{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HI4BLPCXKZC6BSCNLFGU7GV7OX","short_pith_number":"pith:HI4BLPCX","canonical_record":{"source":{"id":"1302.6154","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-25T16:54:06Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"b77ee6af6600755979b6be8c09d543411c4dbbbdca6a3f38ace0e81ec69dfe2b","abstract_canon_sha256":"fd941a72e806297dfef13144771c97589d20b1eca73f136871c646cb8407aae9"},"schema_version":"1.0"},"canonical_sha256":"3a3815bc575645e0c84d594d4f9abf75e93f3518f23a522e6dd790d289df773e","source":{"kind":"arxiv","id":"1302.6154","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6154","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6154v4","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6154","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"pith_short_12","alias_value":"HI4BLPCXKZC6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HI4BLPCXKZC6BSCN","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HI4BLPCX","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HI4BLPCXKZC6BSCNLFGU7GV7OX","target":"record","payload":{"canonical_record":{"source":{"id":"1302.6154","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-25T16:54:06Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"b77ee6af6600755979b6be8c09d543411c4dbbbdca6a3f38ace0e81ec69dfe2b","abstract_canon_sha256":"fd941a72e806297dfef13144771c97589d20b1eca73f136871c646cb8407aae9"},"schema_version":"1.0"},"canonical_sha256":"3a3815bc575645e0c84d594d4f9abf75e93f3518f23a522e6dd790d289df773e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:35.140650Z","signature_b64":"6aZFq5JCB0wIJTjFBckAAZG9cZlGhHs3D88PexFETvooPTXNfpOMTkWeLBXKsGUveUDDnvS/MNC/v4zjpiX/DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a3815bc575645e0c84d594d4f9abf75e93f3518f23a522e6dd790d289df773e","last_reissued_at":"2026-05-18T03:20:35.139838Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:35.139838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.6154","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:20:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6e/8jp2TO97xqnjkRjw5znO5epRHN1huDlsba607oK8C5DYiIcb0JGRxMqIXbNQe/btOivMOIwc25k2FX97BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:27:26.424846Z"},"content_sha256":"59029cff6e50dffc09399367759cd77ac3f256f1216f6429118940d169349778","schema_version":"1.0","event_id":"sha256:59029cff6e50dffc09399367759cd77ac3f256f1216f6429118940d169349778"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HI4BLPCXKZC6BSCNLFGU7GV7OX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper Bounds on the Size of Grain-Correcting Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DM","authors_text":"Gilles Z\\'emor, Navin Kashyap","submitted_at":"2013-02-25T16:54:06Z","abstract_excerpt":"In this paper, we re-visit the combinatorial error model of Mazumdar et al. that models errors in high-density magnetic recording caused by lack of knowledge of grain boundaries in the recording medium. We present new upper bounds on the cardinality/rate of binary block codes that correct errors within this model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6154","kind":"arxiv","version":4},"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":"2026-05-18T03:20:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/75c+9hjXz/cSdFd5J5pW7S4MaSbefMySHdOEQKq0FwEdBalI1litJGdXUVWmySDJX1tKVsqxdx7wcRpiz7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T06:27:26.425185Z"},"content_sha256":"af8f3ce6cebc62541fabfe2de6bc14e421120d8dcec4f4dc9bd753b5fd015e05","schema_version":"1.0","event_id":"sha256:af8f3ce6cebc62541fabfe2de6bc14e421120d8dcec4f4dc9bd753b5fd015e05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HI4BLPCXKZC6BSCNLFGU7GV7OX/bundle.json","state_url":"https://pith.science/pith/HI4BLPCXKZC6BSCNLFGU7GV7OX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HI4BLPCXKZC6BSCNLFGU7GV7OX/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":"2026-06-25T06:27:26Z","links":{"resolver":"https://pith.science/pith/HI4BLPCXKZC6BSCNLFGU7GV7OX","bundle":"https://pith.science/pith/HI4BLPCXKZC6BSCNLFGU7GV7OX/bundle.json","state":"https://pith.science/pith/HI4BLPCXKZC6BSCNLFGU7GV7OX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HI4BLPCXKZC6BSCNLFGU7GV7OX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HI4BLPCXKZC6BSCNLFGU7GV7OX","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":"fd941a72e806297dfef13144771c97589d20b1eca73f136871c646cb8407aae9","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-25T16:54:06Z","title_canon_sha256":"b77ee6af6600755979b6be8c09d543411c4dbbbdca6a3f38ace0e81ec69dfe2b"},"schema_version":"1.0","source":{"id":"1302.6154","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.6154","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"arxiv_version","alias_value":"1302.6154v4","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6154","created_at":"2026-05-18T03:20:35Z"},{"alias_kind":"pith_short_12","alias_value":"HI4BLPCXKZC6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HI4BLPCXKZC6BSCN","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HI4BLPCX","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:af8f3ce6cebc62541fabfe2de6bc14e421120d8dcec4f4dc9bd753b5fd015e05","target":"graph","created_at":"2026-05-18T03:20:35Z","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 re-visit the combinatorial error model of Mazumdar et al. that models errors in high-density magnetic recording caused by lack of knowledge of grain boundaries in the recording medium. We present new upper bounds on the cardinality/rate of binary block codes that correct errors within this model.","authors_text":"Gilles Z\\'emor, Navin Kashyap","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-25T16:54:06Z","title":"Upper Bounds on the Size of Grain-Correcting Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6154","kind":"arxiv","version":4},"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":"sha256:59029cff6e50dffc09399367759cd77ac3f256f1216f6429118940d169349778","target":"record","created_at":"2026-05-18T03:20:35Z","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":"fd941a72e806297dfef13144771c97589d20b1eca73f136871c646cb8407aae9","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-02-25T16:54:06Z","title_canon_sha256":"b77ee6af6600755979b6be8c09d543411c4dbbbdca6a3f38ace0e81ec69dfe2b"},"schema_version":"1.0","source":{"id":"1302.6154","kind":"arxiv","version":4}},"canonical_sha256":"3a3815bc575645e0c84d594d4f9abf75e93f3518f23a522e6dd790d289df773e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a3815bc575645e0c84d594d4f9abf75e93f3518f23a522e6dd790d289df773e","first_computed_at":"2026-05-18T03:20:35.139838Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:35.139838Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6aZFq5JCB0wIJTjFBckAAZG9cZlGhHs3D88PexFETvooPTXNfpOMTkWeLBXKsGUveUDDnvS/MNC/v4zjpiX/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:35.140650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.6154","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59029cff6e50dffc09399367759cd77ac3f256f1216f6429118940d169349778","sha256:af8f3ce6cebc62541fabfe2de6bc14e421120d8dcec4f4dc9bd753b5fd015e05"],"state_sha256":"c17c31a0e60a3d594cb06ad747e1f4e0c43647871deb0d977cca851e9664fc26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nPdAQIHbn5jHbMSmq3LS3Adv29gMD+23gthPmqUze9ofIRDDJvYlBbKQxCcLrNN3BRzJbS71UmWDZTr3V+1TAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T06:27:26.427339Z","bundle_sha256":"2071ac6bd6494e98b661e67845682da10502291cda42d2ac97d5a7266348a824"}}