{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QHCEQ2IHEWWWS53UU3A3QA3GYG","short_pith_number":"pith:QHCEQ2IH","canonical_record":{"source":{"id":"2507.19259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-25T13:37:19Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"ac0bf598f6066756abd11b2f0b38eb9c7ef71ccdf4eeff635f76badb4be7c7e2","abstract_canon_sha256":"535e933cb08cb83ed72d8a43ae514b3e9be1e0cffb5b8bcce6ea65217f35c576"},"schema_version":"1.0"},"canonical_sha256":"81c448690725ad697774a6c1b80366c18e6927fd239e189f7f139c6627c2cbdc","source":{"kind":"arxiv","id":"2507.19259","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.19259","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"arxiv_version","alias_value":"2507.19259v1","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19259","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_12","alias_value":"QHCEQ2IHEWWW","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_16","alias_value":"QHCEQ2IHEWWWS53U","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_8","alias_value":"QHCEQ2IH","created_at":"2026-07-05T11:43:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QHCEQ2IHEWWWS53UU3A3QA3GYG","target":"record","payload":{"canonical_record":{"source":{"id":"2507.19259","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-25T13:37:19Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"ac0bf598f6066756abd11b2f0b38eb9c7ef71ccdf4eeff635f76badb4be7c7e2","abstract_canon_sha256":"535e933cb08cb83ed72d8a43ae514b3e9be1e0cffb5b8bcce6ea65217f35c576"},"schema_version":"1.0"},"canonical_sha256":"81c448690725ad697774a6c1b80366c18e6927fd239e189f7f139c6627c2cbdc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:22.435831Z","signature_b64":"uwrGumPIiCsNyevNWlwxcyVUEwn2zMdOnYSsNF40O6SmN9d2QYp/PL0/ON3LhSVXl639QZ6FlfkD9KGy+M6qAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81c448690725ad697774a6c1b80366c18e6927fd239e189f7f139c6627c2cbdc","last_reissued_at":"2026-07-05T11:43:22.435360Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:22.435360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.19259","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":"2026-07-05T11:43:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tuqqNn6+ewKRf6ulphYcsjaSlyubfpDRWwcY/UpLULnq6oXF0VzZ6qfOzWPcimdL2qz6Ma5ppvBJJ8fqcg1uDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T20:30:30.513209Z"},"content_sha256":"c7217b9e0ebd1f98e78ff7d53c5a36ded9502255d19ac8c5c7254be53b43743a","schema_version":"1.0","event_id":"sha256:c7217b9e0ebd1f98e78ff7d53c5a36ded9502255d19ac8c5c7254be53b43743a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QHCEQ2IHEWWWS53UU3A3QA3GYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding a dense submatrix of a random matrix. Sharp bounds for online algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"David Gamarnik, Shankar Bhamidi, Shuyang Gong","submitted_at":"2025-07-25T13:37:19Z","abstract_excerpt":"We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences \\cites{madeira-survey,shabalin2009finding} and is known to exhibit a computation-to-optimization gap between the optimal value and best values achievable by existing polynomial time algorithms. In this paper we consider the class of online algorithms, which includes the best known algorithm for this problem, and derive a tight approximation factor ${4\\over 3\\sqrt{2}}$ for this cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19259","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/2507.19259/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":"2026-07-05T11:43:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9UfIc1+VE2GsGkrIavzPbgB3U0lERDVmSBamBUwl6UKbzBwuxtD+T+96LZ8QPCZqob2Wrmhu/uR3ECJwfwNPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T20:30:30.513727Z"},"content_sha256":"9cf1b29a995598aecf2e26565867eea3ee39ad491122a1502d7880922ceeb628","schema_version":"1.0","event_id":"sha256:9cf1b29a995598aecf2e26565867eea3ee39ad491122a1502d7880922ceeb628"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHCEQ2IHEWWWS53UU3A3QA3GYG/bundle.json","