{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WHWUCGS43WVYA4XT3M55YDM3OV","short_pith_number":"pith:WHWUCGS4","canonical_record":{"source":{"id":"1512.02990","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-09T18:52:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"88e726723204cb505cf6a328984d8afbbd9dbd544e0cc2b3980a18c62711e63f","abstract_canon_sha256":"908d0339ecb03ef82bdd8c052b2d7f6096cfe0dace03978d627413265c5fe015"},"schema_version":"1.0"},"canonical_sha256":"b1ed411a5cddab8072f3db3bdc0d9b7552778603d2f813ad0973548768c861e7","source":{"kind":"arxiv","id":"1512.02990","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02990","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02990v2","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02990","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"WHWUCGS43WVY","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WHWUCGS43WVYA4XT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WHWUCGS4","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WHWUCGS43WVYA4XT3M55YDM3OV","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02990","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-09T18:52:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"88e726723204cb505cf6a328984d8afbbd9dbd544e0cc2b3980a18c62711e63f","abstract_canon_sha256":"908d0339ecb03ef82bdd8c052b2d7f6096cfe0dace03978d627413265c5fe015"},"schema_version":"1.0"},"canonical_sha256":"b1ed411a5cddab8072f3db3bdc0d9b7552778603d2f813ad0973548768c861e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:12.599161Z","signature_b64":"J52FkjdDYiZAO/ktcSBG4a4Wk2WYcyJYgz61rb5NI8g4e6VJVKLOvqjn3LmiD6fq2bLz/6wpxlX8mad5TsQ5CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1ed411a5cddab8072f3db3bdc0d9b7552778603d2f813ad0973548768c861e7","last_reissued_at":"2026-05-18T01:00:12.598395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:12.598395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02990","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":"2026-05-18T01:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/P6mbcp7BF/RPGzKjPLbqF3JtFk8TRjiJFOJhSGlgiPG5MiyDuu+00Z5NQl3utcU32L911V+LhFSm2++0kWoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:14:48.665918Z"},"content_sha256":"7b1a6e0e58aa2aebe8cff6c8ae4dcf3a2f3c0c1e5c24a54b3951738808e5d2e6","schema_version":"1.0","event_id":"sha256:7b1a6e0e58aa2aebe8cff6c8ae4dcf3a2f3c0c1e5c24a54b3951738808e5d2e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WHWUCGS43WVYA4XT3M55YDM3OV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Staircase Codes for Secret Sharing with Optimal Communication and Read Overheads","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Rawad Bitar, Salim El Rouayheb","submitted_at":"2015-12-09T18:52:17Z","abstract_excerpt":"We study the communication efficient secret sharing (CESS) problem introduced by Huang, Langberg, Kliewer and Bruck. A classical threshold secret sharing scheme randomly encodes a secret into $n$ shares given to $n$ parties, such that any set of at least $t$, $t<n$, parties can reconstruct the secret, and any set of at most $z$, $z<t$, parties cannot obtain any information about the secret. Recently, Huang et al. characterized the achievable minimum communication overhead (CO) necessary for a legitimate user to decode the secret when contacting $d\\geq t$ parties and presented explicit code con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02990","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":"2026-05-18T01:00:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5ulV4lGBomlDGqq+kP072D9ZoRzo+pQ2CxkxtidiaG9W//kTRi+e2nKhvFoFxJvoxi7iSImw5W92dbdlMIjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:14:48.666635Z"},"content_sha256":"ad20d01c8fa21e09e1294b9c8f0864365b7f5bb2f45d04cfe23ef0c57b01ee70","schema_version":"1.0","event_id":"sha256:ad20d01c8fa21e09e1294b9c8f0864365b7f5bb2f45d04cfe23ef0c57b01ee70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WHWUCGS43WVYA4XT3M55YDM3OV/bundle.json","state_url":"https://pith.science/pith/WHWUCGS43WVYA4XT3M55YDM3OV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WHWUCGS43WVYA4XT3M55YDM3OV/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":"2026-05-25T22:14:48Z","links":{"resolver":"https://pith.science/pith/WHWUCGS43WVYA4XT3M55YDM3OV","bundle":"https://pith.science/pith/WHWUCGS43WVYA4XT3M55YDM3OV/bundle.json","state":"https://pith.science/pith/WHWUCGS43WVYA4XT3M55YDM3OV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WHWUCGS43WVYA4XT3M55YDM3OV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WHWUCGS43WVYA4XT3M55YDM3OV","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":"908d0339ecb03ef82bdd8c052b2d7f6096cfe0dace03978d627413265c5fe015","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-09T18:52:17Z","title_canon_sha256":"88e726723204cb505cf6a328984d8afbbd9dbd544e0cc2b3980a18c62711e63f"},"schema_version":"1.0","source":{"id":"1512.02990","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02990","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02990v2","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02990","created_at":"2026-05-18T01:00:12Z"},{"alias_kind":"pith_short_12","alias_value":"WHWUCGS43WVY","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WHWUCGS43WVYA4XT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WHWUCGS4","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:ad20d01c8fa21e09e1294b9c8f0864365b7f5bb2f45d04cfe23ef0c57b01ee70","target":"graph","created_at":"2026-05-18T01:00:12Z","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 study the communication efficient secret sharing (CESS) problem introduced by Huang, Langberg, Kliewer and Bruck. A classical threshold secret sharing scheme randomly encodes a secret into $n$ shares given to $n$ parties, such that any set of at least $t$, $t<n$, parties can reconstruct the secret, and any set of at most $z$, $z<t$, parties cannot obtain any information about the secret. Recently, Huang et al. characterized the achievable minimum communication overhead (CO) necessary for a legitimate user to decode the secret when contacting $d\\geq t$ parties and presented explicit code con","authors_text":"Rawad Bitar, Salim El Rouayheb","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-09T18:52:17Z","title":"Staircase Codes for Secret Sharing with Optimal Communication and Read Overheads"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02990","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":"sha256:7b1a6e0e58aa2aebe8cff6c8ae4dcf3a2f3c0c1e5c24a54b3951738808e5d2e6","target":"record","created_at":"2026-05-18T01:00:12Z","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":"908d0339ecb03ef82bdd8c052b2d7f6096cfe0dace03978d627413265c5fe015","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-12-09T18:52:17Z","title_canon_sha256":"88e726723204cb505cf6a328984d8afbbd9dbd544e0cc2b3980a18c62711e63f"},"schema_version":"1.0","source":{"id":"1512.02990","kind":"arxiv","version":2}},"canonical_sha256":"b1ed411a5cddab8072f3db3bdc0d9b7552778603d2f813ad0973548768c861e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b1ed411a5cddab8072f3db3bdc0d9b7552778603d2f813ad0973548768c861e7","first_computed_at":"2026-05-18T01:00:12.598395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:12.598395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J52FkjdDYiZAO/ktcSBG4a4Wk2WYcyJYgz61rb5NI8g4e6VJVKLOvqjn3LmiD6fq2bLz/6wpxlX8mad5TsQ5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:12.599161Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02990","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b1a6e0e58aa2aebe8cff6c8ae4dcf3a2f3c0c1e5c24a54b3951738808e5d2e6","sha256:ad20d01c8fa21e09e1294b9c8f0864365b7f5bb2f45d04cfe23ef0c57b01ee70"],"state_sha256":"57f516333d92490840b9b53622af91ddd728f894d59af3569d4b4359b7bbf7c8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RB0w1Mj0UbTshpMI+SspIpaWQD4R59T+2b8l9AoDqGmS5HDF1R2Yv1T2daFCppwZgXfIAt9c0G1ejfRPJmpZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:14:48.670631Z","bundle_sha256":"a4be9703da78f65606b0f924d2d67ec2a5c441ef3fe9039c2d7ac10bcab5bc1d"}}