{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HTDKPOTMDEOHWPJ3ZECNKLJ3XY","short_pith_number":"pith:HTDKPOTM","canonical_record":{"source":{"id":"1710.08455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-23T18:49:21Z","cross_cats_sorted":["cs.DM","math.OC"],"title_canon_sha256":"a70fd46a42bbb89f8966697205230ba76159853c75af916832920ac2c16b57bf","abstract_canon_sha256":"e428f49ac2ce1d6eca03977328842620bd1eed40278bf05378e234bf9488aac0"},"schema_version":"1.0"},"canonical_sha256":"3cc6a7ba6c191c7b3d3bc904d52d3bbe3fa50b0c7f78cfba9db1588640c0e4bd","source":{"kind":"arxiv","id":"1710.08455","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08455","created_at":"2026-05-18T00:32:16Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08455v1","created_at":"2026-05-18T00:32:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08455","created_at":"2026-05-18T00:32:16Z"},{"alias_kind":"pith_short_12","alias_value":"HTDKPOTMDEOH","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HTDKPOTMDEOHWPJ3","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HTDKPOTM","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HTDKPOTMDEOHWPJ3ZECNKLJ3XY","target":"record","payload":{"canonical_record":{"source":{"id":"1710.08455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-23T18:49:21Z","cross_cats_sorted":["cs.DM","math.OC"],"title_canon_sha256":"a70fd46a42bbb89f8966697205230ba76159853c75af916832920ac2c16b57bf","abstract_canon_sha256":"e428f49ac2ce1d6eca03977328842620bd1eed40278bf05378e234bf9488aac0"},"schema_version":"1.0"},"canonical_sha256":"3cc6a7ba6c191c7b3d3bc904d52d3bbe3fa50b0c7f78cfba9db1588640c0e4bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:16.012221Z","signature_b64":"33NUEfWT/+thpxo2WErvhRfYpDrr3Nuh4FVMS58IsA6jtHqEhB7CR93n6AepMePgLcAWbT2vfWOKnSdQdlObBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cc6a7ba6c191c7b3d3bc904d52d3bbe3fa50b0c7f78cfba9db1588640c0e4bd","last_reissued_at":"2026-05-18T00:32:16.011688Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:16.011688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.08455","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":"2026-05-18T00:32:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Z8D1sU4gs71a2KOcMozoYX552G3uznDZ9IQQ5zCaWNV252PO7ZLAJb9vqyh2SGHypg6U/eqUeGNBSTwu6NtCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:19:37.208606Z"},"content_sha256":"4f4e38fe862699d754ae554fc8da318d6330e7b857ab3b66c98ccca7662effb2","schema_version":"1.0","event_id":"sha256:4f4e38fe862699d754ae554fc8da318d6330e7b857ab3b66c98ccca7662effb2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HTDKPOTMDEOHWPJ3ZECNKLJ3XY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Unbounded Integrality Gap of a Semidefinite Relaxation of the Traveling Salesman Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.OC"],"primary_cat":"cs.DS","authors_text":"David P. Williamson, Samuel C. Gutekunst","submitted_at":"2017-10-23T18:49:21Z","abstract_excerpt":"We study a semidefinite programming relaxation of the traveling salesman problem introduced by de Klerk, Pasechnik, and Sotirov [8] and show that their relaxation has an unbounded integrality gap. In particular, we give a family of instances such that the gap increases linearly with $n$. To obtain this result, we search for feasible solutions within a highly structured class of matrices; the problem of finding such solutions reduces to finding feasible solutions for a related linear program, which we do analytically. The solutions we find imply the unbounded integrality gap. Further, they impl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08455","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":"2026-05-18T00:32:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Vq1OhHd1b10IRX7NQkFliuJSaG1goQPBJg9uEKKNRHE51nZltsxyLd9FI1ZxRw9D8x5FEayKf5RkVLhAYkvDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:19:37.208961Z"},"content_sha256":"5cbcafb097c170b2175fb2c2d84d5f59bdcbf6c7b6d9756bc6b7067cf05b9458","schema_version":"1.0","event_id":"sha256:5cbcafb097c170b2175fb2c2d84d5f59bdcbf6c7b6d9756bc6b7067cf05b9458"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HTDKPOTMDEOHWPJ3ZECNKLJ3XY/bundle.json","state_url":"https://pith.science/pith/HTDKPOTMDEOHWPJ3ZECNKLJ3XY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HTDKPOTMDEOHWPJ3ZECNKLJ3XY/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":"2026-06-02T12:19:37Z","links":{"resolver":"https://pith.science/pith/HTDKPOTMDEOHWPJ3ZECNKLJ3XY","bundle":"https://pith.science/pith/HTDKPOTMDEOHWPJ3ZECNKLJ3XY/bundle.json","state":"https://pith.science/pith/HTDKPOTMDEOHWPJ3ZECNKLJ3XY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HTDKPOTMDEOHWPJ3ZECNKLJ3XY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HTDKPOTMDEOHWPJ3ZECNKLJ3XY","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":"e428f49ac2ce1d6eca03977328842620bd1eed40278bf05378e234bf9488aac0","cross_cats_sorted":["cs.DM","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-23T18:49:21Z","title_canon_sha256":"a70fd46a42bbb89f8966697205230ba76159853c75af916832920ac2c16b57bf"},"schema_version":"1.0","source":{"id":"1710.08455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.08455","created_at":"2026-05-18T00:32:16Z"},{"alias_kind":"arxiv_version","alias_value":"1710.08455v1","created_at":"2026-05-18T00:32:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.08455","created_at":"2026-05-18T00:32:16Z"},{"alias_kind":"pith_short_12","alias_value":"HTDKPOTMDEOH","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HTDKPOTMDEOHWPJ3","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HTDKPOTM","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:5cbcafb097c170b2175fb2c2d84d5f59bdcbf6c7b6d9756bc6b7067cf05b9458","target":"graph","created_at":"2026-05-18T00:32:16Z","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 study a semidefinite programming relaxation of the traveling salesman problem introduced by de Klerk, Pasechnik, and Sotirov [8] and show that their relaxation has an unbounded integrality gap. In particular, we give a family of instances such that the gap increases linearly with $n$. To obtain this result, we search for feasible solutions within a highly structured class of matrices; the problem of finding such solutions reduces to finding feasible solutions for a related linear program, which we do analytically. The solutions we find imply the unbounded integrality gap. Further, they impl","authors_text":"David P. Williamson, Samuel C. Gutekunst","cross_cats":["cs.DM","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-23T18:49:21Z","title":"The Unbounded Integrality Gap of a Semidefinite Relaxation of the Traveling Salesman Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.08455","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":"sha256:4f4e38fe862699d754ae554fc8da318d6330e7b857ab3b66c98ccca7662effb2","target":"record","created_at":"2026-05-18T00:32:16Z","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":"e428f49ac2ce1d6eca03977328842620bd1eed40278bf05378e234bf9488aac0","cross_cats_sorted":["cs.DM","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-10-23T18:49:21Z","title_canon_sha256":"a70fd46a42bbb89f8966697205230ba76159853c75af916832920ac2c16b57bf"},"schema_version":"1.0","source":{"id":"1710.08455","kind":"arxiv","version":1}},"canonical_sha256":"3cc6a7ba6c191c7b3d3bc904d52d3bbe3fa50b0c7f78cfba9db1588640c0e4bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3cc6a7ba6c191c7b3d3bc904d52d3bbe3fa50b0c7f78cfba9db1588640c0e4bd","first_computed_at":"2026-05-18T00:32:16.011688Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:16.011688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"33NUEfWT/+thpxo2WErvhRfYpDrr3Nuh4FVMS58IsA6jtHqEhB7CR93n6AepMePgLcAWbT2vfWOKnSdQdlObBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:16.012221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.08455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f4e38fe862699d754ae554fc8da318d6330e7b857ab3b66c98ccca7662effb2","sha256:5cbcafb097c170b2175fb2c2d84d5f59bdcbf6c7b6d9756bc6b7067cf05b9458"],"state_sha256":"62850ef7d3241f6f4a52022160756a43cdd5a773fdc0f93a8ae121a1789bb957"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iB1tIWnkkUBkE0IXzyQccrLKexHYOkPBY5bF8QpVUnZ1s9tvQl4cw2KcHT0iucfXHYkAj36+p3OqoHr5JmzTBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:19:37.211052Z","bundle_sha256":"18851b3ab20c8908496de67fd542168dc561955f618aca9086c9d43bdd21b5aa"}}