{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:F3OO4JHA2AB4R42BRAUZSTDXNC","short_pith_number":"pith:F3OO4JHA","canonical_record":{"source":{"id":"1409.8387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-09-30T05:19:20Z","cross_cats_sorted":[],"title_canon_sha256":"ecfdaaedd5e9692ded50a2214cb68e3680f558addfae5c93df03e65d01798349","abstract_canon_sha256":"87f6141f6bf2d4135ac02bf79686466f8158508208bb880586b34d8d25733106"},"schema_version":"1.0"},"canonical_sha256":"2edcee24e0d003c8f3418829994c7768bc1ae2bb7917d054c4db3cd1ce72894d","source":{"kind":"arxiv","id":"1409.8387","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8387","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8387v2","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8387","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"F3OO4JHA2AB4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F3OO4JHA2AB4R42B","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F3OO4JHA","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:F3OO4JHA2AB4R42BRAUZSTDXNC","target":"record","payload":{"canonical_record":{"source":{"id":"1409.8387","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-09-30T05:19:20Z","cross_cats_sorted":[],"title_canon_sha256":"ecfdaaedd5e9692ded50a2214cb68e3680f558addfae5c93df03e65d01798349","abstract_canon_sha256":"87f6141f6bf2d4135ac02bf79686466f8158508208bb880586b34d8d25733106"},"schema_version":"1.0"},"canonical_sha256":"2edcee24e0d003c8f3418829994c7768bc1ae2bb7917d054c4db3cd1ce72894d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:20.835696Z","signature_b64":"L/BalfR0mz2XYVm03oOzZW8QryoJEzlanvGwpwZuKq5gLtZPl8qg7+VXDeBiWanLSBhhpyDUY9nFIshV+vMdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2edcee24e0d003c8f3418829994c7768bc1ae2bb7917d054c4db3cd1ce72894d","last_reissued_at":"2026-05-18T02:16:20.835100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:20.835100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.8387","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":"2026-05-18T02:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LM5QxtoTftq8Yr1P1CdRTONfgkEUm3IiQYmmXADFqMjtNwrtjxPT2hHh15bvYoKfv7rw+pX4ieVt3GoThB73Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T15:28:01.057691Z"},"content_sha256":"8132c201abb41b2c76fb1a630c93510e2567ce1715443da203e57511b1f829ce","schema_version":"1.0","event_id":"sha256:8132c201abb41b2c76fb1a630c93510e2567ce1715443da203e57511b1f829ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:F3OO4JHA2AB4R42BRAUZSTDXNC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Error-correction of linear codes via colon ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Benjamin Anzis, Stefan Tohaneanu","submitted_at":"2014-09-30T05:19:20Z","abstract_excerpt":"We show that errors in data transmitted through linear codes can be thought of as codewords of minimum weight of new linear codes. To determine errors we can then use methods specific to finding such special codewords. One of these methods consists of finding the primary decomposition of the saturation of a certain homogeneous ideal. When good words (i.e. vectors with a unique nearest neighbor) are error-corrected, the saturated ideal is just the prime ideal of a point (so the primary decomposition is superfluously determined); we show that this ideal can be computed by coloning the original h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8387","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":"2026-05-18T02:16:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+Q/GMiBnBSwEisyotRpk0Zjasaf9EwV/pb7mDF7/YzdIn/TkUFzlIQmQ8RgqwoWLtES7wQfxuD0OblC2vMxCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T15:28:01.058028Z"},"content_sha256":"9730cc8c9035f3ed78f25f38e491e0d599df664d9c40583333a43b3d58938744","schema_version":"1.0","event_id":"sha256:9730cc8c9035f3ed78f25f38e491e0d599df664d9c40583333a43b3d58938744"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3OO4JHA2AB4R42BRAUZSTDXNC/bundle.json","state_url":"https://pith.science/pith/F3OO4JHA2AB4R42BRAUZSTDXNC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3OO4JHA2AB4R42BRAUZSTDXNC/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":"2026-06-25T15:28:01Z","links":{"resolver":"https://pith.science/pith/F3OO4JHA2AB4R42BRAUZSTDXNC","bundle":"https://pith.science/pith/F3OO4JHA2AB4R42BRAUZSTDXNC/bundle.json","state":"https://pith.science/pith/F3OO4JHA2AB4R42BRAUZSTDXNC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3OO4JHA2AB4R42BRAUZSTDXNC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:F3OO4JHA2AB4R42BRAUZSTDXNC","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":"87f6141f6bf2d4135ac02bf79686466f8158508208bb880586b34d8d25733106","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-09-30T05:19:20Z","title_canon_sha256":"ecfdaaedd5e9692ded50a2214cb68e3680f558addfae5c93df03e65d01798349"},"schema_version":"1.0","source":{"id":"1409.8387","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8387","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8387v2","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8387","created_at":"2026-05-18T02:16:20Z"},{"alias_kind":"pith_short_12","alias_value":"F3OO4JHA2AB4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"F3OO4JHA2AB4R42B","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"F3OO4JHA","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:9730cc8c9035f3ed78f25f38e491e0d599df664d9c40583333a43b3d58938744","target":"graph","created_at":"2026-05-18T02:16:20Z","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 show that errors in data transmitted through linear codes can be thought of as codewords of minimum weight of new linear codes. To determine errors we can then use methods specific to finding such special codewords. One of these methods consists of finding the primary decomposition of the saturation of a certain homogeneous ideal. When good words (i.e. vectors with a unique nearest neighbor) are error-corrected, the saturated ideal is just the prime ideal of a point (so the primary decomposition is superfluously determined); we show that this ideal can be computed by coloning the original h","authors_text":"Benjamin Anzis, Stefan Tohaneanu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-09-30T05:19:20Z","title":"Error-correction of linear codes via colon ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8387","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":"sha256:8132c201abb41b2c76fb1a630c93510e2567ce1715443da203e57511b1f829ce","target":"record","created_at":"2026-05-18T02:16:20Z","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":"87f6141f6bf2d4135ac02bf79686466f8158508208bb880586b34d8d25733106","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-09-30T05:19:20Z","title_canon_sha256":"ecfdaaedd5e9692ded50a2214cb68e3680f558addfae5c93df03e65d01798349"},"schema_version":"1.0","source":{"id":"1409.8387","kind":"arxiv","version":2}},"canonical_sha256":"2edcee24e0d003c8f3418829994c7768bc1ae2bb7917d054c4db3cd1ce72894d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2edcee24e0d003c8f3418829994c7768bc1ae2bb7917d054c4db3cd1ce72894d","first_computed_at":"2026-05-18T02:16:20.835100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:16:20.835100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L/BalfR0mz2XYVm03oOzZW8QryoJEzlanvGwpwZuKq5gLtZPl8qg7+VXDeBiWanLSBhhpyDUY9nFIshV+vMdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:16:20.835696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8387","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8132c201abb41b2c76fb1a630c93510e2567ce1715443da203e57511b1f829ce","sha256:9730cc8c9035f3ed78f25f38e491e0d599df664d9c40583333a43b3d58938744"],"state_sha256":"b71a525d2ca8000a50effb051504b402a343cc8e97471e0faa16d2979025b635"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LpATWu+u+4UkhjRvYMfAU4DoU1NiGu9bW3klNU9SnGjLYFUF/6/dWm+m/1bjaKKG7OsKpQHxFy2GaDLPCn2sBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T15:28:01.059866Z","bundle_sha256":"4b0855375a5232931109b3c2f16f661af47359a0f354382b14182cbccbb8b982"}}