{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:P5JUX2AD3WMEEJ3J4THRSJCBYV","short_pith_number":"pith:P5JUX2AD","canonical_record":{"source":{"id":"1705.11095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-30T15:01:22Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"93542853e426b3932ba67beff84d040a01b703c148f5b113299780a3f7771283","abstract_canon_sha256":"493ea92631a6d3702df4b8db0465dfb3564c8e2664702e7540aca1eea0909ed1"},"schema_version":"1.0"},"canonical_sha256":"7f534be803dd98422769e4cf192441c55bc37ded58431bfe1951d09aba177d9d","source":{"kind":"arxiv","id":"1705.11095","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.11095","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"arxiv_version","alias_value":"1705.11095v1","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.11095","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"pith_short_12","alias_value":"P5JUX2AD3WME","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P5JUX2AD3WMEEJ3J","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P5JUX2AD","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:P5JUX2AD3WMEEJ3J4THRSJCBYV","target":"record","payload":{"canonical_record":{"source":{"id":"1705.11095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-30T15:01:22Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"93542853e426b3932ba67beff84d040a01b703c148f5b113299780a3f7771283","abstract_canon_sha256":"493ea92631a6d3702df4b8db0465dfb3564c8e2664702e7540aca1eea0909ed1"},"schema_version":"1.0"},"canonical_sha256":"7f534be803dd98422769e4cf192441c55bc37ded58431bfe1951d09aba177d9d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:19.304453Z","signature_b64":"hBGpnUct6jtoPu2Zo4WIaG6HVhN7CAdwgOMKiM0P0H4jvrsBrllxd57vSpjn3GjexlO82qkYdvmpP20PBnuoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f534be803dd98422769e4cf192441c55bc37ded58431bfe1951d09aba177d9d","last_reissued_at":"2026-05-18T00:43:19.303841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:19.303841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.11095","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":"2026-05-18T00:43:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"083rsBie69/znTqlVZ+FYELKg+4IwScqFDy3VXyV3QXb6aR2AwEiPJHkR+xpxXB44wG9ZYQvyj5uV42mmlxsDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:06:16.493799Z"},"content_sha256":"efe9390e2c18dae60340bedd1771e9e516699a5f10e77bfb4acb4c6f90dd7447","schema_version":"1.0","event_id":"sha256:efe9390e2c18dae60340bedd1771e9e516699a5f10e77bfb4acb4c6f90dd7447"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:P5JUX2AD3WMEEJ3J4THRSJCBYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On One Generalization of LRC Codes with Availability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alexey Frolov, Marina Dudina, Stanislav Kruglik, Valeriya Potapova","submitted_at":"2017-05-30T15:01:22Z","abstract_excerpt":"We investigate one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable code rate and still meet load balancing requirements. In this paper we derive an upper bound for the rate of such codes and give explicit constructions of codes with such a property. These constructions utilize LRC codes developed by Wang et al."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.11095","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":"2026-05-18T00:43:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4+03pLdQdVKAhrxcQgHmpNxDMcHhgloZiSy0ygkPlDKtRqA3RvyFWhmzLKHewWoVS3ziPbhKBF3Oib+XfWODQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:06:16.494148Z"},"content_sha256":"29fdf72345f8c3f5f8b2e4cc653433889faac572e86b918331bc367614a0e52c","schema_version":"1.0","event_id":"sha256:29fdf72345f8c3f5f8b2e4cc653433889faac572e86b918331bc367614a0e52c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5JUX2AD3WMEEJ3J4THRSJCBYV/bundle.json","state_url":"https://pith.science/pith/P5JUX2AD3WMEEJ3J4THRSJCBYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5JUX2AD3WMEEJ3J4THRSJCBYV/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":"2026-06-26T07:06:16Z","links":{"resolver":"https://pith.science/pith/P5JUX2AD3WMEEJ3J4THRSJCBYV","bundle":"https://pith.science/pith/P5JUX2AD3WMEEJ3J4THRSJCBYV/bundle.json","state":"https://pith.science/pith/P5JUX2AD3WMEEJ3J4THRSJCBYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5JUX2AD3WMEEJ3J4THRSJCBYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P5JUX2AD3WMEEJ3J4THRSJCBYV","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":"493ea92631a6d3702df4b8db0465dfb3564c8e2664702e7540aca1eea0909ed1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-30T15:01:22Z","title_canon_sha256":"93542853e426b3932ba67beff84d040a01b703c148f5b113299780a3f7771283"},"schema_version":"1.0","source":{"id":"1705.11095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.11095","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"arxiv_version","alias_value":"1705.11095v1","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.11095","created_at":"2026-05-18T00:43:19Z"},{"alias_kind":"pith_short_12","alias_value":"P5JUX2AD3WME","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P5JUX2AD3WMEEJ3J","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P5JUX2AD","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:29fdf72345f8c3f5f8b2e4cc653433889faac572e86b918331bc367614a0e52c","target":"graph","created_at":"2026-05-18T00:43:19Z","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":"We investigate one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable code rate and still meet load balancing requirements. In this paper we derive an upper bound for the rate of such codes and give explicit constructions of codes with such a property. These constructions utilize LRC codes developed by Wang et al.","authors_text":"Alexey Frolov, Marina Dudina, Stanislav Kruglik, Valeriya Potapova","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-30T15:01:22Z","title":"On One Generalization of LRC Codes with Availability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.11095","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:efe9390e2c18dae60340bedd1771e9e516699a5f10e77bfb4acb4c6f90dd7447","target":"record","created_at":"2026-05-18T00:43:19Z","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":"493ea92631a6d3702df4b8db0465dfb3564c8e2664702e7540aca1eea0909ed1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-05-30T15:01:22Z","title_canon_sha256":"93542853e426b3932ba67beff84d040a01b703c148f5b113299780a3f7771283"},"schema_version":"1.0","source":{"id":"1705.11095","kind":"arxiv","version":1}},"canonical_sha256":"7f534be803dd98422769e4cf192441c55bc37ded58431bfe1951d09aba177d9d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f534be803dd98422769e4cf192441c55bc37ded58431bfe1951d09aba177d9d","first_computed_at":"2026-05-18T00:43:19.303841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:19.303841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hBGpnUct6jtoPu2Zo4WIaG6HVhN7CAdwgOMKiM0P0H4jvrsBrllxd57vSpjn3GjexlO82qkYdvmpP20PBnuoBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:19.304453Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.11095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efe9390e2c18dae60340bedd1771e9e516699a5f10e77bfb4acb4c6f90dd7447","sha256:29fdf72345f8c3f5f8b2e4cc653433889faac572e86b918331bc367614a0e52c"],"state_sha256":"4201e08c71d105fd4a9096d6051cad78a52d032e5684de84f3857aa29a9ac299"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nRadMfsCkG6/H5Qy/z+FTaDGrzK8s5EaikkUuDHbKRuw5BtAcoY9Z0gNtprhNBPom6xmv+MuHtHXkTNpINTECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T07:06:16.496120Z","bundle_sha256":"7d728ecce6c475903d8c1385129d88f385740db13396db4ff9d05ea6efb63426"}}