{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CJEMH36LNMG5CVETHGXQLFTFVN","short_pith_number":"pith:CJEMH36L","canonical_record":{"source":{"id":"1802.01242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-05T02:48:36Z","cross_cats_sorted":[],"title_canon_sha256":"422addcec57ba6d67fc8f6e3570fce654cc5fa616a20ebad6e329a5ca50492de","abstract_canon_sha256":"f013e695fa8bc823d01e26e4c7804d8983e9c538f695a46b0d9233a2d593d070"},"schema_version":"1.0"},"canonical_sha256":"1248c3efcb6b0dd1549339af059665ab4e244b604d7b90b925e1372054c1a828","source":{"kind":"arxiv","id":"1802.01242","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01242","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01242v1","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01242","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"CJEMH36LNMG5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CJEMH36LNMG5CVET","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CJEMH36L","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CJEMH36LNMG5CVETHGXQLFTFVN","target":"record","payload":{"canonical_record":{"source":{"id":"1802.01242","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-05T02:48:36Z","cross_cats_sorted":[],"title_canon_sha256":"422addcec57ba6d67fc8f6e3570fce654cc5fa616a20ebad6e329a5ca50492de","abstract_canon_sha256":"f013e695fa8bc823d01e26e4c7804d8983e9c538f695a46b0d9233a2d593d070"},"schema_version":"1.0"},"canonical_sha256":"1248c3efcb6b0dd1549339af059665ab4e244b604d7b90b925e1372054c1a828","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:24:26.968413Z","signature_b64":"mYtY6ozM0REsU61ihKKj363QV+ykwG+zabLmtzR3TQGdiClp1HvcVxGpGAuqLnOxTJ9wOa+XkHnGsg+OKqX1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1248c3efcb6b0dd1549339af059665ab4e244b604d7b90b925e1372054c1a828","last_reissued_at":"2026-05-18T00:24:26.967789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:24:26.967789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.01242","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":"2026-05-18T00:24:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b89czHyBIsAsd4LcrdpaHHRmW7OcDbAqgDoRZSJCeV/T3/9ywnPM3wbtB1MePztsxMFW1nniZuS2GvWBGFHeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:01:43.915820Z"},"content_sha256":"a2babcdb85f3e17cd740d1c7ca3545b02d1df40642995ff6c86a90a6bbc634f7","schema_version":"1.0","event_id":"sha256:a2babcdb85f3e17cd740d1c7ca3545b02d1df40642995ff6c86a90a6bbc634f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CJEMH36LNMG5CVETHGXQLFTFVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast Approximations for Metric-TSP via Linear Programming","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Chandra Chekuri, Kent Quanrud","submitted_at":"2018-02-05T02:48:36Z","abstract_excerpt":"We develop faster approximation algorithms for Metric-TSP building on recent, nearly linear time approximation schemes for the LP relaxation [Chekuri and Quanrud, 2017]. We show that the LP solution can be sparsified via cut-sparsification techniques such as those of Benczur and Karger [2015]. Given a weighted graph $G$ with $m$ edges and $n$ vertices, and $\\epsilon > 0$, our randomized algorithm outputs with high probability a $(1+\\epsilon)$-approximate solution to the LP relaxation whose support has $\\operatorname{O}(n \\log n /\\epsilon^2)$ edges. The running time of the algorithm is $\\operat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01242","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":"2026-05-18T00:24:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KlJnKMEAo5MDmVoN6sTkqqxWC8pKIWwXAPHI0W4AVAUUCqrAtrGWzVyzrehTRq74NlqG0ANnc2IAn+IWXlenBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:01:43.916186Z"},"content_sha256":"3d5928b4f23a12f55be8f4d712ec1f029afe227c551d9929dce689de82ccab0e","schema_version":"1.0","event_id":"sha256:3d5928b4f23a12f55be8f4d712ec1f029afe227c551d9929dce689de82ccab0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CJEMH36LNMG5CVETHGXQLFTFVN/bundle.json","state_url":"https://pith.science/pith/CJEMH36LNMG5CVETHGXQLFTFVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CJEMH36LNMG5CVETHGXQLFTFVN/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":"2026-06-04T18:01:43Z","links":{"resolver":"https://pith.science/pith/CJEMH36LNMG5CVETHGXQLFTFVN","bundle":"https://pith.science/pith/CJEMH36LNMG5CVETHGXQLFTFVN/bundle.json","state":"https://pith.science/pith/CJEMH36LNMG5CVETHGXQLFTFVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CJEMH36LNMG5CVETHGXQLFTFVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CJEMH36LNMG5CVETHGXQLFTFVN","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":"f013e695fa8bc823d01e26e4c7804d8983e9c538f695a46b0d9233a2d593d070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-05T02:48:36Z","title_canon_sha256":"422addcec57ba6d67fc8f6e3570fce654cc5fa616a20ebad6e329a5ca50492de"},"schema_version":"1.0","source":{"id":"1802.01242","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01242","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01242v1","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01242","created_at":"2026-05-18T00:24:26Z"},{"alias_kind":"pith_short_12","alias_value":"CJEMH36LNMG5","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CJEMH36LNMG5CVET","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CJEMH36L","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:3d5928b4f23a12f55be8f4d712ec1f029afe227c551d9929dce689de82ccab0e","target":"graph","created_at":"2026-05-18T00:24:26Z","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 develop faster approximation algorithms for Metric-TSP building on recent, nearly linear time approximation schemes for the LP relaxation [Chekuri and Quanrud, 2017]. We show that the LP solution can be sparsified via cut-sparsification techniques such as those of Benczur and Karger [2015]. Given a weighted graph $G$ with $m$ edges and $n$ vertices, and $\\epsilon > 0$, our randomized algorithm outputs with high probability a $(1+\\epsilon)$-approximate solution to the LP relaxation whose support has $\\operatorname{O}(n \\log n /\\epsilon^2)$ edges. The running time of the algorithm is $\\operat","authors_text":"Chandra Chekuri, Kent Quanrud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-05T02:48:36Z","title":"Fast Approximations for Metric-TSP via Linear Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01242","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:a2babcdb85f3e17cd740d1c7ca3545b02d1df40642995ff6c86a90a6bbc634f7","target":"record","created_at":"2026-05-18T00:24:26Z","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":"f013e695fa8bc823d01e26e4c7804d8983e9c538f695a46b0d9233a2d593d070","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-02-05T02:48:36Z","title_canon_sha256":"422addcec57ba6d67fc8f6e3570fce654cc5fa616a20ebad6e329a5ca50492de"},"schema_version":"1.0","source":{"id":"1802.01242","kind":"arxiv","version":1}},"canonical_sha256":"1248c3efcb6b0dd1549339af059665ab4e244b604d7b90b925e1372054c1a828","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1248c3efcb6b0dd1549339af059665ab4e244b604d7b90b925e1372054c1a828","first_computed_at":"2026-05-18T00:24:26.967789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:26.967789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mYtY6ozM0REsU61ihKKj363QV+ykwG+zabLmtzR3TQGdiClp1HvcVxGpGAuqLnOxTJ9wOa+XkHnGsg+OKqX1Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:26.968413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.01242","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2babcdb85f3e17cd740d1c7ca3545b02d1df40642995ff6c86a90a6bbc634f7","sha256:3d5928b4f23a12f55be8f4d712ec1f029afe227c551d9929dce689de82ccab0e"],"state_sha256":"b9fcfee22a7c693bdb1dd094436e4e1b5ff492f07ecbf429d93d696aa29c9aeb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FpRrNVvNUPi+nwftTiqJ1giMoUH6uIFbJ/rdK+fmitdQbMdj/IdH/u0WhKbIBfvj95/P3J8DEaodQurQ4XFFAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:01:43.918055Z","bundle_sha256":"61c852e94cdb60453f7a3a721b7557bb2dfb6e895cfd617c9181ca22b697c6c7"}}