{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:BY5DN5T5E3S6WUKQ3GANYINYGE","short_pith_number":"pith:BY5DN5T5","canonical_record":{"source":{"id":"1209.3523","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-09-16T21:47:51Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"5c481c8674a3818bf3ca7c160719f7a95f1159085cdc28f08666fcc113bcf94d","abstract_canon_sha256":"801712a3446a64235ab74173266b7034ba5ab34228d933d83d722cd1133fb84f"},"schema_version":"1.0"},"canonical_sha256":"0e3a36f67d26e5eb5150d980dc21b8313b17d688672e2f4438d918b60bf5e5b7","source":{"kind":"arxiv","id":"1209.3523","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3523","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3523v3","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3523","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"BY5DN5T5E3S6","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BY5DN5T5E3S6WUKQ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BY5DN5T5","created_at":"2026-05-18T12:27:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:BY5DN5T5E3S6WUKQ3GANYINYGE","target":"record","payload":{"canonical_record":{"source":{"id":"1209.3523","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-09-16T21:47:51Z","cross_cats_sorted":["cs.DS","math.CO"],"title_canon_sha256":"5c481c8674a3818bf3ca7c160719f7a95f1159085cdc28f08666fcc113bcf94d","abstract_canon_sha256":"801712a3446a64235ab74173266b7034ba5ab34228d933d83d722cd1133fb84f"},"schema_version":"1.0"},"canonical_sha256":"0e3a36f67d26e5eb5150d980dc21b8313b17d688672e2f4438d918b60bf5e5b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:59.638687Z","signature_b64":"gz0Q5GMPqz4tGhGSBBmpsX1M13MNcZ21KIwURaPDTNyvhRHcs5Kq8TxEzENki5+tk7mFJvp/TOWS0VoFmBv6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e3a36f67d26e5eb5150d980dc21b8313b17d688672e2f4438d918b60bf5e5b7","last_reissued_at":"2026-05-18T00:47:59.638228Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:59.638228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.3523","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RDngT5eUH0vYF0ESZoJsJyaAUZqz/FmTS+hCmsxbjocXqJgoMZIYGqDevYeJmAQpBFDxFkeggIvkUv2hY2DkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:49:35.908228Z"},"content_sha256":"00f6a9736dec55b60fe2553202ef6274ddd97bb2aaaa4baf0ff0f3bfaf625360","schema_version":"1.0","event_id":"sha256:00f6a9736dec55b60fe2553202ef6274ddd97bb2aaaa4baf0ff0f3bfaf625360"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:BY5DN5T5E3S6WUKQ3GANYINYGE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eight-Fifth Approximation for TSP Paths","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\\\"o","submitted_at":"2012-09-16T21:47:51Z","abstract_excerpt":"We prove the approximation ratio 8/5 for the metric $\\{s,t\\}$-path-TSP problem, and more generally for shortest connected $T$-joins.\n  The algorithm that achieves this ratio is the simple \"Best of Many\" version of Christofides' algorithm (1976), suggested by An, Kleinberg and Shmoys (2012), which consists in determining the best Christofides $\\{s,t\\}$-tour out of those constructed from a family $\\Fscr_{>0}$ of trees having a convex combination dominated by an optimal solution $x^*$ of the fractional relaxation. They give the approximation guarantee $\\frac{\\sqrt{5}+1}{2}$ for such an $\\{s,t\\}$-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3523","kind":"arxiv","version":3},"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":"2026-05-18T00:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oZe9bA8qigwwfrgAvo5+UXNRVcIAuSx5Q1FN+0dA0uvn1M9vasBSxrmgLf/zCssPzbUpae/dilbFMuhK0c6GDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:49:35.908586Z"},"content_sha256":"75883b77cdff93eec39d2f6ea1f9ebe7bbd52935ad1761ff71978ebefb748049","schema_version":"1.0","event_id":"sha256:75883b77cdff93eec39d2f6ea1f9ebe7bbd52935ad1761ff71978ebefb748049"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BY5DN5T5E3S6WUKQ3GANYINYGE/bundle.json","state_url":"https://pith.science/pith/BY5DN5T5E3S6WUKQ3GANYINYGE