{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BTZWNS7OFTI5O5IGLX2EJG2X4V","short_pith_number":"pith:BTZWNS7O","canonical_record":{"source":{"id":"1610.02578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-08T20:30:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"314a435c3ae4a6397b5a66ca75f3ed6a5c7b6cd0cbf31d6f4af21cbeefc9311f","abstract_canon_sha256":"86eb3c2a5c1fe33f2d0ea7b7c51b5f9762e878160dcf4c3dc66dd2970a2ce32f"},"schema_version":"1.0"},"canonical_sha256":"0cf366cbee2cd1d775065df4449b57e5539927334c4bff1730e7bd73e3fedc17","source":{"kind":"arxiv","id":"1610.02578","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02578","created_at":"2026-05-18T00:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02578v2","created_at":"2026-05-18T00:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02578","created_at":"2026-05-18T00:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"BTZWNS7OFTI5","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BTZWNS7OFTI5O5IG","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BTZWNS7O","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BTZWNS7OFTI5O5IGLX2EJG2X4V","target":"record","payload":{"canonical_record":{"source":{"id":"1610.02578","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-08T20:30:49Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"314a435c3ae4a6397b5a66ca75f3ed6a5c7b6cd0cbf31d6f4af21cbeefc9311f","abstract_canon_sha256":"86eb3c2a5c1fe33f2d0ea7b7c51b5f9762e878160dcf4c3dc66dd2970a2ce32f"},"schema_version":"1.0"},"canonical_sha256":"0cf366cbee2cd1d775065df4449b57e5539927334c4bff1730e7bd73e3fedc17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:03.182600Z","signature_b64":"jyTcA8+cJljbmR2ffeMukQbIpZgL45Pu3iqCb1Vk7LeEqSxAsQDERpRL9rjAugyWQRWbUXR6XxrTobKmCmXNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0cf366cbee2cd1d775065df4449b57e5539927334c4bff1730e7bd73e3fedc17","last_reissued_at":"2026-05-18T00:31:03.182066Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:03.182066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.02578","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":"2026-05-18T00:31:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cDsEqDLugiSRbNvTdoVj4/64MjN/R1SI4Y0H2eccnXuqsmgEOIyv9FuvpHtGLLxWEj2T73XlYxwv/noemI2gBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:17:22.836310Z"},"content_sha256":"3d1445437070d3c57dc4268441956e519c2e9ea338d9bb6c173d2793baa57fe1","schema_version":"1.0","event_id":"sha256:3d1445437070d3c57dc4268441956e519c2e9ea338d9bb6c173d2793baa57fe1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BTZWNS7OFTI5O5IGLX2EJG2X4V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Defect tolerance: fundamental limits and examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Da Wang, Gregory Wornell, Jennifer Tang, Yury Polyanskiy","submitted_at":"2016-10-08T20:30:49Z","abstract_excerpt":"This paper addresses the problem of adding redundancy to a collection of physical objects so that the overall system is more robust to failures. In contrast to its information counterpart, which can exploit parity to protect multiple information symbols from a single erasure, physical redundancy can only be realized through duplication and substitution of objects. We propose a bipartite graph model for designing defect-tolerant systems in which defective objects are replaced by judiciously connected redundant objects. The fundamental limits of this model are characterized under various asympto"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02578","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":"2026-05-18T00:31:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RsTWHNBZFVy7YJdpaQgAhUMypvfmiEapmFQnC7+BFAa11JYLjEF7QWZMKBZBRRakdUctf0RmnbC9Eph9g/4tCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:17:22.836681Z"},"content_sha256":"8f90487cee66c62381ef21dc8e5fc97974b82492da212f79ef2163605b4ceb80","schema_version":"1.0","event_id":"sha256:8f90487cee66c62381ef21dc8e5fc97974b82492da212f79ef2163605b4ceb80"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BTZWNS7OFTI5O5IGLX2EJG2X4V/bundle.json","state_url":"https://pith.science/pith/BTZWNS7OFTI5O5IGLX2EJG2X4V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BTZWNS7OFTI5O5IGLX2EJG2X4V/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":"2026-05-31T16:17:22Z","links":{"resolver":"https://pith.science/pith/BTZWNS7OFTI5O5IGLX2EJG2X4V","bundle":"https://pith.science/pith/BTZWNS7OFTI5O5IGLX2EJG2X4V/bundle.json","state":"https://pith.science/pith/BTZWNS7OFTI5O5IGLX2EJG2X4V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BTZWNS7OFTI5O5IGLX2EJG2X4V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BTZWNS7OFTI5O5IGLX2EJG2X4V","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":"86eb3c2a5c1fe33f2d0ea7b7c51b5f9762e878160dcf4c3dc66dd2970a2ce32f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-08T20:30:49Z","title_canon_sha256":"314a435c3ae4a6397b5a66ca75f3ed6a5c7b6cd0cbf31d6f4af21cbeefc9311f"},"schema_version":"1.0","source":{"id":"1610.02578","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.02578","created_at":"2026-05-18T00:31:03Z"},{"alias_kind":"arxiv_version","alias_value":"1610.02578v2","created_at":"2026-05-18T00:31:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.02578","created_at":"2026-05-18T00:31:03Z"},{"alias_kind":"pith_short_12","alias_value":"BTZWNS7OFTI5","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BTZWNS7OFTI5O5IG","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BTZWNS7O","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:8f90487cee66c62381ef21dc8e5fc97974b82492da212f79ef2163605b4ceb80","target":"graph","created_at":"2026-05-18T00:31:03Z","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":"This paper addresses the problem of adding redundancy to a collection of physical objects so that the overall system is more robust to failures. In contrast to its information counterpart, which can exploit parity to protect multiple information symbols from a single erasure, physical redundancy can only be realized through duplication and substitution of objects. We propose a bipartite graph model for designing defect-tolerant systems in which defective objects are replaced by judiciously connected redundant objects. The fundamental limits of this model are characterized under various asympto","authors_text":"Da Wang, Gregory Wornell, Jennifer Tang, Yury Polyanskiy","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-08T20:30:49Z","title":"Defect tolerance: fundamental limits and examples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02578","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":"sha256:3d1445437070d3c57dc4268441956e519c2e9ea338d9bb6c173d2793baa57fe1","target":"record","created_at":"2026-05-18T00:31:03Z","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":"86eb3c2a5c1fe33f2d0ea7b7c51b5f9762e878160dcf4c3dc66dd2970a2ce32f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-08T20:30:49Z","title_canon_sha256":"314a435c3ae4a6397b5a66ca75f3ed6a5c7b6cd0cbf31d6f4af21cbeefc9311f"},"schema_version":"1.0","source":{"id":"1610.02578","kind":"arxiv","version":2}},"canonical_sha256":"0cf366cbee2cd1d775065df4449b57e5539927334c4bff1730e7bd73e3fedc17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cf366cbee2cd1d775065df4449b57e5539927334c4bff1730e7bd73e3fedc17","first_computed_at":"2026-05-18T00:31:03.182066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:03.182066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jyTcA8+cJljbmR2ffeMukQbIpZgL45Pu3iqCb1Vk7LeEqSxAsQDERpRL9rjAugyWQRWbUXR6XxrTobKmCmXNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:03.182600Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.02578","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d1445437070d3c57dc4268441956e519c2e9ea338d9bb6c173d2793baa57fe1","sha256:8f90487cee66c62381ef21dc8e5fc97974b82492da212f79ef2163605b4ceb80"],"state_sha256":"be50b6417ce1bd97795f5e4d7af8d0e666db849f99fd66ec68a03868f93fc57c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RGOsX9p095ntm62WcBCOhl43NL7ppMxpjGdWD5lFn1Uc+ti+WjE0i9yYRdBitdPFH5pevfRks5KVUc7t5XCeBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:17:22.838975Z","bundle_sha256":"6a4bd01ef88e7544f28eef2aa8e2889e9b8759561130f1a9d562cbfcca549a42"}}