{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:2DAYZJSKK3EUVCFPBIFLDIKBPT","short_pith_number":"pith:2DAYZJSK","canonical_record":{"source":{"id":"1301.6157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-25T20:52:06Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e04fac8e8a33c78e1a4d0e1b0a6d9292d07649df6fcc2e9f1f1c351a948d2c73","abstract_canon_sha256":"58c660defa04aa74a5fdfbabb458b901c73bf733747f2aeb5ed4abf8234493ed"},"schema_version":"1.0"},"canonical_sha256":"d0c18ca64a56c94a88af0a0ab1a1417ce4ba8a0bad35d2a137da443ea7d1b23b","source":{"kind":"arxiv","id":"1301.6157","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6157","created_at":"2026-05-18T03:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6157v2","created_at":"2026-05-18T03:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6157","created_at":"2026-05-18T03:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"2DAYZJSKK3EU","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2DAYZJSKK3EUVCFP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2DAYZJSK","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:2DAYZJSKK3EUVCFPBIFLDIKBPT","target":"record","payload":{"canonical_record":{"source":{"id":"1301.6157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-25T20:52:06Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e04fac8e8a33c78e1a4d0e1b0a6d9292d07649df6fcc2e9f1f1c351a948d2c73","abstract_canon_sha256":"58c660defa04aa74a5fdfbabb458b901c73bf733747f2aeb5ed4abf8234493ed"},"schema_version":"1.0"},"canonical_sha256":"d0c18ca64a56c94a88af0a0ab1a1417ce4ba8a0bad35d2a137da443ea7d1b23b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:20.376354Z","signature_b64":"komPtwk8uH7ixk6eEudXL4Ne+X7KQXvOOCCSJ2T5QQayKDxvcyXHO1knR5bZD+6qea8YvQiA88mepPSWITkLAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0c18ca64a56c94a88af0a0ab1a1417ce4ba8a0bad35d2a137da443ea7d1b23b","last_reissued_at":"2026-05-18T03:31:20.375459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:20.375459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.6157","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":"2026-05-18T03:31:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HEaj3DQbid+lXdBSsz16V0oaabH4gMFpUgGZhqwMYyQ60FUFpzJllQtBgOh6kUFkgJU9tl0BuVIZG88Qoa5+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:25:42.793723Z"},"content_sha256":"3ecd70ab7ceed05d9d0cfec08606d371074be3bd6897c39d57be8cab36fcc6bc","schema_version":"1.0","event_id":"sha256:3ecd70ab7ceed05d9d0cfec08606d371074be3bd6897c39d57be8cab36fcc6bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:2DAYZJSKK3EUVCFPBIFLDIKBPT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"High-Rate Regenerating Codes Through Layering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Birenjith Sasidharan, P. Vijay Kumar","submitted_at":"2013-01-25T20:52:06Z","abstract_excerpt":"In this paper, we provide explicit constructions for a class of exact-repair regenerating codes that possess a layered structure. These regenerating codes correspond to interior points on the storage-repair-bandwidth tradeoff, and compare very well in comparison to scheme that employs space-sharing between MSR and MBR codes. For the parameter set $(n,k,d=k)$ with $n < 2k-1$, we construct a class of codes with an auxiliary parameter $w$, referred to as canonical codes. With $w$ in the range $n-k < w < k$, these codes operate in the region between the MSR point and the MBR point, and perform sig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6157","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":"2026-05-18T03:31:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pJS2C48JB6R1KTXOgrqQx6durEtiXpFcZtax2gIWHNnrppOES7a6EZrIEBaohAN1g1etddhkxT4M4gInZ+/JCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:25:42.794357Z"},"content_sha256":"237110d3906ba8ae4b942e4bd0d682a09aa6fdef752278d9e7a278a64803c1eb","schema_version":"1.0","event_id":"sha256:237110d3906ba8ae4b942e4bd0d682a09aa6fdef752278d9e7a278a64803c1eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2DAYZJSKK3EUVCFPBIFLDIKBPT/bundle.json","state_url":"https://pith.science/pith