{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MQIQVD6TEQS4IKQSMKYUX5PZW6","short_pith_number":"pith:MQIQVD6T","canonical_record":{"source":{"id":"2607.10564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-12T04:42:06Z","cross_cats_sorted":[],"title_canon_sha256":"839268eee2036f56a06c0c9b5ae77dbf011293297d1ff88e24c379a4d1e552c4","abstract_canon_sha256":"75f68fb3361095d90ff294a77a8da8d7d3c1f76267456ad4115e1150d60777ec"},"schema_version":"1.0"},"canonical_sha256":"64110a8fd32425c42a1262b14bf5f9b788c6070b49f7471631024f6d7bb93079","source":{"kind":"arxiv","id":"2607.10564","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.10564","created_at":"2026-07-14T01:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"2607.10564v1","created_at":"2026-07-14T01:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10564","created_at":"2026-07-14T01:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"MQIQVD6TEQS4","created_at":"2026-07-14T01:21:21Z"},{"alias_kind":"pith_short_16","alias_value":"MQIQVD6TEQS4IKQS","created_at":"2026-07-14T01:21:21Z"},{"alias_kind":"pith_short_8","alias_value":"MQIQVD6T","created_at":"2026-07-14T01:21:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MQIQVD6TEQS4IKQSMKYUX5PZW6","target":"record","payload":{"canonical_record":{"source":{"id":"2607.10564","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-12T04:42:06Z","cross_cats_sorted":[],"title_canon_sha256":"839268eee2036f56a06c0c9b5ae77dbf011293297d1ff88e24c379a4d1e552c4","abstract_canon_sha256":"75f68fb3361095d90ff294a77a8da8d7d3c1f76267456ad4115e1150d60777ec"},"schema_version":"1.0"},"canonical_sha256":"64110a8fd32425c42a1262b14bf5f9b788c6070b49f7471631024f6d7bb93079","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:21:21.533595Z","signature_b64":"HlPIvfNQMtSI7L2mVQCFh+IYvyHOAmvbIqts5a9a9PpkC8YFzxFN7PPKtLCtbqCU8mHBxNOIMfTVIDCsY/k3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64110a8fd32425c42a1262b14bf5f9b788c6070b49f7471631024f6d7bb93079","last_reissued_at":"2026-07-14T01:21:21.532776Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:21:21.532776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.10564","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":"2026-07-14T01:21:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IBmDXQ1xDzsPLYoIs7ZzrgCH9aUuY075aaDp7qEW2x6rTPjmNSSEujvP9Xyb2kmdJDs93sO6Sob4cfHK9kE3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T10:25:23.205810Z"},"content_sha256":"aaa1e07f45c63f2bc0567f8e28e180bc930b1e6db4ccc70b45ff505011af39bf","schema_version":"1.0","event_id":"sha256:aaa1e07f45c63f2bc0567f8e28e180bc930b1e6db4ccc70b45ff505011af39bf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MQIQVD6TEQS4IKQSMKYUX5PZW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Power of Arrival Times in Random-Order Online Facility Location","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Shaofeng H.-C. Jiang, Yichen Huang","submitted_at":"2026-07-12T04:42:06Z","abstract_excerpt":"We study online metric facility location with uniform opening costs in the random-order model (Meyerson FOCS'01). The best previous upper bound was a $3$-competitive randomized algorithm (Kaplan, Naori, Raz SODA'23), leaving a gap to the best known lower bound of $2$. In this work, we give two algorithms with improved competitive ratios: (i) a deterministic algorithm with a competitive ratio below $2.42$ and (ii) a randomized algorithm with a competitive ratio below $2.59$ and the additional property that it retains the asymptotically optimal $O(\\log n/\\log \\log n)$ competitive ratio in the ad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10564","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.10564/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":"2026-07-14T01:21:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+rt1Y1DHJFTjYJY36UW5pnOCZYC0sFwwZBU37CnRpNXvEVHev78ThhEA+06F8z3KjdCYq3zmGl8XPlrBLmSZAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T10:25:23.206666Z"},"content_sha256":"a4db5ee14b1447e3c1ac52c8dbd2501303d2bcda546dd1903dac40a1762a7cf3","schema_version":"1.0","event_id":"sha256:a4db5ee14b1447e3c1ac52c8dbd2501303d2bcda546dd1903dac40a1762a7cf3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MQIQVD6TEQS4IKQSMKYUX5PZW6/bundle.json","state_url":"https://pith