{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:XLWHZRRMQMMNCCFODFRAOT2IRP","short_pith_number":"pith:XLWHZRRM","canonical_record":{"source":{"id":"2007.03039","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-07-06T19:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"cfbbe7bbb6010f7ba9ca092857a458060a491ebb373efc78602c0f3936d56d2f","abstract_canon_sha256":"57475b540b7cde714e4020be188f66a0232471ec1932eb7b249429100a9bf98f"},"schema_version":"1.0"},"canonical_sha256":"baec7cc62c8318d108ae1962074f488bd29478fd8ee5799b840bb4c438ecf31a","source":{"kind":"arxiv","id":"2007.03039","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.03039","created_at":"2026-07-05T01:16:58Z"},{"alias_kind":"arxiv_version","alias_value":"2007.03039v1","created_at":"2026-07-05T01:16:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.03039","created_at":"2026-07-05T01:16:58Z"},{"alias_kind":"pith_short_12","alias_value":"XLWHZRRMQMMN","created_at":"2026-07-05T01:16:58Z"},{"alias_kind":"pith_short_16","alias_value":"XLWHZRRMQMMNCCFO","created_at":"2026-07-05T01:16:58Z"},{"alias_kind":"pith_short_8","alias_value":"XLWHZRRM","created_at":"2026-07-05T01:16:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:XLWHZRRMQMMNCCFODFRAOT2IRP","target":"record","payload":{"canonical_record":{"source":{"id":"2007.03039","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-07-06T19:57:52Z","cross_cats_sorted":[],"title_canon_sha256":"cfbbe7bbb6010f7ba9ca092857a458060a491ebb373efc78602c0f3936d56d2f","abstract_canon_sha256":"57475b540b7cde714e4020be188f66a0232471ec1932eb7b249429100a9bf98f"},"schema_version":"1.0"},"canonical_sha256":"baec7cc62c8318d108ae1962074f488bd29478fd8ee5799b840bb4c438ecf31a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:16:58.980441Z","signature_b64":"Mr/MR8JM//tmzJTvA27yxCMIKCSD3jzp3wUPR9A7Q2tA63RoBmJp/skt+1HP1jnHqhdmFHGadATXhdyP3WYMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baec7cc62c8318d108ae1962074f488bd29478fd8ee5799b840bb4c438ecf31a","last_reissued_at":"2026-07-05T01:16:58.980043Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:16:58.980043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.03039","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":"2026-07-05T01:16:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bK/xuJzCLOqxE8IOZNfZPoU2a4wA4lRo7s3lfVbXPEuhcw7ffGshVe012ushOv2IB2VNfeCNqUppHhoEtZd1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T13:33:37.016384Z"},"content_sha256":"436e29c881a0bcc9c82128b354602025437623fb0a07d0a90f772f72b5fa12ed","schema_version":"1.0","event_id":"sha256:436e29c881a0bcc9c82128b354602025437623fb0a07d0a90f772f72b5fa12ed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:XLWHZRRMQMMNCCFODFRAOT2IRP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Streaming Verification for Graph Problems: Optimal Tradeoffs and Nonlinear Sketches","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amit Chakrabarti, Justin Thaler, Prantar Ghosh","submitted_at":"2020-07-06T19:57:52Z","abstract_excerpt":"We study graph computations in an enhanced data streaming setting, where a space-bounded client reading the edge stream of a massive graph may delegate some of its work to a cloud service. We seek algorithms that allow the client to verify a purported proof sent by the cloud service that the work done in the cloud is correct. A line of work starting with Chakrabarti et al. (ICALP 2009) has provided such algorithms, which we call schemes, for several statistical and graph-theoretic problems, many of which exhibit a tradeoff between the length of the proof and the space used by the streaming ver"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.03039","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/2007.03039/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":"2026-07-05T01:16:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vKkOy71JX5SqOl6naR/E5MQNWXR6VYTgiQAkHQy7MYkdjwIgfEGbj3thqRoELAWlFsZK23JRVUhH7wUDK0zUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T13:33:37.017029Z"},"content_sha256":"3a0f5774603de463a7e7fcfaadcdaa395a3e8a508f0251e426a72b2af1e1248e","schema_version":"1.0","event_id":"sha256:3a0f5774603de463a7e7fcfaadcdaa395a3e8a508f0251e426a72b2af1e1248e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XLWHZRRMQMMNCCFODFRAOT2IRP/bundle.json","state_url":"https://pith