/2DAYZJSKK3EUVCFPBIFLDIKBPT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2DAYZJSKK3EUVCFPBIFLDIKBPT/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":"2026-05-31T07:25:42Z","links":{"resolver":"https://pith.science/pith/2DAYZJSKK3EUVCFPBIFLDIKBPT","bundle":"https://pith.science/pith/2DAYZJSKK3EUVCFPBIFLDIKBPT/bundle.json","state":"https://pith.science/pith/2DAYZJSKK3EUVCFPBIFLDIKBPT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2DAYZJSKK3EUVCFPBIFLDIKBPT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:2DAYZJSKK3EUVCFPBIFLDIKBPT","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":"58c660defa04aa74a5fdfbabb458b901c73bf733747f2aeb5ed4abf8234493ed","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-25T20:52:06Z","title_canon_sha256":"e04fac8e8a33c78e1a4d0e1b0a6d9292d07649df6fcc2e9f1f1c351a948d2c73"},"schema_version":"1.0","source":{"id":"1301.6157","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6157","created_at":"2026-05-18T03:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6157v2","created_at":"2026-05-18T03:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6157","created_at":"2026-05-18T03:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"2DAYZJSKK3EU","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"2DAYZJSKK3EUVCFP","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"2DAYZJSK","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:237110d3906ba8ae4b942e4bd0d682a09aa6fdef752278d9e7a278a64803c1eb","target":"graph","created_at":"2026-05-18T03:31:20Z","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":"In this paper, we provide explicit constructions for a class of exact-repair regenerating codes that possess a layered structure. These regenerating codes correspond to interior points on the storage-repair-bandwidth tradeoff, and compare very well in comparison to scheme that employs space-sharing between MSR and MBR codes. For the parameter set $(n,k,d=k)$ with $n < 2k-1$, we construct a class of codes with an auxiliary parameter $w$, referred to as canonical codes. With $w$ in the range $n-k < w < k$, these codes operate in the region between the MSR point and the MBR point, and perform sig","authors_text":"Birenjith Sasidharan, P. Vijay Kumar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-25T20:52:06Z","title":"High-Rate Regenerating Codes Through Layering"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6157","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":"sha256:3ecd70ab7ceed05d9d0cfec08606d371074be3bd6897c39d57be8cab36fcc6bc","target":"record","created_at":"2026-05-18T03:31:20Z","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":"58c660defa04aa74a5fdfbabb458b901c73bf733747f2aeb5ed4abf8234493ed","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-01-25T20:52:06Z","title_canon_sha256":"e04fac8e8a33c78e1a4d0e1b0a6d9292d07649df6fcc2e9f1f1c351a948d2c73"},"schema_version":"1.0","source":{"id":"1301.6157","kind":"arxiv","version":2}},"canonical_sha256":"d0c18ca64a56c94a88af0a0ab1a1417ce4ba8a0bad35d2a137da443ea7d1b23b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0c18ca64a56c94a88af0a0ab1a1417ce4ba8a0bad35d2a137da443ea7d1b23b","first_computed_at":"2026-05-18T03:31:20.375459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:20.375459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"komPtwk8uH7ixk6eEudXL4Ne+X7KQXvOOCCSJ2T5QQayKDxvcyXHO1knR5bZD+6qea8YvQiA88mepPSWITkLAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:20.376354Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.6157","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ecd70ab7ceed05d9d0cfec08606d371074be3bd6897c39d57be8cab36fcc6bc","sha256:237110d3906ba8ae4b942e4bd0d682a09aa6fdef752278d9e7a278a64803c1eb"],"state_sha256":"9abf75fdabf7d8cb3eea09a199c96e8b3bb99acfda36383a8984d5ba91b60979"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XBR5gRElPmwAUWXJaTi3p1VW8XMNsJji2Xm0n6y0Yg79WLRaghMl0pr/DtNbf8GL/DCMGxAUFocWl4N7SaXUBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:25:42.798469Z","bundle_sha256":"670f64aad33e264e821b4b7ab92909aa04677455247bcc4eb13f89f646ce6efc"}}