{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XNMDZ7GZEREPX5ACGMO27TQMDK","short_pith_number":"pith:XNMDZ7GZ","canonical_record":{"source":{"id":"1507.04645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-07-16T16:42:09Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"8a8a7459e6496957b857c3f983a227025ede3d3b18c31b5963fad73c0ef5a744","abstract_canon_sha256":"1daa0fc01b5a3daa27b0aa125f84e55312970af4681e4eed9f9db1812a055a2f"},"schema_version":"1.0"},"canonical_sha256":"bb583cfcd92448fbf402331dafce0c1ab4c36cf70331d8ba2de2e98af7160d5c","source":{"kind":"arxiv","id":"1507.04645","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04645","created_at":"2026-05-18T01:35:34Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04645v1","created_at":"2026-05-18T01:35:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04645","created_at":"2026-05-18T01:35:34Z"},{"alias_kind":"pith_short_12","alias_value":"XNMDZ7GZEREP","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XNMDZ7GZEREPX5AC","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XNMDZ7GZ","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XNMDZ7GZEREPX5ACGMO27TQMDK","target":"record","payload":{"canonical_record":{"source":{"id":"1507.04645","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-07-16T16:42:09Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"8a8a7459e6496957b857c3f983a227025ede3d3b18c31b5963fad73c0ef5a744","abstract_canon_sha256":"1daa0fc01b5a3daa27b0aa125f84e55312970af4681e4eed9f9db1812a055a2f"},"schema_version":"1.0"},"canonical_sha256":"bb583cfcd92448fbf402331dafce0c1ab4c36cf70331d8ba2de2e98af7160d5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:34.590867Z","signature_b64":"5MkRu7kysJZgpKgiBLa2jGqUF3pkqP2QyulXfoRS+XGZj3I42BA0LhOktaEKWR4qzr3fif1mdm6reiV0+VVNDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb583cfcd92448fbf402331dafce0c1ab4c36cf70331d8ba2de2e98af7160d5c","last_reissued_at":"2026-05-18T01:35:34.590205Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:34.590205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.04645","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":"2026-05-18T01:35:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UVM4pjxXhmRIYZKGBJ5qM26XnT7NTYcc19j1SCRRTJJjS/k7MBTs++gWVDzetg4jFc61ms/pL+NRY0bERDpcDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:45:00.050817Z"},"content_sha256":"6f0c4c2f8f64ad4ad511985c9ff3bca9bf8d64730db1f6008d9d42d9d3a3c733","schema_version":"1.0","event_id":"sha256:6f0c4c2f8f64ad4ad511985c9ff3bca9bf8d64730db1f6008d9d42d9d3a3c733"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XNMDZ7GZEREPX5ACGMO27TQMDK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Incidence Geometries and the Pass Complexity of Semi-Streaming Set Cover","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Amit Chakrabarti, Anthony Wirth","submitted_at":"2015-07-16T16:42:09Z","abstract_excerpt":"Set cover, over a universe of size $n$, may be modelled as a data-streaming problem, where the $m$ sets that comprise the instance are to be read one by one. A semi-streaming algorithm is allowed only $O(n\\, \\mathrm{poly}\\{\\log n, \\log m\\})$ space to process this stream. For each $p \\ge 1$, we give a very simple deterministic algorithm that makes $p$ passes over the input stream and returns an appropriately certified $(p+1)n^{1/(p+1)}$-approximation to the optimum set cover. More importantly, we proceed to show that this approximation factor is essentially tight, by showing that a factor bette"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04645","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":"2026-05-18T01:35:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4VguTHrpJyChHJzB5ImIQcWdOBrKPb34tBjF4IXb2DUxzZs+DbV/wa3GTYg9820bwriDRTCr1yg9ns8lcMHTDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T21:45:00.051551Z"},"content_sha256":"592cb3b9f013c1e9c3c796a3044a6a8df3273eb7c47dcd86ad443e2059a4ceaf","schema_version":"1.0","event_id":"sha256:592cb3b9f013c1e9c3c796a3044a6a8df3273eb7c47dcd86ad443e2059a4ceaf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XNMDZ7GZEREPX5ACGMO27TQMDK/bundle.json","state_url":"https://pith.science