state_url":"https://pith.science/pith/QHCEQ2IHEWWWS53UU3A3QA3GYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHCEQ2IHEWWWS53UU3A3QA3GYG/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":"2026-08-21T20:30:30Z","links":{"resolver":"https://pith.science/pith/QHCEQ2IHEWWWS53UU3A3QA3GYG","bundle":"https://pith.science/pith/QHCEQ2IHEWWWS53UU3A3QA3GYG/bundle.json","state":"https://pith.science/pith/QHCEQ2IHEWWWS53UU3A3QA3GYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHCEQ2IHEWWWS53UU3A3QA3GYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QHCEQ2IHEWWWS53UU3A3QA3GYG","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":"535e933cb08cb83ed72d8a43ae514b3e9be1e0cffb5b8bcce6ea65217f35c576","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-25T13:37:19Z","title_canon_sha256":"ac0bf598f6066756abd11b2f0b38eb9c7ef71ccdf4eeff635f76badb4be7c7e2"},"schema_version":"1.0","source":{"id":"2507.19259","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.19259","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"arxiv_version","alias_value":"2507.19259v1","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.19259","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_12","alias_value":"QHCEQ2IHEWWW","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_16","alias_value":"QHCEQ2IHEWWWS53U","created_at":"2026-07-05T11:43:22Z"},{"alias_kind":"pith_short_8","alias_value":"QHCEQ2IH","created_at":"2026-07-05T11:43:22Z"}],"graph_snapshots":[{"event_id":"sha256:9cf1b29a995598aecf2e26565867eea3ee39ad491122a1502d7880922ceeb628","target":"graph","created_at":"2026-07-05T11:43:22Z","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/2507.19259/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences \\cites{madeira-survey,shabalin2009finding} and is known to exhibit a computation-to-optimization gap between the optimal value and best values achievable by existing polynomial time algorithms. In this paper we consider the class of online algorithms, which includes the best known algorithm for this problem, and derive a tight approximation factor ${4\\over 3\\sqrt{2}}$ for this cla","authors_text":"David Gamarnik, Shankar Bhamidi, Shuyang Gong","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-25T13:37:19Z","title":"Finding a dense submatrix of a random matrix. Sharp bounds for online algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19259","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:c7217b9e0ebd1f98e78ff7d53c5a36ded9502255d19ac8c5c7254be53b43743a","target":"record","created_at":"2026-07-05T11:43:22Z","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":"535e933cb08cb83ed72d8a43ae514b3e9be1e0cffb5b8bcce6ea65217f35c576","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-25T13:37:19Z","title_canon_sha256":"ac0bf598f6066756abd11b2f0b38eb9c7ef71ccdf4eeff635f76badb4be7c7e2"},"schema_version":"1.0","source":{"id":"2507.19259","kind":"arxiv","version":1}},"canonical_sha256":"81c448690725ad697774a6c1b80366c18e6927fd239e189f7f139c6627c2cbdc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81c448690725ad697774a6c1b80366c18e6927fd239e189f7f139c6627c2cbdc","first_computed_at":"2026-07-05T11:43:22.435360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:43:22.435360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uwrGumPIiCsNyevNWlwxcyVUEwn2zMdOnYSsNF40O6SmN9d2QYp/PL0/ON3LhSVXl639QZ6FlfkD9KGy+M6qAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:43:22.435831Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.19259","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7217b9e0ebd1f98e78ff7d53c5a36ded9502255d19ac8c5c7254be53b43743a","sha256:9cf1b29a995598aecf2e26565867eea3ee39ad491122a1502d7880922ceeb628"],"state_sha256":"f3bebdaa2a0a7663cd414a5b33f3e5a5e0e951c2c51fe9e7a10b91e7d0ba94be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3PwndqLVNAKZ5njy/pLMVVYyUkJ5AZ5TwSez4Nw55iL3OjkG8u+AkvseZM0PjIzueDvxFlTBQKZ69tIhIpSSCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T20:30:30.519040Z","bundle_sha256":"6e880c3eafed7219767b56010ad318a44e6a8acea1af57559ffb02cc900f43ed"}}