{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UIYZBM2HKSZJV6BPLH67VE6L5S","short_pith_number":"pith:UIYZBM2H","canonical_record":{"source":{"id":"1107.2321","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-12T15:19:54Z","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"title_canon_sha256":"b5ad3d0514546ecc4f494d60e7f5725adb0692516bfa135aa907c1bc91425557","abstract_canon_sha256":"c02588415fca13a629eb7913ade8a36069a5afba985c6276fb4367dbdc18f7b0"},"schema_version":"1.0"},"canonical_sha256":"a23190b34754b29af82f59fdfa93cbec986dd51635fbdae195946bd7eff1ffb5","source":{"kind":"arxiv","id":"1107.2321","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2321","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2321v2","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2321","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"pith_short_12","alias_value":"UIYZBM2HKSZJ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UIYZBM2HKSZJV6BP","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UIYZBM2H","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UIYZBM2HKSZJV6BPLH67VE6L5S","target":"record","payload":{"canonical_record":{"source":{"id":"1107.2321","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-12T15:19:54Z","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"title_canon_sha256":"b5ad3d0514546ecc4f494d60e7f5725adb0692516bfa135aa907c1bc91425557","abstract_canon_sha256":"c02588415fca13a629eb7913ade8a36069a5afba985c6276fb4367dbdc18f7b0"},"schema_version":"1.0"},"canonical_sha256":"a23190b34754b29af82f59fdfa93cbec986dd51635fbdae195946bd7eff1ffb5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:36.881880Z","signature_b64":"VjE1Tp6Gvl8tjP6Als0iwIM5kWlslD1qVZ3x9eHON9ToYYF6hQfwzScEAQM16hKkyOdmp5FhU/W2V+wvovG3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a23190b34754b29af82f59fdfa93cbec986dd51635fbdae195946bd7eff1ffb5","last_reissued_at":"2026-05-18T03:58:36.880974Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:36.880974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.2321","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":"2026-05-18T03:58:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3qsAkaTIoxyKYZPdzjj8JwY3hIgBjcJdoImNbV3KbOA9j8fSOLKpNqiDjz5i4HkZLuMmYiiMpGQx843p0CsvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:26:15.930802Z"},"content_sha256":"b0264d5295754903a77b70d1f98ea30f243eb99d3e6b5f8ea925a6d45e6fbe3a","schema_version":"1.0","event_id":"sha256:b0264d5295754903a77b70d1f98ea30f243eb99d3e6b5f8ea925a6d45e6fbe3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UIYZBM2HKSZJV6BPLH67VE6L5S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An algorithm for list decoding number field codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.IT","math.IT"],"primary_cat":"math.NT","authors_text":"Guillaume Quintin, Jean-Fran\\c{c}ois Biasse","submitted_at":"2011-07-12T15:19:54Z","abstract_excerpt":"We present an algorithm for list decoding codewords of algebraic number field codes in polynomial time. This is the first explicit procedure for decoding number field codes whose construction were previously described by Lenstra and Guruswami. We rely on an equivalent of the LLL reduction algorithm for $\\OK$-modules due to Fieker and Stehl\\'e and on algorithms due to Cohen for computing the Hermite normal form of matrices representing modules over Dedekind domains."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2321","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":"2026-05-18T03:58:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUYlvJnNruEneuzG/nKHOROWM3haS82XrwQzd5L932uOU4xIE0dyx5EQkUgjeYinmNKDm8in0jJyGUP6GqXQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T09:26:15.931151Z"},"content_sha256":"6071581beda08a6b1af31b927f1765727f6607e87d4a79f87731262ad04cae94","schema_version":"1.0","event_id":"sha256:6071581beda08a6b1af31b927f1765727f6607e87d4a79f87731262ad04cae94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UIYZBM2HKSZJV6BPLH67VE6L5S/bundle.json","state_url":"https://pith.science/pith/UIYZBM2HKSZJV6BPLH67VE6L5S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UIYZBM2HKSZJV6BPLH67VE6L5S/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":"2026-06-24T09:26:15Z","links":{"resolver":"https://pith.science/pith/UIYZBM2HKSZJV6BPLH67VE6L5S","bundle":"https://pith.science/pith/UIYZBM2HKSZJV6BPLH67VE6L5S/bundle.json","state":"https://pith.science/pith/UIYZBM2HKSZJV6BPLH67VE6L5S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UIYZBM2HKSZJV6BPLH67VE6L5S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UIYZBM2HKSZJV6BPLH67VE6L5S","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":"c02588415fca13a629eb7913ade8a36069a5afba985c6276fb4367dbdc18f7b0","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-12T15:19:54Z","title_canon_sha256":"b5ad3d0514546ecc4f494d60e7f5725adb0692516bfa135aa907c1bc91425557"},"schema_version":"1.0","source":{"id":"1107.2321","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2321","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2321v2","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2321","created_at":"2026-05-18T03:58:36Z"},{"alias_kind":"pith_short_12","alias_value":"UIYZBM2HKSZJ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UIYZBM2HKSZJV6BP","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UIYZBM2H","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6071581beda08a6b1af31b927f1765727f6607e87d4a79f87731262ad04cae94","target":"graph","created_at":"2026-05-18T03:58:36Z","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 present an algorithm for list decoding codewords of algebraic number field codes in polynomial time. This is the first explicit procedure for decoding number field codes whose construction were previously described by Lenstra and Guruswami. We rely on an equivalent of the LLL reduction algorithm for $\\OK$-modules due to Fieker and Stehl\\'e and on algorithms due to Cohen for computing the Hermite normal form of matrices representing modules over Dedekind domains.","authors_text":"Guillaume Quintin, Jean-Fran\\c{c}ois Biasse","cross_cats":["cs.CC","cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-12T15:19:54Z","title":"An algorithm for list decoding number field codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2321","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:b0264d5295754903a77b70d1f98ea30f243eb99d3e6b5f8ea925a6d45e6fbe3a","target":"record","created_at":"2026-05-18T03:58:36Z","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":"c02588415fca13a629eb7913ade8a36069a5afba985c6276fb4367dbdc18f7b0","cross_cats_sorted":["cs.CC","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-07-12T15:19:54Z","title_canon_sha256":"b5ad3d0514546ecc4f494d60e7f5725adb0692516bfa135aa907c1bc91425557"},"schema_version":"1.0","source":{"id":"1107.2321","kind":"arxiv","version":2}},"canonical_sha256":"a23190b34754b29af82f59fdfa93cbec986dd51635fbdae195946bd7eff1ffb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a23190b34754b29af82f59fdfa93cbec986dd51635fbdae195946bd7eff1ffb5","first_computed_at":"2026-05-18T03:58:36.880974Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:36.880974Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VjE1Tp6Gvl8tjP6Als0iwIM5kWlslD1qVZ3x9eHON9ToYYF6hQfwzScEAQM16hKkyOdmp5FhU/W2V+wvovG3BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:36.881880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2321","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0264d5295754903a77b70d1f98ea30f243eb99d3e6b5f8ea925a6d45e6fbe3a","sha256:6071581beda08a6b1af31b927f1765727f6607e87d4a79f87731262ad04cae94"],"state_sha256":"9573909c83f43ee1c333f4745980ec64a9e9ff33eff7094a90345108092d5443"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ne+EhYrENZCm4QVBtkkhUHAzW6bCjm+CSuaNMlFfoxrmQ7hFtfpoxlp4hneSLgQ+1bJekVutmZ2OCkoDqHReAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T09:26:15.933034Z","bundle_sha256":"15fc5573cfcb92b6624372e59858c4a51ed20e60d6ac2f81d0e2cd57559e9a65"}}