{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:N3Y73SC5XG5TFRAHSBDJX6IKOB","short_pith_number":"pith:N3Y73SC5","canonical_record":{"source":{"id":"2111.09290","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-11-17T18:42:54Z","cross_cats_sorted":[],"title_canon_sha256":"ff2441d79a6fc35384ca2525d837d3bc6646f92c6d09537344977c4cdf5bf7d8","abstract_canon_sha256":"67063ab6fedbacd6ccfebfcbe9bfd4e0b0a75d585904774fc8ce85ba02a6d5e5"},"schema_version":"1.0"},"canonical_sha256":"6ef1fdc85db9bb32c40790469bf90a705abde014de3c003ba04a38baf40b9911","source":{"kind":"arxiv","id":"2111.09290","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.09290","created_at":"2026-07-05T11:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"2111.09290v2","created_at":"2026-07-05T11:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.09290","created_at":"2026-07-05T11:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"N3Y73SC5XG5T","created_at":"2026-07-05T11:37:40Z"},{"alias_kind":"pith_short_16","alias_value":"N3Y73SC5XG5TFRAH","created_at":"2026-07-05T11:37:40Z"},{"alias_kind":"pith_short_8","alias_value":"N3Y73SC5","created_at":"2026-07-05T11:37:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:N3Y73SC5XG5TFRAHSBDJX6IKOB","target":"record","payload":{"canonical_record":{"source":{"id":"2111.09290","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-11-17T18:42:54Z","cross_cats_sorted":[],"title_canon_sha256":"ff2441d79a6fc35384ca2525d837d3bc6646f92c6d09537344977c4cdf5bf7d8","abstract_canon_sha256":"67063ab6fedbacd6ccfebfcbe9bfd4e0b0a75d585904774fc8ce85ba02a6d5e5"},"schema_version":"1.0"},"canonical_sha256":"6ef1fdc85db9bb32c40790469bf90a705abde014de3c003ba04a38baf40b9911","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:37:40.877305Z","signature_b64":"t+wGwpHMZvS/YAZxPJPey0EH0yhoTYpy3Gs0mPIr9p7Z2eE9woIWjb7LG2JGiacYECZOrWZkuFmbB5dqW3WVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ef1fdc85db9bb32c40790469bf90a705abde014de3c003ba04a38baf40b9911","last_reissued_at":"2026-07-05T11:37:40.876740Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:37:40.876740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.09290","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":"2026-07-05T11:37:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GYAgz6YjSBxZh6XXAQqZCMwXwHchRQ437pNvVnROPMfz1X7i3rdeEfq2eoTvq6YySX7lJK7xUHzhEUrJGqCYAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T16:39:09.858061Z"},"content_sha256":"99151cf6683ff2cc4c69fc8438f0ec7ab566463d56e2fe6d61dfa6e795f45244","schema_version":"1.0","event_id":"sha256:99151cf6683ff2cc4c69fc8438f0ec7ab566463d56e2fe6d61dfa6e795f45244"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:N3Y73SC5XG5TFRAHSBDJX6IKOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matroid-Based TSP Rounding for Half-Integral Solutions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anupam Gupta, Euiwoong Lee, Heather Newman, Jason Li, Marcin Mucha, Sherry Sarkar","submitted_at":"2021-11-17T18:42:54Z","abstract_excerpt":"We show how to round any half-integral solution to the subtour-elimination relaxation for the TSP, while losing a less-than-1.5 factor. Such a rounding algorithm was recently given by Karlin, Klein, and Oveis Gharan based on sampling from max-entropy distributions. We build on an approach of Haddadan and Newman to show how sampling from the matroid intersection polytope, and a new use of max-entropy sampling, can give better guarantees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.09290","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.09290/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:37:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G409O0xqROLNOXj217s0f1IFhI+VDIwZCHSjWHFjO+oLhu7Y3p6Ku+plRP5X565brTG11eqZgPC8EoFIQAaaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T16:39:09.858361Z"},"content_sha256":"785166d71c4874593bce6acfb657882df092750a8191f763e23e99da2f975956","schema_version":"1.0","event_id":"sha256:785166d71c4874593bce6acfb657882df092750a8191f763e23e99da2f975956"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N3Y73SC5XG5TFRAHSBDJX6IKOB/bundle.json","state_url":"https://pith.science