/pith/XNMDZ7GZEREPX5ACGMO27TQMDK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XNMDZ7GZEREPX5ACGMO27TQMDK/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":"2026-05-27T21:45:00Z","links":{"resolver":"https://pith.science/pith/XNMDZ7GZEREPX5ACGMO27TQMDK","bundle":"https://pith.science/pith/XNMDZ7GZEREPX5ACGMO27TQMDK/bundle.json","state":"https://pith.science/pith/XNMDZ7GZEREPX5ACGMO27TQMDK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XNMDZ7GZEREPX5ACGMO27TQMDK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XNMDZ7GZEREPX5ACGMO27TQMDK","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":"1daa0fc01b5a3daa27b0aa125f84e55312970af4681e4eed9f9db1812a055a2f","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-07-16T16:42:09Z","title_canon_sha256":"8a8a7459e6496957b857c3f983a227025ede3d3b18c31b5963fad73c0ef5a744"},"schema_version":"1.0","source":{"id":"1507.04645","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04645","created_at":"2026-05-18T01:35:34Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04645v1","created_at":"2026-05-18T01:35:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04645","created_at":"2026-05-18T01:35:34Z"},{"alias_kind":"pith_short_12","alias_value":"XNMDZ7GZEREP","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XNMDZ7GZEREPX5AC","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XNMDZ7GZ","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:592cb3b9f013c1e9c3c796a3044a6a8df3273eb7c47dcd86ad443e2059a4ceaf","target":"graph","created_at":"2026-05-18T01:35:34Z","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":"Set cover, over a universe of size $n$, may be modelled as a data-streaming problem, where the $m$ sets that comprise the instance are to be read one by one. A semi-streaming algorithm is allowed only $O(n\\, \\mathrm{poly}\\{\\log n, \\log m\\})$ space to process this stream. For each $p \\ge 1$, we give a very simple deterministic algorithm that makes $p$ passes over the input stream and returns an appropriately certified $(p+1)n^{1/(p+1)}$-approximation to the optimum set cover. More importantly, we proceed to show that this approximation factor is essentially tight, by showing that a factor bette","authors_text":"Amit Chakrabarti, Anthony Wirth","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-07-16T16:42:09Z","title":"Incidence Geometries and the Pass Complexity of Semi-Streaming Set Cover"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04645","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":"sha256:6f0c4c2f8f64ad4ad511985c9ff3bca9bf8d64730db1f6008d9d42d9d3a3c733","target":"record","created_at":"2026-05-18T01:35:34Z","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":"1daa0fc01b5a3daa27b0aa125f84e55312970af4681e4eed9f9db1812a055a2f","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-07-16T16:42:09Z","title_canon_sha256":"8a8a7459e6496957b857c3f983a227025ede3d3b18c31b5963fad73c0ef5a744"},"schema_version":"1.0","source":{"id":"1507.04645","kind":"arxiv","version":1}},"canonical_sha256":"bb583cfcd92448fbf402331dafce0c1ab4c36cf70331d8ba2de2e98af7160d5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb583cfcd92448fbf402331dafce0c1ab4c36cf70331d8ba2de2e98af7160d5c","first_computed_at":"2026-05-18T01:35:34.590205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:34.590205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5MkRu7kysJZgpKgiBLa2jGqUF3pkqP2QyulXfoRS+XGZj3I42BA0LhOktaEKWR4qzr3fif1mdm6reiV0+VVNDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:34.590867Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04645","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f0c4c2f8f64ad4ad511985c9ff3bca9bf8d64730db1f6008d9d42d9d3a3c733","sha256:592cb3b9f013c1e9c3c796a3044a6a8df3273eb7c47dcd86ad443e2059a4ceaf"],"state_sha256":"68dd49b1ae4984e7fd2f700f60a2729ce8034d6d003ea35c70afebd481839e6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2fb99D3WWjAPYxeJ7ubYsj7Ok8zq/4YnaocSU3+inAFbf3BC3kvrW5QgYivOXPukrOtIdbVr8XzGrJyVYhFlBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T21:45:00.055509Z","bundle_sha256":"9ffab81608c869da1200ce2d130f21ac19a9194ef13bbdeaff7e89c82641a091"}}