canon_sha256":"aeb08e118c269d54754a738784365af2b80d05d0f8c1ced5da3ce722809ddb2c"},"schema_version":"1.0"},"canonical_sha256":"8d020270cdffcdf66bf1d88babd1e4d4793837a3717203565405e9bcd0ebf6bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:04.898926Z","signature_b64":"gfnrV/MNG+9ExBbCSDS8Ly3w0KBNN+XHhMTkapiIJ/6JRfOX0CqVNwFCro3JmR99ntTTD6i6Y/ISDpyMvtbVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d020270cdffcdf66bf1d88babd1e4d4793837a3717203565405e9bcd0ebf6bc","last_reissued_at":"2026-05-17T23:45:04.898412Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:04.898412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.05123","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":"2026-05-17T23:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ya2GXJOOVh+KqXmmnP9UeCiAqS14t8FfS5GvRkzdwo6E13Fk+QVnacNoB+Y3Dng0k+z+/c8Q7RXrIzVCqD1xAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:38:44.988249Z"},"content_sha256":"1dc9c1bb78eff20c42d05d1a20e0c46841cb9cf3cd0d3adb27f733ae768164bd","schema_version":"1.0","event_id":"sha256:1dc9c1bb78eff20c42d05d1a20e0c46841cb9cf3cd0d3adb27f733ae768164bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RUBAE4GN77G7M27R3CF2XUPE2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Purely Combinatorial Algorithms for Approximate Directed Minimum Degree Spanning Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Ran Duan, Tianyi Zhang","submitted_at":"2017-07-17T12:47:39Z","abstract_excerpt":"Given a directed graph $G$ on $n$ vertices with a special vertex $s$, the directed minimum degree spanning tree problem requires computing a incoming spanning tree rooted at $s$ whose maximum tree in-degree is the smallest among all such trees. The problem is known to be NP-hard, since it generalizes the Hamiltonian path problem. The best LP-based polynomial time algorithm can achieve an approximation of $\\Delta^*+2$ [Bansal et al, 2009], where $\\Delta^*$ denotes the optimal maximum tree in-degree. As for purely combinatorial algorithms (algorithms that do not use LP), the best approximation i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05123","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":"2026-05-17T23:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LkIHw1uA01IvRLIr1iKQRSytOq/gUmBYIlQix9/DFNKEf8K6aZspdWbA0i7j+mPQXO9pUn06+4AuYlVs74IlBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:38:44.988902Z"},"content_sha256":"e7394d3cc928f570008230d93d0402866f0e770c6f2c0b0506cb8882fa1aadfd","schema_version":"1.0","event_id":"sha256:e7394d3cc928f570008230d93d0402866f0e770c6f2c0b0506cb8882fa1aadfd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUBAE4GN77G7M27R3CF2XUPE2R/bundle.json","state_url":"https://pith.science/pith/RUBAE4GN77G7M27R3CF2XUPE2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUBAE4GN77G7M27R3CF2XUPE2R/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":"2026-05-27T11:38:44Z","links":{"resolver":"https://pith.science/pith/RUBAE4GN77G7M27R3CF2XUPE2R","bundle":"https://pith.science/pith/RUBAE4GN77G7M27R3CF2XUPE2R/bundle.json","state":"https://pith.science/pith/RUBAE4GN77G7M27R3CF2XUPE2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUBAE4GN77G7M27R3CF2XUPE2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RUBAE4GN77G7M27R3CF2XUPE2R","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":"aeb08e118c269d54754a738784365af2b80d05d0f8c1ced5da3ce722809ddb2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-17T12:47:39Z","title_canon_sha256":"8c5459c7098f33e3d20859c368887a604c5fdadc400286d95640adaf3417560c"},"schema_version":"1.0","source":{"id":"1707.05123","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.05123","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1707.05123v3","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.05123","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"RUBAE4GN77G7","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RUBAE4GN77G7M27R","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RUBAE4GN","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:e7394d3cc928f570008230d93d0402866f0e770c6f2c0b0506cb8882fa1aadfd","target":"graph","created_at":"2026-05-17T23:45:04Z","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":"Given a directed graph $G$ on $n$ vertices with a special vertex $s$, the directed minimum degree spanning tree problem requires computing a incoming spanning tree rooted at $s$ whose maximum tree in-degree is the smallest among all such trees. The problem is known to be NP-hard, since it generalizes the Hamiltonian path problem. The best LP-based polynomial time algorithm can achieve an approximation of $\\Delta^*+2$ [Bansal et al, 2009], where $\\Delta^*$ denotes the optimal maximum tree in-degree. As for purely combinatorial algorithms (algorithms that do not use LP), the best approximation i","authors_text":"Ran Duan, Tianyi Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-17T12:47:39Z","title":"Purely Combinatorial Algorithms for Approximate Directed Minimum Degree Spanning Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05123","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":"sha256:1dc9c1bb78eff20c42d05d1a20e0c46841cb9cf3cd0d3adb27f733ae768164bd","target":"record","created_at":"2026-05-17T23:45:04Z","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":"aeb08e118c269d54754a738784365af2b80d05d0f8c1ced5da3ce722809ddb2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-07-17T12:47:39Z","title_canon_sha256":"8c5459c7098f33e3d20859c368887a604c5fdadc400286d95640adaf3417560c"},"schema_version":"1.0","source":{"id":"1707.05123","kind":"arxiv","version":3}},"canonical_sha256":"8d020270cdffcdf66bf1d88babd1e4d4793837a3717203565405e9bcd0ebf6bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d020270cdffcdf66bf1d88babd1e4d4793837a3717203565405e9bcd0ebf6bc","first_computed_at":"2026-05-17T23:45:04.898412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:04.898412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gfnrV/MNG+9ExBbCSDS8Ly3w0KBNN+XHhMTkapiIJ/6JRfOX0CqVNwFCro3JmR99ntTTD6i6Y/ISDpyMvtbVCg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:04.898926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.05123","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dc9c1bb78eff20c42d05d1a20e0c46841cb9cf3cd0d3adb27f733ae768164bd","sha256:e7394d3cc928f570008230d93d0402866f0e770c6f2c0b0506cb8882fa1aadfd"],"state_sha256":"a604f77e4749314011cfd97170dc225197d3dc8410ed49ff8f897b5d9b4604ab"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qyoH1ak+Ahn3xe1s+cMyR/t/RJmLct3UdUQtfk88hdy8G+kZKL5f32f5owN4NEUo/gjnr86aJpX56T+Pcp2MAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:38:44.991463Z","bundle_sha256":"439b2da91d4ca9d54476da0b6c0308c48485ac2177f1576298d581413cab1cf3"}}