{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NQBZKENUWA4UM4BZKQPN5RXZFA","short_pith_number":"pith:NQBZKENU","canonical_record":{"source":{"id":"1907.02390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-04T13:18:25Z","cross_cats_sorted":[],"title_canon_sha256":"90784da346c6bc86771ae34f4d2935af1f4503d674d2706b710f1ecc9141204a","abstract_canon_sha256":"ab4103cafec5fb9ecc13bb512a38de0ae958c46e4696140ef98d6aa829e29de1"},"schema_version":"1.0"},"canonical_sha256":"6c039511b4b039467039541edec6f9281d6df87b7bcf0866d326c57b309bacc3","source":{"kind":"arxiv","id":"1907.02390","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02390","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02390v1","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02390","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"NQBZKENUWA4U","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NQBZKENUWA4UM4BZ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NQBZKENU","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NQBZKENUWA4UM4BZKQPN5RXZFA","target":"record","payload":{"canonical_record":{"source":{"id":"1907.02390","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-04T13:18:25Z","cross_cats_sorted":[],"title_canon_sha256":"90784da346c6bc86771ae34f4d2935af1f4503d674d2706b710f1ecc9141204a","abstract_canon_sha256":"ab4103cafec5fb9ecc13bb512a38de0ae958c46e4696140ef98d6aa829e29de1"},"schema_version":"1.0"},"canonical_sha256":"6c039511b4b039467039541edec6f9281d6df87b7bcf0866d326c57b309bacc3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:28.736532Z","signature_b64":"MC5tDKLS9N4rD3MDt7SUJKrOn5bKAy7MT9Dv+wF9+GsoP6zcN21QTQNOCluDY0lrFOKB0Q29wnklRHsAVlu6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c039511b4b039467039541edec6f9281d6df87b7bcf0866d326c57b309bacc3","last_reissued_at":"2026-05-17T23:41:28.735726Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:28.735726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.02390","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":"2026-05-17T23:41:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HuTLdJQXJQkmFCXNeof6u2KoFUpFvx7+JQoRFnYbxYnjPrjdZ/uWF0mlgVgFo+od0iKqrdva2ZPKX+9O2Q6+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:44:08.206062Z"},"content_sha256":"f5e6bd599f5388480b8b18c76db2603871c822e9131b4717e1db74a6caadd759","schema_version":"1.0","event_id":"sha256:f5e6bd599f5388480b8b18c76db2603871c822e9131b4717e1db74a6caadd759"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NQBZKENUWA4UM4BZKQPN5RXZFA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Improved Lower Bound for the Traveling Salesman Constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Julia Gaudio, Patrick Jaillet","submitted_at":"2019-07-04T13:18:25Z","abstract_excerpt":"Let $X_1, X_2, \\dots, X_n$ be independent uniform random variables on $[0,1]^2$. Let $L(X_1, \\dots, X_n)$ be the length of the shortest Traveling Salesman tour through these points. It is known that there exists a constant $\\beta$ such that $$\\lim_{n \\to \\infty} \\frac{L(X_1, \\dots, X_n)}{\\sqrt{n}} = \\beta$$ almost surely (Beardwood 1959). The original analysis in (Beardwood 1959) showed that $\\beta \\geq 0.625$. Building upon an approach proposed in (Steinerberger 2015), we improve the lower bound to $\\beta \\geq 0.6277$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02390","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":"2026-05-17T23:41:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cT1BixHhboAbcgfopqqDjTGK+V2V8+Kqc0tERY9D4t9jv9OZQOWDeV2jR2WXybWBsTVD76VyRHjino1T+xGTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:44:08.206434Z"},"content_sha256":"995981b515f97d772e46791f2f48c9456cb8d0d0314d01e800df429153b84072","schema_version":"1.0","event_id":"sha256:995981b515f97d772e46791f2f48c9456cb8d0d0314d01e800df429153b84072"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NQBZKENUWA4UM4BZKQPN5RXZFA/bundle.json","state_url":"https://pith.science/pith/NQBZKENUWA4UM4BZKQPN5RXZFA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NQBZKENUWA4UM4BZKQPN5RXZFA/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":"2026-06-28T12:44:08Z","links":{"resolver":"https://pith.science/pith/NQBZKENUWA4UM4BZKQPN5RXZFA","bundle":"https://pith.science/pith/NQBZKENUWA4UM4BZKQPN5RXZFA/bundle.json","state":"https://pith.science/pith/NQBZKENUWA4UM4BZKQPN5RXZFA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NQBZKENUWA4UM4BZKQPN5RXZFA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NQBZKENUWA4UM4BZKQPN5RXZFA","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":"ab4103cafec5fb9ecc13bb512a38de0ae958c46e4696140ef98d6aa829e29de1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-04T13:18:25Z","title_canon_sha256":"90784da346c6bc86771ae34f4d2935af1f4503d674d2706b710f1ecc9141204a"},"schema_version":"1.0","source":{"id":"1907.02390","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02390","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02390v1","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02390","created_at":"2026-05-17T23:41:28Z"},{"alias_kind":"pith_short_12","alias_value":"NQBZKENUWA4U","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NQBZKENUWA4UM4BZ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NQBZKENU","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:995981b515f97d772e46791f2f48c9456cb8d0d0314d01e800df429153b84072","target":"graph","created_at":"2026-05-17T23:41:28Z","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":"Let $X_1, X_2, \\dots, X_n$ be independent uniform random variables on $[0,1]^2$. Let $L(X_1, \\dots, X_n)$ be the length of the shortest Traveling Salesman tour through these points. It is known that there exists a constant $\\beta$ such that $$\\lim_{n \\to \\infty} \\frac{L(X_1, \\dots, X_n)}{\\sqrt{n}} = \\beta$$ almost surely (Beardwood 1959). The original analysis in (Beardwood 1959) showed that $\\beta \\geq 0.625$. Building upon an approach proposed in (Steinerberger 2015), we improve the lower bound to $\\beta \\geq 0.6277$.","authors_text":"Julia Gaudio, Patrick Jaillet","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-04T13:18:25Z","title":"An Improved Lower Bound for the Traveling Salesman Constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02390","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:f5e6bd599f5388480b8b18c76db2603871c822e9131b4717e1db74a6caadd759","target":"record","created_at":"2026-05-17T23:41:28Z","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":"ab4103cafec5fb9ecc13bb512a38de0ae958c46e4696140ef98d6aa829e29de1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-04T13:18:25Z","title_canon_sha256":"90784da346c6bc86771ae34f4d2935af1f4503d674d2706b710f1ecc9141204a"},"schema_version":"1.0","source":{"id":"1907.02390","kind":"arxiv","version":1}},"canonical_sha256":"6c039511b4b039467039541edec6f9281d6df87b7bcf0866d326c57b309bacc3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c039511b4b039467039541edec6f9281d6df87b7bcf0866d326c57b309bacc3","first_computed_at":"2026-05-17T23:41:28.735726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:28.735726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MC5tDKLS9N4rD3MDt7SUJKrOn5bKAy7MT9Dv+wF9+GsoP6zcN21QTQNOCluDY0lrFOKB0Q29wnklRHsAVlu6AA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:28.736532Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02390","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5e6bd599f5388480b8b18c76db2603871c822e9131b4717e1db74a6caadd759","sha256:995981b515f97d772e46791f2f48c9456cb8d0d0314d01e800df429153b84072"],"state_sha256":"fd8d35146157394cecb4d3455b9b5d6a3a5a712fd1f8cb1115a6dc5a91982e98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cF64X++Xu4bUa+HhOB60iT4l8nJtG1dSvtvbv6XhtI9UKyKKekh9Ga4QVBAC7FdV58K/e0D/u09TcEx67Un6AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T12:44:08.208309Z","bundle_sha256":"4db818b749d0a5fc00b0d8f6e77540f553b9c2e4ca5e911d0d3f6b7d507cb682"}}