{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OIORXHNPEZRVZLS4RPSVSK4DSS","short_pith_number":"pith:OIORXHNP","canonical_record":{"source":{"id":"1111.5473","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-23T12:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"576bbe43271a296e94a9ba5f32253d0c844633308d2c7ea785c28d938d8e8917","abstract_canon_sha256":"4e4b8c720f535f240827ee2fa8519ed1b0827804dba72291a19f1d80af499630"},"schema_version":"1.0"},"canonical_sha256":"721d1b9daf26635cae5c8be5592b8394a656e2ab6a1094cebce862284362181c","source":{"kind":"arxiv","id":"1111.5473","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5473","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5473v2","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5473","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"OIORXHNPEZRV","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OIORXHNPEZRVZLS4","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OIORXHNP","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OIORXHNPEZRVZLS4RPSVSK4DSS","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5473","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-23T12:21:33Z","cross_cats_sorted":[],"title_canon_sha256":"576bbe43271a296e94a9ba5f32253d0c844633308d2c7ea785c28d938d8e8917","abstract_canon_sha256":"4e4b8c720f535f240827ee2fa8519ed1b0827804dba72291a19f1d80af499630"},"schema_version":"1.0"},"canonical_sha256":"721d1b9daf26635cae5c8be5592b8394a656e2ab6a1094cebce862284362181c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:44.971503Z","signature_b64":"rBaQ/+xoTEHklUO8ybqSzWk0horHF65rckHhdif/uBz98Ta9SrDHr/E+ZsedgzMiWpiu7o+cmP2R3Q4CQIZyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"721d1b9daf26635cae5c8be5592b8394a656e2ab6a1094cebce862284362181c","last_reissued_at":"2026-05-18T03:53:44.970789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:44.970789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5473","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:53:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dNepz74V5SIcArd0Ph/y4BOQPn1YaZ9qLhVBI/QbHgNHBhL1kVAoBbt3FuVwtgz20zZ5TI2+3HPCCaGkwuRQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:41:16.417377Z"},"content_sha256":"cbd4c87a07704b3e2c53ec3af8e1a1bdac7a5f69934c82b95c97631dec6c6dba","schema_version":"1.0","event_id":"sha256:cbd4c87a07704b3e2c53ec3af8e1a1bdac7a5f69934c82b95c97631dec6c6dba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OIORXHNPEZRVZLS4RPSVSK4DSS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Directed Steiner Tree and the Lasserre Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Thomas Rothvo{\\ss}","submitted_at":"2011-11-23T12:21:33Z","abstract_excerpt":"The goal for the Directed Steiner Tree problem is to find a minimum cost tree in a directed graph G=(V,E) that connects all terminals X to a given root r. It is well known that modulo a logarithmic factor it suffices to consider acyclic graphs where the nodes are arranged in L <= log |X| levels. Unfortunately the natural LP formulation has a |X|^(1/2) integrality gap already for 5 levels. We show that for every L, the O(L)-round Lasserre Strengthening of this LP has integrality gap O(L log |X|). This provides a polynomial time |X|^{epsilon}-approximation and a O(log^3 |X|) approximation in O(n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5473","kind":"arxiv","version":2},"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":"2026-05-18T03:53:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"73FGFTKylEy5mnlOCgGJdMjO3pzWCx46vJM0L2jKh1DlELNoj2mFhAJYWivlVO3JppLQqB73uO55RaIkm4pbDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T19:41:16.418085Z"},"content_sha256":"76c98cc71ea3f18aeec1be41551c1ad7ffd4f5fcd4d3df9aed230572956dff56","schema_version":"1.0","event_id":"sha256:76c98cc71ea3f18aeec1be41551c1ad7ffd4f5fcd4d3df9aed230572956dff56"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OIORXHNPEZRVZLS4RPSVSK4DSS/bundle.json","state_url":"https://pith.science/pith/OIORXHNPEZRVZLS4RPSVSK4DSS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OIORXHNPEZRVZLS4RPSVSK4DSS/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":"2026-06-08T19:41:16Z","links":{"resolver":"https://pith.science/pith/OIORXHNPEZRVZLS4RPSVSK4DSS","bundle":"https://pith.science/pith/OIORXHNPEZRVZLS4RPSVSK4DSS/bundle.json","state":"https://pith.science/pith/OIORXHNPEZRVZLS4RPSVSK4DSS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OIORXHNPEZRVZLS4RPSVSK4DSS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OIORXHNPEZRVZLS4RPSVSK4DSS","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":"4e4b8c720f535f240827ee2fa8519ed1b0827804dba72291a19f1d80af499630","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-23T12:21:33Z","title_canon_sha256":"576bbe43271a296e94a9ba5f32253d0c844633308d2c7ea785c28d938d8e8917"},"schema_version":"1.0","source":{"id":"1111.5473","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5473","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5473v2","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5473","created_at":"2026-05-18T03:53:44Z"},{"alias_kind":"pith_short_12","alias_value":"OIORXHNPEZRV","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OIORXHNPEZRVZLS4","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OIORXHNP","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:76c98cc71ea3f18aeec1be41551c1ad7ffd4f5fcd4d3df9aed230572956dff56","target":"graph","created_at":"2026-05-18T03:53:44Z","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":"The goal for the Directed Steiner Tree problem is to find a minimum cost tree in a directed graph G=(V,E) that connects all terminals X to a given root r. It is well known that modulo a logarithmic factor it suffices to consider acyclic graphs where the nodes are arranged in L <= log |X| levels. Unfortunately the natural LP formulation has a |X|^(1/2) integrality gap already for 5 levels. We show that for every L, the O(L)-round Lasserre Strengthening of this LP has integrality gap O(L log |X|). This provides a polynomial time |X|^{epsilon}-approximation and a O(log^3 |X|) approximation in O(n","authors_text":"Thomas Rothvo{\\ss}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-23T12:21:33Z","title":"Directed Steiner Tree and the Lasserre Hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5473","kind":"arxiv","version":2},"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:cbd4c87a07704b3e2c53ec3af8e1a1bdac7a5f69934c82b95c97631dec6c6dba","target":"record","created_at":"2026-05-18T03:53:44Z","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":"4e4b8c720f535f240827ee2fa8519ed1b0827804dba72291a19f1d80af499630","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-23T12:21:33Z","title_canon_sha256":"576bbe43271a296e94a9ba5f32253d0c844633308d2c7ea785c28d938d8e8917"},"schema_version":"1.0","source":{"id":"1111.5473","kind":"arxiv","version":2}},"canonical_sha256":"721d1b9daf26635cae5c8be5592b8394a656e2ab6a1094cebce862284362181c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"721d1b9daf26635cae5c8be5592b8394a656e2ab6a1094cebce862284362181c","first_computed_at":"2026-05-18T03:53:44.970789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:44.970789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rBaQ/+xoTEHklUO8ybqSzWk0horHF65rckHhdif/uBz98Ta9SrDHr/E+ZsedgzMiWpiu7o+cmP2R3Q4CQIZyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:44.971503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5473","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbd4c87a07704b3e2c53ec3af8e1a1bdac7a5f69934c82b95c97631dec6c6dba","sha256:76c98cc71ea3f18aeec1be41551c1ad7ffd4f5fcd4d3df9aed230572956dff56"],"state_sha256":"4a8afc0ee37bad96f3778d4c741955c23bd98592c3b24c8824d93fb14a7f7b0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Eqk967/QQLckZwhEDQrJfLLQ1wNdtDdrNoItjqUF5Uo2IHItpWVl0lHU5nC03nfFjc738UQu4nGxF+70qHpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T19:41:16.422474Z","bundle_sha256":"fc3b29e11b5c93b688873a3c3ead0c832fa778f68308fd8880155f00107481bd"}}