{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:SL5I3QR77WOXFUBJ42VZZDTL6Z","short_pith_number":"pith:SL5I3QR7","canonical_record":{"source":{"id":"1203.6127","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-28T01:36:24Z","cross_cats_sorted":["cs.SC","math.AC","math.AG","math.IT"],"title_canon_sha256":"23c36e63e4fed6a7437f5aeb5f51e39c6e8d9c8669a53ba9477ce7ded5384820","abstract_canon_sha256":"e3ef4ac8a9b01e5989e4999b0324bf7c44523699ef53724966269f360f4bbbff"},"schema_version":"1.0"},"canonical_sha256":"92fa8dc23ffd9d72d029e6ab9c8e6bf6724dd12f9163902bcc9dfd2376ad98c2","source":{"kind":"arxiv","id":"1203.6127","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6127","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6127v6","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6127","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"pith_short_12","alias_value":"SL5I3QR77WOX","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SL5I3QR77WOXFUBJ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SL5I3QR7","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:SL5I3QR77WOXFUBJ42VZZDTL6Z","target":"record","payload":{"canonical_record":{"source":{"id":"1203.6127","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-28T01:36:24Z","cross_cats_sorted":["cs.SC","math.AC","math.AG","math.IT"],"title_canon_sha256":"23c36e63e4fed6a7437f5aeb5f51e39c6e8d9c8669a53ba9477ce7ded5384820","abstract_canon_sha256":"e3ef4ac8a9b01e5989e4999b0324bf7c44523699ef53724966269f360f4bbbff"},"schema_version":"1.0"},"canonical_sha256":"92fa8dc23ffd9d72d029e6ab9c8e6bf6724dd12f9163902bcc9dfd2376ad98c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:26.639258Z","signature_b64":"VUlW2czVeeyHLz7XmgewxlmFQvpWFJsYJKL7s6BdaliTVPrJ6kGJh5tN170mnOaIKX+yyowaj0LA+tu2L0R8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92fa8dc23ffd9d72d029e6ab9c8e6bf6724dd12f9163902bcc9dfd2376ad98c2","last_reissued_at":"2026-05-18T00:46:26.638674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:26.638674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.6127","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:46:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qmkChR6QcoKzBdrQwwoKHQvR7i8tAv9RcS7NQbmVoCldf+a3o2TvJKNAz0byUBpDXJsXLVZtFJH+D/RZ6Ri5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:26:15.753942Z"},"content_sha256":"6e457ec0b24f2d70edb67a798a086887b15108ae6e3d2d91a6d69215a620ca9e","schema_version":"1.0","event_id":"sha256:6e457ec0b24f2d70edb67a798a086887b15108ae6e3d2d91a6d69215a620ca9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:SL5I3QR77WOXFUBJ42VZZDTL6Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"List Decoding Algorithm based on Voting in Groebner Bases for General One-Point AG Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.AC","math.AG","math.IT"],"primary_cat":"cs.IT","authors_text":"Diego Ruano, Olav Geil, Ryutaroh Matsumoto","submitted_at":"2012-03-28T01:36:24Z","abstract_excerpt":"We generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee, Bras-Amor\\'os and O'Sullivan (2012) to general one-point AG codes, without any assumption. We also extend their unique decoding algorithm to list decoding, modify it so that it can be used with the Feng-Rao improved code construction, prove equality between its error correcting capability and half the minimum distance lower bound by Andersen and Geil (2008) that has not been done in the original proposal except for one-point Hermitian codes, remove the unnecessary computational "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6127","kind":"arxiv","version":6},"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":"2026-05-18T00:46:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l3ZVPtnGoBJvATC1PRkxUCHxYNEEv5iG2TskSW0IXbPYMdMNZm1MrCv/PBpBCWdV1yoQNd5EITDIjzVT2RBHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T03:26:15.754293Z"},"content_sha256":"f772daa41cd3b748fd141a187c578183c2f724508a1213c480c4dafe7e71e394","schema_version":"1.0","event_id":"sha256:f772daa41cd3b748fd141a187c578183c2f724508a1213c480c4dafe7e71e394"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SL5I3QR77WOXFUBJ42VZZDTL6Z/bundle.json","state_url":"https://pith.science/pith/SL5I3QR77WOXFUBJ42