{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:QVJCU5PUILUFY3BJ56QTLWWKFS","short_pith_number":"pith:QVJCU5PU","canonical_record":{"source":{"id":"1604.02486","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-04-08T21:05:05Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"93589c128f2ab8c62ffbbaa8f3d5b2d83a55725bb7fa4f0ea93de545c55cb75b","abstract_canon_sha256":"f86c62f88f3f865c15acaab5030fb1d87d22b862677a37f827022a17e9313ee8"},"schema_version":"1.0"},"canonical_sha256":"85522a75f442e85c6c29efa135daca2cb3537bf8f1ed50c6d4b44c6e3edd60d8","source":{"kind":"arxiv","id":"1604.02486","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02486","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02486v2","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02486","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"QVJCU5PUILUF","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QVJCU5PUILUFY3BJ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QVJCU5PU","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:QVJCU5PUILUFY3BJ56QTLWWKFS","target":"record","payload":{"canonical_record":{"source":{"id":"1604.02486","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-04-08T21:05:05Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"93589c128f2ab8c62ffbbaa8f3d5b2d83a55725bb7fa4f0ea93de545c55cb75b","abstract_canon_sha256":"f86c62f88f3f865c15acaab5030fb1d87d22b862677a37f827022a17e9313ee8"},"schema_version":"1.0"},"canonical_sha256":"85522a75f442e85c6c29efa135daca2cb3537bf8f1ed50c6d4b44c6e3edd60d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:12.609606Z","signature_b64":"o2o3RuQhmXvrBPx+INg/Vj+F/boB8f1EBll2nypM02K1+fDLIaCQnl5YEBX1L9uVS5jozWhpk/fwBb6NO1tGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85522a75f442e85c6c29efa135daca2cb3537bf8f1ed50c6d4b44c6e3edd60d8","last_reissued_at":"2026-05-18T00:07:12.608955Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:12.608955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.02486","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":"2026-05-18T00:07:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A2txRsZZua5GBk6JjTKk5Qp64tb447yvjyOWco1lYdASUYAJl/GUiSKOQrEMMZ8dpKSSxGAYYl6Y5I25be25Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:29:02.401467Z"},"content_sha256":"4854fe5acd2b256cc6dad2b8a244a0fd66fdd11f39508d7effd7b0007effb95e","schema_version":"1.0","event_id":"sha256:4854fe5acd2b256cc6dad2b8a244a0fd66fdd11f39508d7effd7b0007effb95e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:QVJCU5PUILUFY3BJ56QTLWWKFS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Salesman's Improved Paths: 3/2+1/34 Integrality Gap and Approximation Ratio","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.CO"],"primary_cat":"cs.DM","authors_text":"Andr\\'as Seb\\H{o}, Anke van Zuylen","submitted_at":"2016-04-08T21:05:05Z","abstract_excerpt":"We give a new, strongly polynomial-time algorithm and improved analysis for the metric $s-t$ path TSP. It finds a tour of cost less than 1.53 times the optimum of the subtour elimination LP, while known examples show that 1.5 is a lower bound for the integrality gap.\n  A key new idea is the deletion of some edges of Christofides' trees, which is then accompanied by novel arguments of the analysis: edge-deletion disconnects the trees, which are then partly reconnected by `parity correction'. We show that the arising `connectivity correction' can be achieved for a minor extra cost.\n  On the one "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02486","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":"2026-05-18T00:07:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"srhnjZ15ctZWiJFlx+s2xp7BaLa9CuaCPVlkPD2WWs4unHujTx/CJUTdp79ayRAlx0FjlvWKlrmGOVbd+vefBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:29:02.402226Z"},"content_sha256":"378e315baf720d411b5d163f26c879c058963eae41787d545947fffe29e50ccc","schema_version":"1.0","event_id":"sha256:378e315baf720d411b5d163f26c879c058963eae41787d545947fffe29e50ccc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVJCU5PUILUFY3BJ56QTLWWKFS/bundle.json","state_url":"https://pith.science/pith/QVJCU5PUILUFY3BJ56QTLWWKFS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVJCU5PUILUFY3BJ56QTLWWKFS/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":"2026-06-05T21:29:02Z","links":{"resolver":"https://pith.science/pith/QVJCU5PUILUFY3BJ56QTLWWKFS","bundle":"https://pith.science/pith/QVJCU5PUILUFY3BJ56QTLWWKFS/bundle.json","state":"https://pith.science/pith/QVJCU5PUILUFY3BJ56QTLWWKFS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVJCU5PUILUFY3BJ56QTLWWKFS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QVJCU5PUILUFY3BJ56QTLWWKFS","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":"f86c62f88f3f865c15acaab5030fb1d87d22b862677a37f827022a17e9313ee8","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-04-08T21:05:05Z","title_canon_sha256":"93589c128f2ab8c62ffbbaa8f3d5b2d83a55725bb7fa4f0ea93de545c55cb75b"},"schema_version":"1.0","source":{"id":"1604.02486","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02486","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02486v2","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02486","created_at":"2026-05-18T00:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"QVJCU5PUILUF","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"QVJCU5PUILUFY3BJ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"QVJCU5PU","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:378e315baf720d411b5d163f26c879c058963eae41787d545947fffe29e50ccc","target":"graph","created_at":"2026-05-18T00:07:12Z","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 give a new, strongly polynomial-time algorithm and improved analysis for the metric $s-t$ path TSP. It finds a tour of cost less than 1.53 times the optimum of the subtour elimination LP, while known examples show that 1.5 is a lower bound for the integrality gap.\n  A key new idea is the deletion of some edges of Christofides' trees, which is then accompanied by novel arguments of the analysis: edge-deletion disconnects the trees, which are then partly reconnected by `parity correction'. We show that the arising `connectivity correction' can be achieved for a minor extra cost.\n  On the one ","authors_text":"Andr\\'as Seb\\H{o}, Anke van Zuylen","cross_cats":["cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-04-08T21:05:05Z","title":"The Salesman's Improved Paths: 3/2+1/34 Integrality Gap and Approximation Ratio"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02486","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":"sha256:4854fe5acd2b256cc6dad2b8a244a0fd66fdd11f39508d7effd7b0007effb95e","target":"record","created_at":"2026-05-18T00:07:12Z","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":"f86c62f88f3f865c15acaab5030fb1d87d22b862677a37f827022a17e9313ee8","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2016-04-08T21:05:05Z","title_canon_sha256":"93589c128f2ab8c62ffbbaa8f3d5b2d83a55725bb7fa4f0ea93de545c55cb75b"},"schema_version":"1.0","source":{"id":"1604.02486","kind":"arxiv","version":2}},"canonical_sha256":"85522a75f442e85c6c29efa135daca2cb3537bf8f1ed50c6d4b44c6e3edd60d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85522a75f442e85c6c29efa135daca2cb3537bf8f1ed50c6d4b44c6e3edd60d8","first_computed_at":"2026-05-18T00:07:12.608955Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:12.608955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o2o3RuQhmXvrBPx+INg/Vj+F/boB8f1EBll2nypM02K1+fDLIaCQnl5YEBX1L9uVS5jozWhpk/fwBb6NO1tGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:12.609606Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02486","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4854fe5acd2b256cc6dad2b8a244a0fd66fdd11f39508d7effd7b0007effb95e","sha256:378e315baf720d411b5d163f26c879c058963eae41787d545947fffe29e50ccc"],"state_sha256":"6f0f8de70607daa9420323ca238b151bdcc05eff75878a0b5628fd73ee34e734"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B96zxINY/lCz/70HIYHJd3K+QfAKgJLeij9kGuh3hOo4UdJejTg+Uv9Gfv7ymKbdZkiwwxOIjO9g2VnUQcsXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:29:02.406472Z","bundle_sha256":"2d0c35230ab3aba94a4e04ec1516d9893c5c1f8b75490989ecf6a22944031fcc"}}