.science/pith/MQIQVD6TEQS4IKQSMKYUX5PZW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MQIQVD6TEQS4IKQSMKYUX5PZW6/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":"2026-08-12T10:25:23Z","links":{"resolver":"https://pith.science/pith/MQIQVD6TEQS4IKQSMKYUX5PZW6","bundle":"https://pith.science/pith/MQIQVD6TEQS4IKQSMKYUX5PZW6/bundle.json","state":"https://pith.science/pith/MQIQVD6TEQS4IKQSMKYUX5PZW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MQIQVD6TEQS4IKQSMKYUX5PZW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MQIQVD6TEQS4IKQSMKYUX5PZW6","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":"75f68fb3361095d90ff294a77a8da8d7d3c1f76267456ad4115e1150d60777ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-12T04:42:06Z","title_canon_sha256":"839268eee2036f56a06c0c9b5ae77dbf011293297d1ff88e24c379a4d1e552c4"},"schema_version":"1.0","source":{"id":"2607.10564","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.10564","created_at":"2026-07-14T01:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"2607.10564v1","created_at":"2026-07-14T01:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.10564","created_at":"2026-07-14T01:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"MQIQVD6TEQS4","created_at":"2026-07-14T01:21:21Z"},{"alias_kind":"pith_short_16","alias_value":"MQIQVD6TEQS4IKQS","created_at":"2026-07-14T01:21:21Z"},{"alias_kind":"pith_short_8","alias_value":"MQIQVD6T","created_at":"2026-07-14T01:21:21Z"}],"graph_snapshots":[{"event_id":"sha256:a4db5ee14b1447e3c1ac52c8dbd2501303d2bcda546dd1903dac40a1762a7cf3","target":"graph","created_at":"2026-07-14T01:21:21Z","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/2607.10564/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study online metric facility location with uniform opening costs in the random-order model (Meyerson FOCS'01). The best previous upper bound was a $3$-competitive randomized algorithm (Kaplan, Naori, Raz SODA'23), leaving a gap to the best known lower bound of $2$. In this work, we give two algorithms with improved competitive ratios: (i) a deterministic algorithm with a competitive ratio below $2.42$ and (ii) a randomized algorithm with a competitive ratio below $2.59$ and the additional property that it retains the asymptotically optimal $O(\\log n/\\log \\log n)$ competitive ratio in the ad","authors_text":"Shaofeng H.-C. Jiang, Yichen Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-12T04:42:06Z","title":"The Power of Arrival Times in Random-Order Online Facility Location"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.10564","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:aaa1e07f45c63f2bc0567f8e28e180bc930b1e6db4ccc70b45ff505011af39bf","target":"record","created_at":"2026-07-14T01:21:21Z","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":"75f68fb3361095d90ff294a77a8da8d7d3c1f76267456ad4115e1150d60777ec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-12T04:42:06Z","title_canon_sha256":"839268eee2036f56a06c0c9b5ae77dbf011293297d1ff88e24c379a4d1e552c4"},"schema_version":"1.0","source":{"id":"2607.10564","kind":"arxiv","version":1}},"canonical_sha256":"64110a8fd32425c42a1262b14bf5f9b788c6070b49f7471631024f6d7bb93079","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64110a8fd32425c42a1262b14bf5f9b788c6070b49f7471631024f6d7bb93079","first_computed_at":"2026-07-14T01:21:21.532776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:21:21.532776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HlPIvfNQMtSI7L2mVQCFh+IYvyHOAmvbIqts5a9a9PpkC8YFzxFN7PPKtLCtbqCU8mHBxNOIMfTVIDCsY/k3Cw==","signature_status":"signed_v1","signed_at":"2026-07-14T01:21:21.533595Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.10564","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaa1e07f45c63f2bc0567f8e28e180bc930b1e6db4ccc70b45ff505011af39bf","sha256:a4db5ee14b1447e3c1ac52c8dbd2501303d2bcda546dd1903dac40a1762a7cf3"],"state_sha256":"04a1ba35d6e237ef3a9cb8ed5190725796234866ba227a710eab37e243eb2ffd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cP+FWEnZT3+9wVA+t9wrzgu3CZO44osdzV3jbj9rCa4e2wSk6ztsdGMFaot5YAOcwEi382DjL4QSIXOL7efvCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T10:25:23.213102Z","bundle_sha256":"7718506fb149d53ba1033fefb1cd20abda8a95a826fc7e1d58eb72cd3a3609dd"}}