.science/pith/XLWHZRRMQMMNCCFODFRAOT2IRP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XLWHZRRMQMMNCCFODFRAOT2IRP/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":"2026-07-05T13:33:37Z","links":{"resolver":"https://pith.science/pith/XLWHZRRMQMMNCCFODFRAOT2IRP","bundle":"https://pith.science/pith/XLWHZRRMQMMNCCFODFRAOT2IRP/bundle.json","state":"https://pith.science/pith/XLWHZRRMQMMNCCFODFRAOT2IRP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XLWHZRRMQMMNCCFODFRAOT2IRP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:XLWHZRRMQMMNCCFODFRAOT2IRP","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":"57475b540b7cde714e4020be188f66a0232471ec1932eb7b249429100a9bf98f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-07-06T19:57:52Z","title_canon_sha256":"cfbbe7bbb6010f7ba9ca092857a458060a491ebb373efc78602c0f3936d56d2f"},"schema_version":"1.0","source":{"id":"2007.03039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.03039","created_at":"2026-07-05T01:16:58Z"},{"alias_kind":"arxiv_version","alias_value":"2007.03039v1","created_at":"2026-07-05T01:16:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.03039","created_at":"2026-07-05T01:16:58Z"},{"alias_kind":"pith_short_12","alias_value":"XLWHZRRMQMMN","created_at":"2026-07-05T01:16:58Z"},{"alias_kind":"pith_short_16","alias_value":"XLWHZRRMQMMNCCFO","created_at":"2026-07-05T01:16:58Z"},{"alias_kind":"pith_short_8","alias_value":"XLWHZRRM","created_at":"2026-07-05T01:16:58Z"}],"graph_snapshots":[{"event_id":"sha256:3a0f5774603de463a7e7fcfaadcdaa395a3e8a508f0251e426a72b2af1e1248e","target":"graph","created_at":"2026-07-05T01:16:58Z","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/2007.03039/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study graph computations in an enhanced data streaming setting, where a space-bounded client reading the edge stream of a massive graph may delegate some of its work to a cloud service. We seek algorithms that allow the client to verify a purported proof sent by the cloud service that the work done in the cloud is correct. A line of work starting with Chakrabarti et al. (ICALP 2009) has provided such algorithms, which we call schemes, for several statistical and graph-theoretic problems, many of which exhibit a tradeoff between the length of the proof and the space used by the streaming ver","authors_text":"Amit Chakrabarti, Justin Thaler, Prantar Ghosh","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-07-06T19:57:52Z","title":"Streaming Verification for Graph Problems: Optimal Tradeoffs and Nonlinear Sketches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.03039","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":"sha256:436e29c881a0bcc9c82128b354602025437623fb0a07d0a90f772f72b5fa12ed","target":"record","created_at":"2026-07-05T01:16:58Z","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":"57475b540b7cde714e4020be188f66a0232471ec1932eb7b249429100a9bf98f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2020-07-06T19:57:52Z","title_canon_sha256":"cfbbe7bbb6010f7ba9ca092857a458060a491ebb373efc78602c0f3936d56d2f"},"schema_version":"1.0","source":{"id":"2007.03039","kind":"arxiv","version":1}},"canonical_sha256":"baec7cc62c8318d108ae1962074f488bd29478fd8ee5799b840bb4c438ecf31a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baec7cc62c8318d108ae1962074f488bd29478fd8ee5799b840bb4c438ecf31a","first_computed_at":"2026-07-05T01:16:58.980043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:16:58.980043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mr/MR8JM//tmzJTvA27yxCMIKCSD3jzp3wUPR9A7Q2tA63RoBmJp/skt+1HP1jnHqhdmFHGadATXhdyP3WYMBw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:16:58.980441Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.03039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:436e29c881a0bcc9c82128b354602025437623fb0a07d0a90f772f72b5fa12ed","sha256:3a0f5774603de463a7e7fcfaadcdaa395a3e8a508f0251e426a72b2af1e1248e"],"state_sha256":"a2bcfaf099f780fdc5de7dbda763b107f57a5971e8ba48cbcb8a1c0a76b8d68a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xwfjNEz72DtBU3LZrFk78mi0YRLY4eOuvcTn7Aj3DWsR2HQ+FS3OX+FAdysr4APByB2rcaXDq5g2RnNSrLrRCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T13:33:37.020785Z","bundle_sha256":"0c6106b8f4eb076a9913a9a33a024970f15fec6bf89c687a16eb95c8845e90d1"}}