{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RHKMTK5XLUYP63ZU6C4TI4NHF6","short_pith_number":"pith:RHKMTK5X","canonical_record":{"source":{"id":"1501.04264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-18T04:39:15Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"db4bc44bf765aa1f034cc43d9a1ab4d2c0b1b8e2b808eeeacc819c5f4a51b280","abstract_canon_sha256":"b0647b5b13d0874f178f604c336b66ee089a35ab18b53b398a812df51624e120"},"schema_version":"1.0"},"canonical_sha256":"89d4c9abb75d30ff6f34f0b93471a72fb5b4363c8be58dcf594258d831d6b2f8","source":{"kind":"arxiv","id":"1501.04264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04264","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04264v1","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04264","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"pith_short_12","alias_value":"RHKMTK5XLUYP","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RHKMTK5XLUYP63ZU","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RHKMTK5X","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RHKMTK5XLUYP63ZU6C4TI4NHF6","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-18T04:39:15Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"db4bc44bf765aa1f034cc43d9a1ab4d2c0b1b8e2b808eeeacc819c5f4a51b280","abstract_canon_sha256":"b0647b5b13d0874f178f604c336b66ee089a35ab18b53b398a812df51624e120"},"schema_version":"1.0"},"canonical_sha256":"89d4c9abb75d30ff6f34f0b93471a72fb5b4363c8be58dcf594258d831d6b2f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:09.570921Z","signature_b64":"djAEkDy74Qx7e1jiKUOQA22J2j1AJUm7QhmfXIUknCzsWTjC5T4xIUFH2/Fj67XKKOUnvs1LJMso907Tm9g0DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89d4c9abb75d30ff6f34f0b93471a72fb5b4363c8be58dcf594258d831d6b2f8","last_reissued_at":"2026-05-18T02:29:09.570209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:09.570209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04264","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":"2026-05-18T02:29:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nu4nVtzOjn3Uta954y2UF7mCKiSW6qqvXM0L/kgArHNF1anNYXnGBU8myw5cPk7Sb0U+9BX8mOIxEBy6yCvMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:55:09.677584Z"},"content_sha256":"c7bda6c00d8fa52a967bf442f07eecfbd1f719eab9092992405bc3239bff81af","schema_version":"1.0","event_id":"sha256:c7bda6c00d8fa52a967bf442f07eecfbd1f719eab9092992405bc3239bff81af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RHKMTK5XLUYP63ZU6C4TI4NHF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Achieving Arbitrary Locality and Availability in Binary Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Anyu Wang, Zhifang Zhang","submitted_at":"2015-01-18T04:39:15Z","abstract_excerpt":"The $i$th coordinate of an $(n,k)$ code is said to have locality $r$ and availability $t$ if there exist $t$ disjoint groups, each containing at most $r$ other coordinates that can together recover the value of the $i$th coordinate. This property is particularly useful for codes for distributed storage systems because it permits local repair and parallel accesses of hot data. In this paper, for any positive integers $r$ and $t$, we construct a binary linear code of length $\\binom{r+t}{t}$ which has locality $r$ and availability $t$ for all coordinates. The information rate of this code attains"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04264","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":"2026-05-18T02:29:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mC8j8WC7bI54MsvAi5kDTid/RKJutomYcHHu2Tw1wyTKePfeTBxoAQ3LNPfFa2/aIcx1WyWQpOom/L7OfnJODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:55:09.678225Z"},"content_sha256":"4c80fe5c7013d3a70d36a0627d0e79ee3965645d985f35a3190f7d06342b90cf","schema_version":"1.0","event_id":"sha256:4c80fe5c7013d3a70d36a0627d0e79ee3965645d985f35a3190f7d06342b90cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RHKMTK5XLUYP63ZU6C4TI4NHF6/bundle.json","state_url":"https://pith.science