{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:XZXE4GXUP4NSLBKIZ6GBRKXUHF","short_pith_number":"pith:XZXE4GXU","canonical_record":{"source":{"id":"2605.07150","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-08T02:36:07Z","cross_cats_sorted":[],"title_canon_sha256":"1eab4b930b623a781fc3b470939b1acaffabf67a5821ceaff6441b3547cde345","abstract_canon_sha256":"1b3bdbdd36988499d5032f4cd074f81fdb90746fe643e4c64e5928f8e8b9b5a6"},"schema_version":"1.0"},"canonical_sha256":"be6e4e1af47f1b258548cf8c18aaf4396f78e34362b87d12ba98ab862e31c9e9","source":{"kind":"arxiv","id":"2605.07150","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.07150","created_at":"2026-06-01T01:02:41Z"},{"alias_kind":"arxiv_version","alias_value":"2605.07150v2","created_at":"2026-06-01T01:02:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.07150","created_at":"2026-06-01T01:02:41Z"},{"alias_kind":"pith_short_12","alias_value":"XZXE4GXUP4NS","created_at":"2026-06-01T01:02:41Z"},{"alias_kind":"pith_short_16","alias_value":"XZXE4GXUP4NSLBKI","created_at":"2026-06-01T01:02:41Z"},{"alias_kind":"pith_short_8","alias_value":"XZXE4GXU","created_at":"2026-06-01T01:02:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:XZXE4GXUP4NSLBKIZ6GBRKXUHF","target":"record","payload":{"canonical_record":{"source":{"id":"2605.07150","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-08T02:36:07Z","cross_cats_sorted":[],"title_canon_sha256":"1eab4b930b623a781fc3b470939b1acaffabf67a5821ceaff6441b3547cde345","abstract_canon_sha256":"1b3bdbdd36988499d5032f4cd074f81fdb90746fe643e4c64e5928f8e8b9b5a6"},"schema_version":"1.0"},"canonical_sha256":"be6e4e1af47f1b258548cf8c18aaf4396f78e34362b87d12ba98ab862e31c9e9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T01:02:41.965599Z","signature_b64":"n2uSk9YhXCBFLIgsxLiU/OOh5l5I3/xZGuwtAhN5qmR5rKLTGjqV+jVPKP1x4g3RFY4eZ3chMpNEBiP4vBlpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"be6e4e1af47f1b258548cf8c18aaf4396f78e34362b87d12ba98ab862e31c9e9","last_reissued_at":"2026-06-01T01:02:41.964469Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T01:02:41.964469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.07150","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":"2026-06-01T01:02:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JEIsBYI6KHgTSMf2mTA64TE0+RqI9AlikCtCYNBVJCUSrpeKsSy6ScMDLTaCbQznDDSGa8f3dUz3vy5N/Z6WDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:36:39.658071Z"},"content_sha256":"60001e1393bfa0e55dc6f52b641763318e6c6f18f54fa6f093fb8f386334cc4e","schema_version":"1.0","event_id":"sha256:60001e1393bfa0e55dc6f52b641763318e6c6f18f54fa6f093fb8f386334cc4e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:XZXE4GXUP4NSLBKIZ6GBRKXUHF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deterministic Monotone Min-Plus Product and Convolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Deterministic algorithm for Monotone Min-Plus Product achieves O(n^{2.686}) time matching the randomized bound","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Barna Saha, Ce Jin, Jaewoo Park, Yinzhan Xu","submitted_at":"2026-05-08T02:36:07Z","abstract_excerpt":"The Monotone Min-Plus Product problem is a useful primitive that has seen many algorithmic applications over the past decade. In this problem, we are given two $n\\times n$ integer matrices $A$ and $B$, where each row of $B$ is a monotone non-decreasing sequence of integers from $\\{1,\\dots,n\\}$, and the goal is to compute their Min-Plus product, defined as the $n\\times n$ matrix $C$ with $C_{i,j} = \\min_{k}\\{A_{i,k} + B_{k,j}\\}$. The fastest known algorithm for this task [Chi, Duan, Xie, and Zhang, STOC'22] runs in $n^{(\\omega+3)/2+o(1)} = O(n^{2.686})$ time, significantly improving over the br"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our main result is a deterministic algorithm for Monotone Min-Plus product with the same time complexity n^{(ω+3)/2+o(1)} = O(n^{2.686}) as its randomized counterpart, improving upon the previous deterministic bound O(n^{2.875}).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The derandomization techniques preserve the exact asymptotic time bound of the randomized algorithm without hidden logarithmic or polynomial factors, and the same techniques extend to the listed variants and applications.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Deterministic Monotone Min-Plus Product in O(n^{2.686}) time matching the randomized bound and derandomizing applications including Language Edit Distance and RNA Folding.