{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UFMH46XNBNVTSDYJP7UX6OU4KQ","short_pith_number":"pith:UFMH46XN","canonical_record":{"source":{"id":"1901.02816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-09T16:47:55Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"904ab276045317c2fb365d2b5743848b6018b55aeed406325157e95b18f78a15","abstract_canon_sha256":"886d5d7f3fc9abc67e5079d996da0b8a34e490daa35163ca2948aa054d87e1b0"},"schema_version":"1.0"},"canonical_sha256":"a1587e7aed0b6b390f097fe97f3a9c540f65daaa15a9224f9c0e569e78397445","source":{"kind":"arxiv","id":"1901.02816","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02816","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02816v1","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02816","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"pith_short_12","alias_value":"UFMH46XNBNVT","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UFMH46XNBNVTSDYJ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UFMH46XN","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UFMH46XNBNVTSDYJP7UX6OU4KQ","target":"record","payload":{"canonical_record":{"source":{"id":"1901.02816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-09T16:47:55Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"904ab276045317c2fb365d2b5743848b6018b55aeed406325157e95b18f78a15","abstract_canon_sha256":"886d5d7f3fc9abc67e5079d996da0b8a34e490daa35163ca2948aa054d87e1b0"},"schema_version":"1.0"},"canonical_sha256":"a1587e7aed0b6b390f097fe97f3a9c540f65daaa15a9224f9c0e569e78397445","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:39.382582Z","signature_b64":"GlSuzCZnKSp/+UabXnku2+FfnjFrfa3fKQTZcBE4ctp4gt1nU9KcvQ1C62nr31vvfr/6nMlbPaUbrO3r4rcdDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1587e7aed0b6b390f097fe97f3a9c540f65daaa15a9224f9c0e569e78397445","last_reissued_at":"2026-05-17T23:56:39.381994Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:39.381994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.02816","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":"2026-05-17T23:56:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shlxYcfE8Niv/qaJbsZyPl9y04gTBnlk3vFw4076OyMP1wbhLe+nQn5NSbMpWevXy4HsX/i5L2MqgtUSlrgQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:24:58.414966Z"},"content_sha256":"e38f2da2845f83720250378d6a5b626dad2e0feae1acad7f8273eb199cd44935","schema_version":"1.0","event_id":"sha256:e38f2da2845f83720250378d6a5b626dad2e0feae1acad7f8273eb199cd44935"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UFMH46XNBNVTSDYJP7UX6OU4KQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Codes for Updating Linear Functions over Small Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Lakshmi Natarajan, Suman Ghosh","submitted_at":"2019-01-09T16:47:55Z","abstract_excerpt":"We consider a point-to-point communication scenario where the receiver maintains a specific linear function of a message vector over a finite field. When the value of the message vector undergoes a sparse update, the transmitter broadcasts a coded version of the modified message while the receiver uses this codeword and the current value of the linear function to update its contents. It is assumed that the transmitter has access to the modified message but is unaware of the exact difference vector between the original and modified messages. Under the assumption that the difference vector is sp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02816","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":"2026-05-17T23:56:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9S7wR/4vhnNGc3UyQtqpIEu9dU97TrR4RlUiybJppyGSZofv0SN8xkH+kZGVMnd3lz/89NAVosDc+vin+2hxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:24:58.415339Z"},"content_sha256":"2fdd8c2f0b22a7d8e02f93648fa9dafb5def518e7d24ace7f1f8053bc29eba39","schema_version":"1.0","event_id":"sha256:2fdd8c2f0b22a7d8e02f93648fa9dafb5def518e7d24ace7f1f8053bc29eba39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UFMH46XNBNVTSDYJP7UX6OU4KQ/bundle.json","state_url":"https://pith.science/pith/UFMH46XNBNVTSDYJP7UX6OU4KQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UFMH46XNBNVTSDYJP7UX6OU4KQ/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":"2026-05-31T09:24:58Z","links":{"resolver":"https://pith.science/pith/UFMH46XNBNVTSDYJP7UX6OU4KQ","bundle":"https://pith.science/pith/UFMH46XNBNVTSDYJP7UX6OU4KQ/bundle.json","state":"https://pith.science/pith/UFMH46XNBNVTSDYJP7UX6OU4KQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UFMH46XNBNVTSDYJP7UX6OU4KQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UFMH46XNBNVTSDYJP7UX6OU4KQ","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":"886d5d7f3fc9abc67e5079d996da0b8a34e490daa35163ca2948aa054d87e1b0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-09T16:47:55Z","title_canon_sha256":"904ab276045317c2fb365d2b5743848b6018b55aeed406325157e95b18f78a15"},"schema_version":"1.0","source":{"id":"1901.02816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.02816","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.02816v1","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02816","created_at":"2026-05-17T23:56:39Z"},{"alias_kind":"pith_short_12","alias_value":"UFMH46XNBNVT","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UFMH46XNBNVTSDYJ","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UFMH46XN","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:2fdd8c2f0b22a7d8e02f93648fa9dafb5def518e7d24ace7f1f8053bc29eba39","target":"graph","created_at":"2026-05-17T23:56:39Z","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 consider a point-to-point communication scenario where the receiver maintains a specific linear function of a message vector over a finite field. When the value of the message vector undergoes a sparse update, the transmitter broadcasts a coded version of the modified message while the receiver uses this codeword and the current value of the linear function to update its contents. It is assumed that the transmitter has access to the modified message but is unaware of the exact difference vector between the original and modified messages. Under the assumption that the difference vector is sp","authors_text":"Lakshmi Natarajan, Suman Ghosh","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-09T16:47:55Z","title":"Codes for Updating Linear Functions over Small Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02816","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:e38f2da2845f83720250378d6a5b626dad2e0feae1acad7f8273eb199cd44935","target":"record","created_at":"2026-05-17T23:56:39Z","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":"886d5d7f3fc9abc67e5079d996da0b8a34e490daa35163ca2948aa054d87e1b0","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-09T16:47:55Z","title_canon_sha256":"904ab276045317c2fb365d2b5743848b6018b55aeed406325157e95b18f78a15"},"schema_version":"1.0","source":{"id":"1901.02816","kind":"arxiv","version":1}},"canonical_sha256":"a1587e7aed0b6b390f097fe97f3a9c540f65daaa15a9224f9c0e569e78397445","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1587e7aed0b6b390f097fe97f3a9c540f65daaa15a9224f9c0e569e78397445","first_computed_at":"2026-05-17T23:56:39.381994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:39.381994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GlSuzCZnKSp/+UabXnku2+FfnjFrfa3fKQTZcBE4ctp4gt1nU9KcvQ1C62nr31vvfr/6nMlbPaUbrO3r4rcdDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:39.382582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.02816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e38f2da2845f83720250378d6a5b626dad2e0feae1acad7f8273eb199cd44935","sha256:2fdd8c2f0b22a7d8e02f93648fa9dafb5def518e7d24ace7f1f8053bc29eba39"],"state_sha256":"017b108f9047791b7e2199f6836a29004c8cf72bbf791065684ebf9a69dcd2d0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iv6veroTbknyLSKDjzbrr2jPK96XK/7dBSHZ5t4ZBKGcQtMObytoYHbWZq6kp5JHQTUVgZbIMqN4t9jhhWNvAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:24:58.417533Z","bundle_sha256":"86dca3864b7d215dc638aa2b273877ec196893d7395cc6909cf5b0008b953a45"}}