{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7RKBVVZA44QGQPEB72G42Z6Z2Y","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":"3e04c0be0967aa6af3084e7e4476b5a4283145a92dc1889142d0fe7563d218bc","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-09-16T05:48:52Z","title_canon_sha256":"d3cfd4ba199800ea647111ae5a137897bce5c569a04505a5046f6142b1389182"},"schema_version":"1.0","source":{"id":"1709.05466","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05466","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05466v1","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05466","created_at":"2026-05-18T00:35:00Z"},{"alias_kind":"pith_short_12","alias_value":"7RKBVVZA44QG","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7RKBVVZA44QGQPEB","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7RKBVVZA","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:0c6214ff77eba04f5107997f3237e6a324f9415fddc31eb78374f90fa0e8a68b","target":"graph","created_at":"2026-05-18T00:35:00Z","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":"In this work, we study the structure of multivariable modular codes over finite chain rings when the ambient space is a principal ideal ring. We also provide some applications to additive modular codes over the finite field $\\mathbb{F}_4$.","authors_text":"A. Pi\\~nera-Nicol\\'as, E. Mart\\'inez-Moro, I.F. R\\'ua","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-09-16T05:48:52Z","title":"Multivariable codes in principal ideal polynomial quotient rings with applications to additive modular bivariate codes over $\\mathbb{F}_4$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05466","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":"sha256:1e6aa9b8f3c35396dacbafc12e9c5257c4570a0bc3d140a921780018ef18df9d","target":"record","created_at":"2026-05-18T00:35:00Z","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":"3e04c0be0967aa6af3084e7e4476b5a4283145a92dc1889142d0fe7563d218bc","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-09-16T05:48:52Z","title_canon_sha256":"d3cfd4ba199800ea647111ae5a137897bce5c569a04505a5046f6142b1389182"},"schema_version":"1.0","source":{"id":"1709.05466","kind":"arxiv","version":1}},"canonical_sha256":"fc541ad720e720683c81fe8dcd67d9d6183c6ab5dff95400510d54981a9b4723","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc541ad720e720683c81fe8dcd67d9d6183c6ab5dff95400510d54981a9b4723","first_computed_at":"2026-05-18T00:35:00.672896Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:00.672896Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZBjs1Qkup4j32J2DWd3fWhwP8BuUU4FwVxfZgAkvb/Hv9z5bvO819yF+SlDAVRfGuS267I0ZtTZYUkTzDqOpAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:00.673446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05466","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e6aa9b8f3c35396dacbafc12e9c5257c4570a0bc3d140a921780018ef18df9d","sha256:0c6214ff77eba04f5107997f3237e6a324f9415fddc31eb78374f90fa0e8a68b"],"state_sha256":"e5be4af3a51555c919a827d8df8ff560b65ee4e58c3f969326717b69f8ad0dd6"}