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BY5DN5T5E3S6WUKQ3GANYINYGE/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":"2026-06-24T05:49:35Z","links":{"resolver":"https://pith.science/pith/BY5DN5T5E3S6WUKQ3GANYINYGE","bundle":"https://pith.science/pith/BY5DN5T5E3S6WUKQ3GANYINYGE/bundle.json","state":"https://pith.science/pith/BY5DN5T5E3S6WUKQ3GANYINYGE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BY5DN5T5E3S6WUKQ3GANYINYGE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:BY5DN5T5E3S6WUKQ3GANYINYGE","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":"801712a3446a64235ab74173266b7034ba5ab34228d933d83d722cd1133fb84f","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-09-16T21:47:51Z","title_canon_sha256":"5c481c8674a3818bf3ca7c160719f7a95f1159085cdc28f08666fcc113bcf94d"},"schema_version":"1.0","source":{"id":"1209.3523","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.3523","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1209.3523v3","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.3523","created_at":"2026-05-18T00:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"BY5DN5T5E3S6","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"BY5DN5T5E3S6WUKQ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"BY5DN5T5","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:75883b77cdff93eec39d2f6ea1f9ebe7bbd52935ad1761ff71978ebefb748049","target":"graph","created_at":"2026-05-18T00:47:59Z","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 prove the approximation ratio 8/5 for the metric $\\{s,t\\}$-path-TSP problem, and more generally for shortest connected $T$-joins.\n  The algorithm that achieves this ratio is the simple \"Best of Many\" version of Christofides' algorithm (1976), suggested by An, Kleinberg and Shmoys (2012), which consists in determining the best Christofides $\\{s,t\\}$-tour out of those constructed from a family $\\Fscr_{>0}$ of trees having a convex combination dominated by an optimal solution $x^*$ of the fractional relaxation. They give the approximation guarantee $\\frac{\\sqrt{5}+1}{2}$ for such an $\\{s,t\\}$-","authors_text":"Andr\\'as Seb\\\"o","cross_cats":["cs.DS","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-09-16T21:47:51Z","title":"Eight-Fifth Approximation for TSP Paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3523","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":"sha256:00f6a9736dec55b60fe2553202ef6274ddd97bb2aaaa4baf0ff0f3bfaf625360","target":"record","created_at":"2026-05-18T00:47:59Z","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":"801712a3446a64235ab74173266b7034ba5ab34228d933d83d722cd1133fb84f","cross_cats_sorted":["cs.DS","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2012-09-16T21:47:51Z","title_canon_sha256":"5c481c8674a3818bf3ca7c160719f7a95f1159085cdc28f08666fcc113bcf94d"},"schema_version":"1.0","source":{"id":"1209.3523","kind":"arxiv","version":3}},"canonical_sha256":"0e3a36f67d26e5eb5150d980dc21b8313b17d688672e2f4438d918b60bf5e5b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e3a36f67d26e5eb5150d980dc21b8313b17d688672e2f4438d918b60bf5e5b7","first_computed_at":"2026-05-18T00:47:59.638228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:59.638228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gz0Q5GMPqz4tGhGSBBmpsX1M13MNcZ21KIwURaPDTNyvhRHcs5Kq8TxEzENki5+tk7mFJvp/TOWS0VoFmBv6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:59.638687Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.3523","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00f6a9736dec55b60fe2553202ef6274ddd97bb2aaaa4baf0ff0f3bfaf625360","sha256:75883b77cdff93eec39d2f6ea1f9ebe7bbd52935ad1761ff71978ebefb748049"],"state_sha256":"92429fd4ec53854c18a41b830bdcc3c896529a7743a6479317f636807793d040"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2Rlk7WCIm9yoGJ+ub+0qtExu16npdoxMXnkpRV2zUY082bdPqFvocuBZ9IdbcCDpXoFQ6Y6dffQvqvjpL+UCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:49:35.911045Z","bundle_sha256":"7b4ae1df0e2b5c368a5c594d1d9feeaac40db49dc5cf615a8e7b279e6bb6d327"}}