{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:BR3MESHMNYGS5ELMJR4WN7JCDD","short_pith_number":"pith:BR3MESHM","canonical_record":{"source":{"id":"math/0304292","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2003-04-21T16:18:51Z","cross_cats_sorted":["cs.IT","math.AG","math.IT","math.RA"],"title_canon_sha256":"ce2d936e98d0bfcd0f19e3a6f3acd99d0adec88392f1d9761bea39228f9428a5","abstract_canon_sha256":"c50c58cd5e683bb599a9d47166c9978e4a4fad9ff1b97a691a9c9dbf42432086"},"schema_version":"1.0"},"canonical_sha256":"0c76c248ec6e0d2e916c4c7966fd2218f381918e67570ac0872baf3771c415b2","source":{"kind":"arxiv","id":"math/0304292","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0304292","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0304292v2","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0304292","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"pith_short_12","alias_value":"BR3MESHMNYGS","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"pith_short_16","alias_value":"BR3MESHMNYGS5ELM","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"pith_short_8","alias_value":"BR3MESHM","created_at":"2026-07-04T15:10:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:BR3MESHMNYGS5ELMJR4WN7JCDD","target":"record","payload":{"canonical_record":{"source":{"id":"math/0304292","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.AC","submitted_at":"2003-04-21T16:18:51Z","cross_cats_sorted":["cs.IT","math.AG","math.IT","math.RA"],"title_canon_sha256":"ce2d936e98d0bfcd0f19e3a6f3acd99d0adec88392f1d9761bea39228f9428a5","abstract_canon_sha256":"c50c58cd5e683bb599a9d47166c9978e4a4fad9ff1b97a691a9c9dbf42432086"},"schema_version":"1.0"},"canonical_sha256":"0c76c248ec6e0d2e916c4c7966fd2218f381918e67570ac0872baf3771c415b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:10:21.995999Z","signature_b64":"FUh3w/MVujdm5bLsLvZhpt4aU7k4ZvMi2vrB/EOrJcJ7BeA3Shl4UwbEzcT6Qz07f+DwZSCMqcMlBxjQHmDuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c76c248ec6e0d2e916c4c7966fd2218f381918e67570ac0872baf3771c415b2","last_reissued_at":"2026-07-04T15:10:21.995533Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:10:21.995533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0304292","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":"2026-07-04T15:10:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/KVda4siWdYLG4/x2DOzfDaeUFsxC0jPniaebgEwQ+/DpDnzq+rhi/E/hZSYx4sMhdqjbY8Pagc9MKJCtt/1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T05:58:40.569623Z"},"content_sha256":"48628c75d1c47a825dbef3eafac44b203fa597f793742476e6d0aab098b07a6a","schema_version":"1.0","event_id":"sha256:48628c75d1c47a825dbef3eafac44b203fa597f793742476e6d0aab098b07a6a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:BR3MESHMNYGS5ELMJR4WN7JCDD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Ubiquity of Order Domains for the Construction of Error Control Codes","license":"","headline":"","cross_cats":["cs.IT","math.AG","math.IT","math.RA"],"primary_cat":"math.AC","authors_text":"John B. Little","submitted_at":"2003-04-21T16:18:51Z","abstract_excerpt":"The order domains are a class of commutative rings introduced by H{\\o}holdt, van Lint, and Pellikaan to simplify the theory of error control codes using ideas from algebraic geometry. The definition is largely motivated by the structures utilized in the Berlekamp-Massey-Sakata (BMS) decoding algorithm, with Feng-Rao majority voting for unknown syndromes, applied to one-point geometric Goppa codes constructed from curves. However, order domains are much more general, and O'Sullivan has shown that the BMS algorithm can be applied to decode all codes constructed from order domains by a suitable g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304292","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0304292/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:10:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2IVtQ1+p9EWVyLufx3uLDtQRkp1JLC8/B9BdBrfKgvMKIwC6ybDndOmwVAYXZpyn0O81dtBR+R5RiVxIm9zMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T05:58:40.570292Z"},"content_sha256":"21ab99c1d21bb74e5392cbfe4d7fc7e1a548c3ce42703b14966b68279273f9cc","schema_version":"1.0","event_id":"sha256:21ab99c1d21bb74e5392cbfe4d7fc7e1a548c3ce42703b14966b68279273f9cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BR3MESHMNYGS5ELMJR4WN7JCDD/bundle.json","state_url":"https://pith.science/pith/BR3MESHMNYGS5ELMJR4WN7JCDD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BR3MESHMNYGS5ELMJR4WN7JCDD/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":"2026-07-09T05:58:40Z","links":{"resolver":"https://pith.science/pith/BR3MESHMNYGS5ELMJR4WN7JCDD","bundle":"https://pith.science/pith/BR3MESHMNYGS5ELMJR4WN7JCDD/bundle.json","state":"https://pith.science/pith/BR3MESHMNYGS5ELMJR4WN7JCDD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BR3MESHMNYGS5ELMJR4WN7JCDD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:BR3MESHMNYGS5ELMJR4WN7JCDD","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":"c50c58cd5e683bb599a9d47166c9978e4a4fad9ff1b97a691a9c9dbf42432086","cross_cats_sorted":["cs.IT","math.AG","math.IT","math.RA"],"license":"","primary_cat":"math.AC","submitted_at":"2003-04-21T16:18:51Z","title_canon_sha256":"ce2d936e98d0bfcd0f19e3a6f3acd99d0adec88392f1d9761bea39228f9428a5"},"schema_version":"1.0","source":{"id":"math/0304292","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0304292","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0304292v2","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0304292","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"pith_short_12","alias_value":"BR3MESHMNYGS","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"pith_short_16","alias_value":"BR3MESHMNYGS5ELM","created_at":"2026-07-04T15:10:21Z"},{"alias_kind":"pith_short_8","alias_value":"BR3MESHM","created_at":"2026-07-04T15:10:21Z"}],"graph_snapshots":[{"event_id":"sha256:21ab99c1d21bb74e5392cbfe4d7fc7e1a548c3ce42703b14966b68279273f9cc","target":"graph","created_at":"2026-07-04T15:10:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0304292/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The order domains are a class of commutative rings introduced by H{\\o}holdt, van Lint, and Pellikaan to simplify the theory of error control codes using ideas from algebraic geometry. The definition is largely motivated by the structures utilized in the Berlekamp-Massey-Sakata (BMS) decoding algorithm, with Feng-Rao majority voting for unknown syndromes, applied to one-point geometric Goppa codes constructed from curves. However, order domains are much more general, and O'Sullivan has shown that the BMS algorithm can be applied to decode all codes constructed from order domains by a suitable g","authors_text":"John B. Little","cross_cats":["cs.IT","math.AG","math.IT","math.RA"],"headline":"","license":"","primary_cat":"math.AC","submitted_at":"2003-04-21T16:18:51Z","title":"The Ubiquity of Order Domains for the Construction of Error Control Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0304292","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":"sha256:48628c75d1c47a825dbef3eafac44b203fa597f793742476e6d0aab098b07a6a","target":"record","created_at":"2026-07-04T15:10:21Z","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":"c50c58cd5e683bb599a9d47166c9978e4a4fad9ff1b97a691a9c9dbf42432086","cross_cats_sorted":["cs.IT","math.AG","math.IT","math.RA"],"license":"","primary_cat":"math.AC","submitted_at":"2003-04-21T16:18:51Z","title_canon_sha256":"ce2d936e98d0bfcd0f19e3a6f3acd99d0adec88392f1d9761bea39228f9428a5"},"schema_version":"1.0","source":{"id":"math/0304292","kind":"arxiv","version":2}},"canonical_sha256":"0c76c248ec6e0d2e916c4c7966fd2218f381918e67570ac0872baf3771c415b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c76c248ec6e0d2e916c4c7966fd2218f381918e67570ac0872baf3771c415b2","first_computed_at":"2026-07-04T15:10:21.995533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:10:21.995533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FUh3w/MVujdm5bLsLvZhpt4aU7k4ZvMi2vrB/EOrJcJ7BeA3Shl4UwbEzcT6Qz07f+DwZSCMqcMlBxjQHmDuCw==","signature_status":"signed_v1","signed_at":"2026-07-04T15:10:21.995999Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0304292","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48628c75d1c47a825dbef3eafac44b203fa597f793742476e6d0aab098b07a6a","sha256:21ab99c1d21bb74e5392cbfe4d7fc7e1a548c3ce42703b14966b68279273f9cc"],"state_sha256":"d825cc77202c0c81573ac2d5c4a8bee04c7b7326c1109a220ae9d053f039f10e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9K/j+3pKv9/zXOjRl7ql7EmlI9VMGbGllsw8toyXiQjG0E+JrCuN8yl5epSLtElhZcAl2p8AO4foqKyHoALcCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T05:58:40.574124Z","bundle_sha256":"491429fc390f822123cf68ecb1a625aba80a3ebb2b56358f75579306d6f06a38"}}