{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DWW3PQD3XDWEEBTLL6YSTFVBRF","short_pith_number":"pith:DWW3PQD3","canonical_record":{"source":{"id":"1102.4951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-24T10:39:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"50b5f78c98b91ecb92f7693d4040951ca0f3fc9b693e3fb1906b13fbc8f43fb8","abstract_canon_sha256":"23f4abc63cfce8b96b922b4e1109f2f01211886ab3040154e665c1cc5f6a0327"},"schema_version":"1.0"},"canonical_sha256":"1dadb7c07bb8ec42066b5fb12996a1894ce7b554dd81b5a2021b4adb66f0c724","source":{"kind":"arxiv","id":"1102.4951","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4951","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4951v1","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4951","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"DWW3PQD3XDWE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DWW3PQD3XDWEEBTL","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DWW3PQD3","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DWW3PQD3XDWEEBTLL6YSTFVBRF","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4951","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-24T10:39:46Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"50b5f78c98b91ecb92f7693d4040951ca0f3fc9b693e3fb1906b13fbc8f43fb8","abstract_canon_sha256":"23f4abc63cfce8b96b922b4e1109f2f01211886ab3040154e665c1cc5f6a0327"},"schema_version":"1.0"},"canonical_sha256":"1dadb7c07bb8ec42066b5fb12996a1894ce7b554dd81b5a2021b4adb66f0c724","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:57.697206Z","signature_b64":"Sosf0wa3fTgXG6sJsx0pwupn5A9fuTf5dVuFZfNDp4otz/t/SWk9lcuD0lOqsZIcmw+6TdDJBuOw7DGaHN3+Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dadb7c07bb8ec42066b5fb12996a1894ce7b554dd81b5a2021b4adb66f0c724","last_reissued_at":"2026-05-18T04:27:57.696557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:57.696557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4951","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":"2026-05-18T04:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JrKBpFyhxjLEGZxA7Ih3i7BnNabhBRkQEoj4bqGxGUo5zTKtLVLDLprt/BcErQxUMdF/SC2oPqw6Mr4oqQeTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:05:45.726736Z"},"content_sha256":"0824866fad9da6eb01ce633f0bce818acecdc92b5efeaae448943a0e82507b50","schema_version":"1.0","event_id":"sha256:0824866fad9da6eb01ce633f0bce818acecdc92b5efeaae448943a0e82507b50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DWW3PQD3XDWEEBTLL6YSTFVBRF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Combinatorial Batch Codes: A Lower Bound and Optimal Constructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Bimal Roy, Srimanta Bhattacharya, Sushmita Ruj","submitted_at":"2011-02-24T10:39:46Z","abstract_excerpt":"Batch codes, introduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [1], are methods for solving the following data storage problem: n data items are to be stored in m servers in such a way that any k of the n items can be retrieved by reading at most t items from each server, and that the total number of items stored in m servers is N . A Combinatorial batch code (CBC) is a batch code where each data item is stored without change, i.e., each stored data item is a copy of one of the n data items. One of the basic yet challenging problems is to find optimal CBCs, i.e., CBCs for which total st"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4951","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":"2026-05-18T04:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DSUpGEoT4e9SBa1nrNtO8gPFtZ+rlwjIFLYl3MhavnlrrLnl/WYkTaxpZnItFjhXOL6yCR3AiB4utRXGZIc3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:05:45.727390Z"},"content_sha256":"c8a60ace34572a9f5a0e3b2dff3e35d47104a1d336ea01b5aa32037ab4b6ed6c","schema_version":"1.0","event_id":"sha256:c8a60ace34572a9f5a0e3b2dff3e35d47104a1d336ea01b5aa32037ab4b6ed6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DWW3PQD3XDWEEBTLL6YSTFVBRF/bundle.json","state_url":"https://pith.science/pith/DWW3PQD3XDWEEBTLL6YSTFVBRF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DWW3PQD3XDWEEBTLL6YSTFVBRF/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":"2026-05-27T09:05:45Z","links":{"resolver":"https://pith.science/pith/DWW3PQD3XDWEEBTLL6YSTFVBRF","bundle":"https://pith.science/pith/DWW3PQD3XDWEEBTLL6YSTFVBRF/bundle.json","state":"https://pith.science/pith/DWW3PQD3XDWEEBTLL6YSTFVBRF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DWW3PQD3XDWEEBTLL6YSTFVBRF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DWW3PQD3XDWEEBTLL6YSTFVBRF","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":"23f4abc63cfce8b96b922b4e1109f2f01211886ab3040154e665c1cc5f6a0327","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-24T10:39:46Z","title_canon_sha256":"50b5f78c98b91ecb92f7693d4040951ca0f3fc9b693e3fb1906b13fbc8f43fb8"},"schema_version":"1.0","source":{"id":"1102.4951","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4951","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4951v1","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4951","created_at":"2026-05-18T04:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"DWW3PQD3XDWE","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DWW3PQD3XDWEEBTL","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DWW3PQD3","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:c8a60ace34572a9f5a0e3b2dff3e35d47104a1d336ea01b5aa32037ab4b6ed6c","target":"graph","created_at":"2026-05-18T04:27:57Z","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":"Batch codes, introduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [1], are methods for solving the following data storage problem: n data items are to be stored in m servers in such a way that any k of the n items can be retrieved by reading at most t items from each server, and that the total number of items stored in m servers is N . A Combinatorial batch code (CBC) is a batch code where each data item is stored without change, i.e., each stored data item is a copy of one of the n data items. One of the basic yet challenging problems is to find optimal CBCs, i.e., CBCs for which total st","authors_text":"Bimal Roy, Srimanta Bhattacharya, Sushmita Ruj","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-24T10:39:46Z","title":"Combinatorial Batch Codes: A Lower Bound and Optimal Constructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4951","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":"sha256:0824866fad9da6eb01ce633f0bce818acecdc92b5efeaae448943a0e82507b50","target":"record","created_at":"2026-05-18T04:27:57Z","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":"23f4abc63cfce8b96b922b4e1109f2f01211886ab3040154e665c1cc5f6a0327","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-24T10:39:46Z","title_canon_sha256":"50b5f78c98b91ecb92f7693d4040951ca0f3fc9b693e3fb1906b13fbc8f43fb8"},"schema_version":"1.0","source":{"id":"1102.4951","kind":"arxiv","version":1}},"canonical_sha256":"1dadb7c07bb8ec42066b5fb12996a1894ce7b554dd81b5a2021b4adb66f0c724","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dadb7c07bb8ec42066b5fb12996a1894ce7b554dd81b5a2021b4adb66f0c724","first_computed_at":"2026-05-18T04:27:57.696557Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:57.696557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sosf0wa3fTgXG6sJsx0pwupn5A9fuTf5dVuFZfNDp4otz/t/SWk9lcuD0lOqsZIcmw+6TdDJBuOw7DGaHN3+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:57.697206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4951","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0824866fad9da6eb01ce633f0bce818acecdc92b5efeaae448943a0e82507b50","sha256:c8a60ace34572a9f5a0e3b2dff3e35d47104a1d336ea01b5aa32037ab4b6ed6c"],"state_sha256":"c2963890a36546f9c61fa60b9b114ee73785eaf1db5c48dc31951b5a7d51ae7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dGLOr1dXQ60oyGpsU4CVBbhnAXyDHYi9Y5FjUBkWe9KSv4IzSbZKhLZVBiGEqmEpLyFEsdkJWtU1d2GAdmX5Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:05:45.730932Z","bundle_sha256":"fe5874a71bfbe0a21edfe519f32cad79d9c8dd5fb1cb8479d374bca2f8f7a242"}}