VZZDTL6Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SL5I3QR77WOXFUBJ42VZZDTL6Z/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":"2026-06-27T03:26:15Z","links":{"resolver":"https://pith.science/pith/SL5I3QR77WOXFUBJ42VZZDTL6Z","bundle":"https://pith.science/pith/SL5I3QR77WOXFUBJ42VZZDTL6Z/bundle.json","state":"https://pith.science/pith/SL5I3QR77WOXFUBJ42VZZDTL6Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SL5I3QR77WOXFUBJ42VZZDTL6Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SL5I3QR77WOXFUBJ42VZZDTL6Z","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":"e3ef4ac8a9b01e5989e4999b0324bf7c44523699ef53724966269f360f4bbbff","cross_cats_sorted":["cs.SC","math.AC","math.AG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-28T01:36:24Z","title_canon_sha256":"23c36e63e4fed6a7437f5aeb5f51e39c6e8d9c8669a53ba9477ce7ded5384820"},"schema_version":"1.0","source":{"id":"1203.6127","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.6127","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"arxiv_version","alias_value":"1203.6127v6","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.6127","created_at":"2026-05-18T00:46:26Z"},{"alias_kind":"pith_short_12","alias_value":"SL5I3QR77WOX","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SL5I3QR77WOXFUBJ","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SL5I3QR7","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:f772daa41cd3b748fd141a187c578183c2f724508a1213c480c4dafe7e71e394","target":"graph","created_at":"2026-05-18T00:46:26Z","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 generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee, Bras-Amor\\'os and O'Sullivan (2012) to general one-point AG codes, without any assumption. We also extend their unique decoding algorithm to list decoding, modify it so that it can be used with the Feng-Rao improved code construction, prove equality between its error correcting capability and half the minimum distance lower bound by Andersen and Geil (2008) that has not been done in the original proposal except for one-point Hermitian codes, remove the unnecessary computational ","authors_text":"Diego Ruano, Olav Geil, Ryutaroh Matsumoto","cross_cats":["cs.SC","math.AC","math.AG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-28T01:36:24Z","title":"List Decoding Algorithm based on Voting in Groebner Bases for General One-Point AG Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6127","kind":"arxiv","version":6},"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":"sha256:6e457ec0b24f2d70edb67a798a086887b15108ae6e3d2d91a6d69215a620ca9e","target":"record","created_at":"2026-05-18T00:46:26Z","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":"e3ef4ac8a9b01e5989e4999b0324bf7c44523699ef53724966269f360f4bbbff","cross_cats_sorted":["cs.SC","math.AC","math.AG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-03-28T01:36:24Z","title_canon_sha256":"23c36e63e4fed6a7437f5aeb5f51e39c6e8d9c8669a53ba9477ce7ded5384820"},"schema_version":"1.0","source":{"id":"1203.6127","kind":"arxiv","version":6}},"canonical_sha256":"92fa8dc23ffd9d72d029e6ab9c8e6bf6724dd12f9163902bcc9dfd2376ad98c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92fa8dc23ffd9d72d029e6ab9c8e6bf6724dd12f9163902bcc9dfd2376ad98c2","first_computed_at":"2026-05-18T00:46:26.638674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:26.638674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VUlW2czVeeyHLz7XmgewxlmFQvpWFJsYJKL7s6BdaliTVPrJ6kGJh5tN170mnOaIKX+yyowaj0LA+tu2L0R8Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:26.639258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.6127","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e457ec0b24f2d70edb67a798a086887b15108ae6e3d2d91a6d69215a620ca9e","sha256:f772daa41cd3b748fd141a187c578183c2f724508a1213c480c4dafe7e71e394"],"state_sha256":"0db57eab0dc72fcc7af85d4da9519f061e3684bcb183ed89f15d7dbce00051a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OBZ3d8RuML8fjrCiqLcXsX3Z5AK3d+7qr/FHFqZh/snEtbiPo3pAlP8MAVRS90f29CirJPLQ9afwUIMCm89mAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T03:26:15.756229Z","bundle_sha256":"b604c9238c022d776ea5a336b2033b981ffde06485d958fe9e41bbcb6d9f8dc0"}}