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Deterministic algorithm for Monotone Min-Plus Product achieves O(n^{2.686}) time matching the randomized bound","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"93d145e511a9e2ce6052d32d23217ef5d8301fefd2f040b48c311a5822df8fd3"},"source":{"id":"2605.07150","kind":"arxiv","version":2},"verdict":{"id":"96b422e0-9133-4804-aa75-fdc9bc671f60","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-11T01:06:24.308880Z","strongest_claim":"Our main result is a deterministic algorithm for Monotone Min-Plus product with the same time complexity n^{(ω+3)/2+o(1)} = O(n^{2.686}) as its randomized counterpart, improving upon the previous deterministic bound O(n^{2.875}).","one_line_summary":"Deterministic Monotone Min-Plus Product in O(n^{2.686}) time matching the randomized bound and derandomizing applications including Language Edit Distance and RNA Folding.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The derandomization techniques preserve the exact asymptotic time bound of the randomized algorithm without hidden logarithmic or polynomial factors, and the same techniques extend to the listed variants and applications.","pith_extraction_headline":"Deterministic algorithm for Monotone Min-Plus Product achieves O(n^{2.686}) time matching the randomized bound"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.07150/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T11:22:03.372591Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T06:35:53.726718Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T17:01:19.937851Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:02:48.854907Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"0435d8db5d1426e6aed85ca2ef74a01819e30d4ad44224fd27545828d9cc4035"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d79f6afcff0bafb8a433407bf91930677b6a3937dd5149b65ec9e936f45fca32"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"96b422e0-9133-4804-aa75-fdc9bc671f60"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-01T01:02:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TAyd3eW3nn4dYhL6NaVB469ZmgJksFydea/+uJYdT0OsaNyUaLo+YpguYt2Ei32jA451C8ECoRcRNi4RnB9TBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:36:39.659163Z"},"content_sha256":"8ec42a5197d97b0d6b55145f6d594341300a8d06d9c00aff7326babd39f3cbd4","schema_version":"1.0","event_id":"sha256:8ec42a5197d97b0d6b55145f6d594341300a8d06d9c00aff7326babd39f3cbd4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XZXE4GXUP4NSLBKIZ6GBRKXUHF/bundle.json","state_url":"https://pith.science/pith/XZXE4GXUP4NSLBKIZ6GBRKXUHF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XZXE4GXUP4NSLBKIZ6GBRKXUHF/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":"2026-06-06T19:36:39Z","links":{"resolver":"https://pith.science/pith/XZXE4GXUP4NSLBKIZ6GBRKXUHF","bundle":"https://pith.science/pith/XZXE4GXUP4NSLBKIZ6GBRKXUHF/bundle.json","state":"https://pith.science/pith/XZXE4GXUP4NSLBKIZ6GBRKXUHF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XZXE4GXUP4NSLBKIZ6GBRKXUHF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XZXE4GXUP4NSLBKIZ6GBRKXUHF","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":"1b3bdbdd36988499d5032f4cd074f81fdb90746fe643e4c64e5928f8e8b9b5a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-08T02:36:07Z","title_canon_sha256":"1eab4b930b623a781fc3b470939b1acaffabf67a5821ceaff6441b3547cde345"},"schema_version":"1.0","source":{"id":"2605.07150","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.07150","created_at":"2026-06-01T01:02:41Z"},{"alias_kind":"arxiv_version","alias_value":"2605.07150v2","created_at":"2026-06-01T01:02:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.07150","created_at":"2026-06-01T01:02:41Z"},{"alias_kind":"pith_short_12","alias_value":"XZXE4GXUP4NS","created_at":"2026-06-01T01:02:41Z"},{"alias_kind":"pith_short_16","alias_value":"XZXE4GXUP4NSLBKI","created_at":"2026-06-01T01:02:41Z"},{"alias_kind":"pith_short_8","alias_value":"XZXE4GXU","created_at":"2026-06-01T01:02:41Z"}],"graph_snapshots":[{"event_id":"sha256:8ec42a5197d97b0d6b55145f6d594341300a8d06d9c00aff7326babd39f3cbd4","target":"graph","created_at":"2026-06-01T01:02:41Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"Our main result is a deterministic algorithm for Monotone Min-Plus product with the same time complexity n^{(ω+3)/2+o(1)} = O(n^{2.686}) as its randomized counterpart, improving upon the previous deterministic bound O(n^{2.875})."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The derandomization techniques preserve the exact asymptotic time bound of the randomized algorithm without hidden logarithmic or polynomial factors, and the same techniques extend to the listed variants and applications."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Deterministic Monotone Min-Plus Product in O(n^{2.686}) time matching the randomized bound and derandomizing applications including Language Edit Distance and RNA Folding."