/pith/N3Y73SC5XG5TFRAHSBDJX6IKOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N3Y73SC5XG5TFRAHSBDJX6IKOB/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":"2026-07-31T16:39:09Z","links":{"resolver":"https://pith.science/pith/N3Y73SC5XG5TFRAHSBDJX6IKOB","bundle":"https://pith.science/pith/N3Y73SC5XG5TFRAHSBDJX6IKOB/bundle.json","state":"https://pith.science/pith/N3Y73SC5XG5TFRAHSBDJX6IKOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N3Y73SC5XG5TFRAHSBDJX6IKOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:N3Y73SC5XG5TFRAHSBDJX6IKOB","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":"67063ab6fedbacd6ccfebfcbe9bfd4e0b0a75d585904774fc8ce85ba02a6d5e5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-11-17T18:42:54Z","title_canon_sha256":"ff2441d79a6fc35384ca2525d837d3bc6646f92c6d09537344977c4cdf5bf7d8"},"schema_version":"1.0","source":{"id":"2111.09290","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.09290","created_at":"2026-07-05T11:37:40Z"},{"alias_kind":"arxiv_version","alias_value":"2111.09290v2","created_at":"2026-07-05T11:37:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.09290","created_at":"2026-07-05T11:37:40Z"},{"alias_kind":"pith_short_12","alias_value":"N3Y73SC5XG5T","created_at":"2026-07-05T11:37:40Z"},{"alias_kind":"pith_short_16","alias_value":"N3Y73SC5XG5TFRAH","created_at":"2026-07-05T11:37:40Z"},{"alias_kind":"pith_short_8","alias_value":"N3Y73SC5","created_at":"2026-07-05T11:37:40Z"}],"graph_snapshots":[{"event_id":"sha256:785166d71c4874593bce6acfb657882df092750a8191f763e23e99da2f975956","target":"graph","created_at":"2026-07-05T11:37:40Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2111.09290/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show how to round any half-integral solution to the subtour-elimination relaxation for the TSP, while losing a less-than-1.5 factor. Such a rounding algorithm was recently given by Karlin, Klein, and Oveis Gharan based on sampling from max-entropy distributions. We build on an approach of Haddadan and Newman to show how sampling from the matroid intersection polytope, and a new use of max-entropy sampling, can give better guarantees.","authors_text":"Anupam Gupta, Euiwoong Lee, Heather Newman, Jason Li, Marcin Mucha, Sherry Sarkar","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-11-17T18:42:54Z","title":"Matroid-Based TSP Rounding for Half-Integral Solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.09290","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":"sha256:99151cf6683ff2cc4c69fc8438f0ec7ab566463d56e2fe6d61dfa6e795f45244","target":"record","created_at":"2026-07-05T11:37:40Z","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":"67063ab6fedbacd6ccfebfcbe9bfd4e0b0a75d585904774fc8ce85ba02a6d5e5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-11-17T18:42:54Z","title_canon_sha256":"ff2441d79a6fc35384ca2525d837d3bc6646f92c6d09537344977c4cdf5bf7d8"},"schema_version":"1.0","source":{"id":"2111.09290","kind":"arxiv","version":2}},"canonical_sha256":"6ef1fdc85db9bb32c40790469bf90a705abde014de3c003ba04a38baf40b9911","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ef1fdc85db9bb32c40790469bf90a705abde014de3c003ba04a38baf40b9911","first_computed_at":"2026-07-05T11:37:40.876740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:37:40.876740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t+wGwpHMZvS/YAZxPJPey0EH0yhoTYpy3Gs0mPIr9p7Z2eE9woIWjb7LG2JGiacYECZOrWZkuFmbB5dqW3WVDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:37:40.877305Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.09290","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99151cf6683ff2cc4c69fc8438f0ec7ab566463d56e2fe6d61dfa6e795f45244","sha256:785166d71c4874593bce6acfb657882df092750a8191f763e23e99da2f975956"],"state_sha256":"f43e0513ad4f2ad51d435970a51da48a4aac9599f24f56c227e772f01bda20e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JesqoOujO2DcYgz3/Y8guEeRaYBT8Q9sr5rx7Y/LGS2Sy9uHNPc02RGIQMp2pRwqdz3+HSVYLAxQUJRv0DMIBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T16:39:09.862436Z","bundle_sha256":"124b79b979824566bec4c9de1dc951ed715c5a52bf45c05bb5ebf37aba5d33d8"}}