{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CAABHQW2YUGI4Q7RHCFYJSMTRL","short_pith_number":"pith:CAABHQW2","canonical_record":{"source":{"id":"1611.06980","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-21T19:57:35Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d9b10b3edb08dce949245aced10faff6f19a9abfb271152edaa88d3906b1acd6","abstract_canon_sha256":"d50224a27974155b9eaa1802fef96bb9121b2f686ec9961cce98fb925cf1b49f"},"schema_version":"1.0"},"canonical_sha256":"100013c2dac50c8e43f1388b84c9938ad5f8c4cf18705144a77940ebc4c8bcf7","source":{"kind":"arxiv","id":"1611.06980","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06980","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06980v2","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06980","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"CAABHQW2YUGI","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CAABHQW2YUGI4Q7R","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CAABHQW2","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CAABHQW2YUGI4Q7RHCFYJSMTRL","target":"record","payload":{"canonical_record":{"source":{"id":"1611.06980","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-21T19:57:35Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"d9b10b3edb08dce949245aced10faff6f19a9abfb271152edaa88d3906b1acd6","abstract_canon_sha256":"d50224a27974155b9eaa1802fef96bb9121b2f686ec9961cce98fb925cf1b49f"},"schema_version":"1.0"},"canonical_sha256":"100013c2dac50c8e43f1388b84c9938ad5f8c4cf18705144a77940ebc4c8bcf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:22.204421Z","signature_b64":"VZ9T+PjNGgRSW+m6kIc1jLlTY48ZkQ90jJ0S4Lo/C/FKJ/wjmb1wSPXZxgsmrTjC3t76RB/UbAJbuptDMvl7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"100013c2dac50c8e43f1388b84c9938ad5f8c4cf18705144a77940ebc4c8bcf7","last_reissued_at":"2026-05-18T00:45:22.203916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:22.203916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1611.06980","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":"2026-05-18T00:45:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U/lC+I61Rwd0qrwbsiNowykRcuIlqPrFVoHxrxN0rzFZfzPzT2ifNyRDQFxRv54RapgZuV9CrXdyhNgDUOBMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:20:53.896955Z"},"content_sha256":"b17cd5baa48253a55f500cbac1df9419ae6456aa13ecaa992a4b415c6f3ba429","schema_version":"1.0","event_id":"sha256:b17cd5baa48253a55f500cbac1df9419ae6456aa13ecaa992a4b415c6f3ba429"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CAABHQW2YUGI4Q7RHCFYJSMTRL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower bounds for 2-query LCCs over large alphabet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.CC","authors_text":"Arnab Bhattacharyya, Avishay Tal, Sivakanth Gopi","submitted_at":"2016-11-21T19:57:35Z","abstract_excerpt":"A locally correctable code (LCC) is an error correcting code that allows correction of any arbitrary coordinate of a corrupted codeword by querying only a few coordinates. We show that any {\\em zero-error} $2$-query locally correctable code $\\mathcal{C}: \\{0,1\\}^k \\to \\Sigma^n$ that can correct a constant fraction of corrupted symbols must have $n \\geq \\exp(k/\\log|\\Sigma|)$. We say that an LCC is zero-error if there exists a non-adaptive corrector algorithm that succeeds with probability $1$ when the input is an uncorrupted codeword. All known constructions of LCCs are zero-error.\n  Our result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06980","kind":"arxiv","version":2},"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":"2026-05-18T00:45:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hxq3oFgxPtmyn/WvGamowDiU4jDTET7JJ01+wR6QN1Bypm9MVpu8m7khFYTVpiZORg5PQtLCH1l0bVjFUt36Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:20:53.897533Z"},"content_sha256":"44f32946adbae1f0b10d78a88be04e696b789dbd873fcd7427c0265825ba3a05","schema_version":"1.0","event_id":"sha256:44f32946adbae1f0b10d78a88be04e696b789dbd873fcd7427c0265825ba3a05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CAABHQW2YUGI4Q7RHCFYJSMTRL/bundle.json","state_url":"https://pith.science/pith/CAABHQW2YUGI4Q7RHCFYJSMTRL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CAABHQW2YUGI4Q7RHCFYJSMTRL/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":"2026-06-11T01:20:53Z","links":{"resolver":"https://pith.science/pith/CAABHQW2YUGI4Q7RHCFYJSMTRL","bundle":"https://pith.science/pith/CAABHQW2YUGI4Q7RHCFYJSMTRL/bundle.json","state":"https://pith.science/pith/CAABHQW2YUGI4Q7RHCFYJSMTRL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CAABHQW2YUGI4Q7RHCFYJSMTRL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CAABHQW2YUGI4Q7RHCFYJSMTRL","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":"d50224a27974155b9eaa1802fef96bb9121b2f686ec9961cce98fb925cf1b49f","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-21T19:57:35Z","title_canon_sha256":"d9b10b3edb08dce949245aced10faff6f19a9abfb271152edaa88d3906b1acd6"},"schema_version":"1.0","source":{"id":"1611.06980","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06980","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06980v2","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06980","created_at":"2026-05-18T00:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"CAABHQW2YUGI","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CAABHQW2YUGI4Q7R","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CAABHQW2","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:44f32946adbae1f0b10d78a88be04e696b789dbd873fcd7427c0265825ba3a05","target":"graph","created_at":"2026-05-18T00:45:22Z","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"},"paper":{"abstract_excerpt":"A locally correctable code (LCC) is an error correcting code that allows correction of any arbitrary coordinate of a corrupted codeword by querying only a few coordinates. We show that any {\\em zero-error} $2$-query locally correctable code $\\mathcal{C}: \\{0,1\\}^k \\to \\Sigma^n$ that can correct a constant fraction of corrupted symbols must have $n \\geq \\exp(k/\\log|\\Sigma|)$. We say that an LCC is zero-error if there exists a non-adaptive corrector algorithm that succeeds with probability $1$ when the input is an uncorrupted codeword. All known constructions of LCCs are zero-error.\n  Our result","authors_text":"Arnab Bhattacharyya, Avishay Tal, Sivakanth Gopi","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-21T19:57:35Z","title":"Lower bounds for 2-query LCCs over large alphabet"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06980","kind":"arxiv","version":2},"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:b17cd5baa48253a55f500cbac1df9419ae6456aa13ecaa992a4b415c6f3ba429","target":"record","created_at":"2026-05-18T00:45:22Z","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":"d50224a27974155b9eaa1802fef96bb9121b2f686ec9961cce98fb925cf1b49f","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2016-11-21T19:57:35Z","title_canon_sha256":"d9b10b3edb08dce949245aced10faff6f19a9abfb271152edaa88d3906b1acd6"},"schema_version":"1.0","source":{"id":"1611.06980","kind":"arxiv","version":2}},"canonical_sha256":"100013c2dac50c8e43f1388b84c9938ad5f8c4cf18705144a77940ebc4c8bcf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"100013c2dac50c8e43f1388b84c9938ad5f8c4cf18705144a77940ebc4c8bcf7","first_computed_at":"2026-05-18T00:45:22.203916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:22.203916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VZ9T+PjNGgRSW+m6kIc1jLlTY48ZkQ90jJ0S4Lo/C/FKJ/wjmb1wSPXZxgsmrTjC3t76RB/UbAJbuptDMvl7Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:22.204421Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06980","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b17cd5baa48253a55f500cbac1df9419ae6456aa13ecaa992a4b415c6f3ba429","sha256:44f32946adbae1f0b10d78a88be04e696b789dbd873fcd7427c0265825ba3a05"],"state_sha256":"522b0993477ff4d5d209fa74acd0457d7cfbde4a1c1d3fa0baa3f0ac49247726"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PJpk4qZUFYysYrH6O084FP6OpBkPbCdaGEFIxlvKffDnpEwiQgc0lUIsfzSUxHiQ3UJnO0gl2xyfAdnuU9vlAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T01:20:53.901164Z","bundle_sha256":"fdf5c32ef2c81218142544d288e099cee9cf5a550966c95d7b2e941884fd9368"}}