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Deterministic algorithm for Monotone Min-Plus Product achieves O(n^{2.686}) time matching the randomized bound"}],"snapshot_sha256":"93d145e511a9e2ce6052d32d23217ef5d8301fefd2f040b48c311a5822df8fd3"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d79f6afcff0bafb8a433407bf91930677b6a3937dd5149b65ec9e936f45fca32"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-20T11:22:03.372591Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-20T06:35:53.726718Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T17:01:19.937851Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T12:02:48.854907Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.07150/integrity.json","findings":[],"snapshot_sha256":"0435d8db5d1426e6aed85ca2ef74a01819e30d4ad44224fd27545828d9cc4035","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Monotone Min-Plus Product problem is a useful primitive that has seen many algorithmic applications over the past decade. In this problem, we are given two $n\\times n$ integer matrices $A$ and $B$, where each row of $B$ is a monotone non-decreasing sequence of integers from $\\{1,\\dots,n\\}$, and the goal is to compute their Min-Plus product, defined as the $n\\times n$ matrix $C$ with $C_{i,j} = \\min_{k}\\{A_{i,k} + B_{k,j}\\}$. The fastest known algorithm for this task [Chi, Duan, Xie, and Zhang, STOC'22] runs in $n^{(\\omega+3)/2+o(1)} = O(n^{2.686})$ time, significantly improving over the br","authors_text":"Barna Saha, Ce Jin, Jaewoo Park, Yinzhan Xu","cross_cats":[],"headline":"Deterministic algorithm for Monotone Min-Plus Product achieves O(n^{2.686}) time matching the randomized bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-08T02:36:07Z","title":"Deterministic Monotone Min-Plus Product and Convolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.07150","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-11T01:06:24.308880Z","id":"96b422e0-9133-4804-aa75-fdc9bc671f60","model_set":{"reader":"grok-4.3"},"one_line_summary":"Deterministic Monotone Min-Plus Product in O(n^{2.686}) time matching the randomized bound and derandomizing applications including Language Edit Distance and RNA Folding.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Deterministic algorithm for Monotone Min-Plus Product achieves O(n^{2.686}) time matching the randomized bound","strongest_claim":"Our main result is a deterministic algorithm for Monotone Min-Plus product with the same time complexity n^{(ω+3)/2+o(1)} = O(n^{2.686}) as its randomized counterpart, improving upon the previous deterministic bound O(n^{2.875}).","weakest_assumption":"The derandomization techniques preserve the exact asymptotic time bound of the randomized algorithm without hidden logarithmic or polynomial factors, and the same techniques extend to the listed variants and applications."}},"verdict_id":"96b422e0-9133-4804-aa75-fdc9bc671f60"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:60001e1393bfa0e55dc6f52b641763318e6c6f18f54fa6f093fb8f386334cc4e","target":"record","created_at":"2026-06-01T01:02:41Z","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":"1b3bdbdd36988499d5032f4cd074f81fdb90746fe643e4c64e5928f8e8b9b5a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-05-08T02:36:07Z","title_canon_sha256":"1eab4b930b623a781fc3b470939b1acaffabf67a5821ceaff6441b3547cde345"},"schema_version":"1.0","source":{"id":"2605.07150","kind":"arxiv","version":2}},"canonical_sha256":"be6e4e1af47f1b258548cf8c18aaf4396f78e34362b87d12ba98ab862e31c9e9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be6e4e1af47f1b258548cf8c18aaf4396f78e34362b87d12ba98ab862e31c9e9","first_computed_at":"2026-06-01T01:02:41.964469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-01T01:02:41.964469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n2uSk9YhXCBFLIgsxLiU/OOh5l5I3/xZGuwtAhN5qmR5rKLTGjqV+jVPKP1x4g3RFY4eZ3chMpNEBiP4vBlpAg==","signature_status":"signed_v1","signed_at":"2026-06-01T01:02:41.965599Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.07150","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60001e1393bfa0e55dc6f52b641763318e6c6f18f54fa6f093fb8f386334cc4e","sha256:8ec42a5197d97b0d6b55145f6d594341300a8d06d9c00aff7326babd39f3cbd4"],"state_sha256":"f6032f1439a56dfab8e8b354a7c7878f6ba172cb6f6d4c1718598435f50f34f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VQDBgrBpUlsEn8qIM1vHx0uEipDzI6rzZUdOCVy7Fj5fqW3Z2AciXCvHNc9/noXUuxyOOX2H51oFXCix0F8QBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:36:39.663051Z","bundle_sha256":"ec3a56b4fc2a6f701987b723865ecde06b970a229a987c2ee99115fab208a83a"}}