{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:R25G77D7AX4KEEG5WPD5QJMEAW","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":"c33b09d5e7f1daae92c83b4979b3fed0dfaef7f6f9f28d9c938aaad73ba8b998","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-08T13:39:09Z","title_canon_sha256":"4dcdb644126a835a9e0a0607294589da9149bbfe5f3a0c68adb9c3c4ffe868f7"},"schema_version":"1.0","source":{"id":"1107.1630","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.1630","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"arxiv_version","alias_value":"1107.1630v3","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.1630","created_at":"2026-05-18T02:58:00Z"},{"alias_kind":"pith_short_12","alias_value":"R25G77D7AX4K","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"R25G77D7AX4KEEG5","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"R25G77D7","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:6a801506505499142c6c22a1011c230f69ed861c9a4a275b0d3cf75b675827e0","target":"graph","created_at":"2026-05-18T02:58:00Z","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":"In this paper, we study the integrality gap of the subtour LP relaxation for the traveling salesman problem in the special case when all edge costs are either 1 or 2. For the general case of symmetric costs that obey triangle inequality, a famous conjecture is that the integrality gap is 4/3. Little progress towards resolving this conjecture has been made in thirty years. We conjecture that when all edge costs $c_{ij}\\in \\{1,2\\}$, the integrality gap is $10/9$. We show that this conjecture is true when the optimal subtour LP solution has a certain structure. Under a weaker assumption, which is","authors_text":"Anke van Zuylen, David P. Williamson, Frans Schalekamp, Jiawei Qian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-08T13:39:09Z","title":"On the Integrality Gap of the Subtour LP for the 1,2-TSP"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1630","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":"sha256:0cde053b7f770b7adec6778044880e059c4184816009e7c15600197c53beaaf6","target":"record","created_at":"2026-05-18T02:58:00Z","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":"c33b09d5e7f1daae92c83b4979b3fed0dfaef7f6f9f28d9c938aaad73ba8b998","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-07-08T13:39:09Z","title_canon_sha256":"4dcdb644126a835a9e0a0607294589da9149bbfe5f3a0c68adb9c3c4ffe868f7"},"schema_version":"1.0","source":{"id":"1107.1630","kind":"arxiv","version":3}},"canonical_sha256":"8eba6ffc7f05f8a210ddb3c7d8258405bcc61c40f29208ff5b1453c1210ff579","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8eba6ffc7f05f8a210ddb3c7d8258405bcc61c40f29208ff5b1453c1210ff579","first_computed_at":"2026-05-18T02:58:00.763465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:00.763465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TihQJMwG/wipBYL1BMAQt6RJzdvGSWmaHRZqNYmmvzYTAeHUeXN0ai6SZmPqgU3Tc4HlAJIVT1Bv/w+jCrVEAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:00.764052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.1630","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cde053b7f770b7adec6778044880e059c4184816009e7c15600197c53beaaf6","sha256:6a801506505499142c6c22a1011c230f69ed861c9a4a275b0d3cf75b675827e0"],"state_sha256":"a0b5eacd1aeb3b1460d4b02ca5f3da61186ea5fffb4dc8946e9eae7442834ca5"}