/pith/RHKMTK5XLUYP63ZU6C4TI4NHF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RHKMTK5XLUYP63ZU6C4TI4NHF6/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":"2026-06-11T00:55:09Z","links":{"resolver":"https://pith.science/pith/RHKMTK5XLUYP63ZU6C4TI4NHF6","bundle":"https://pith.science/pith/RHKMTK5XLUYP63ZU6C4TI4NHF6/bundle.json","state":"https://pith.science/pith/RHKMTK5XLUYP63ZU6C4TI4NHF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RHKMTK5XLUYP63ZU6C4TI4NHF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RHKMTK5XLUYP63ZU6C4TI4NHF6","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":"b0647b5b13d0874f178f604c336b66ee089a35ab18b53b398a812df51624e120","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-18T04:39:15Z","title_canon_sha256":"db4bc44bf765aa1f034cc43d9a1ab4d2c0b1b8e2b808eeeacc819c5f4a51b280"},"schema_version":"1.0","source":{"id":"1501.04264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04264","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04264v1","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04264","created_at":"2026-05-18T02:29:09Z"},{"alias_kind":"pith_short_12","alias_value":"RHKMTK5XLUYP","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RHKMTK5XLUYP63ZU","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RHKMTK5X","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:4c80fe5c7013d3a70d36a0627d0e79ee3965645d985f35a3190f7d06342b90cf","target":"graph","created_at":"2026-05-18T02:29:09Z","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":"The $i$th coordinate of an $(n,k)$ code is said to have locality $r$ and availability $t$ if there exist $t$ disjoint groups, each containing at most $r$ other coordinates that can together recover the value of the $i$th coordinate. This property is particularly useful for codes for distributed storage systems because it permits local repair and parallel accesses of hot data. In this paper, for any positive integers $r$ and $t$, we construct a binary linear code of length $\\binom{r+t}{t}$ which has locality $r$ and availability $t$ for all coordinates. The information rate of this code attains","authors_text":"Anyu Wang, Zhifang Zhang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-18T04:39:15Z","title":"Achieving Arbitrary Locality and Availability in Binary Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04264","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:c7bda6c00d8fa52a967bf442f07eecfbd1f719eab9092992405bc3239bff81af","target":"record","created_at":"2026-05-18T02:29:09Z","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":"b0647b5b13d0874f178f604c336b66ee089a35ab18b53b398a812df51624e120","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-01-18T04:39:15Z","title_canon_sha256":"db4bc44bf765aa1f034cc43d9a1ab4d2c0b1b8e2b808eeeacc819c5f4a51b280"},"schema_version":"1.0","source":{"id":"1501.04264","kind":"arxiv","version":1}},"canonical_sha256":"89d4c9abb75d30ff6f34f0b93471a72fb5b4363c8be58dcf594258d831d6b2f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89d4c9abb75d30ff6f34f0b93471a72fb5b4363c8be58dcf594258d831d6b2f8","first_computed_at":"2026-05-18T02:29:09.570209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:09.570209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"djAEkDy74Qx7e1jiKUOQA22J2j1AJUm7QhmfXIUknCzsWTjC5T4xIUFH2/Fj67XKKOUnvs1LJMso907Tm9g0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:09.570921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7bda6c00d8fa52a967bf442f07eecfbd1f719eab9092992405bc3239bff81af","sha256:4c80fe5c7013d3a70d36a0627d0e79ee3965645d985f35a3190f7d06342b90cf"],"state_sha256":"094bbd3f3a75b7f16fff14f5925520d44dabfd06184efa2c93bc9eff44ed2ee6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dUrQvr2VzBNfY00VlJCSsSvtNgfw2SLd1rYQxmzQjN41czKMFD1QpyvoKVuQiF3klAuewq8mROyD8N1vVBIoCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:55:09.682124Z","bundle_sha256":"b1218f1cbe3c46744cfab44e3fda865b251e265e7f2eae51557a9373172d3ec0"}}