{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SEPV2B7UQ5RT6GY7QRA5RVW4MJ","short_pith_number":"pith:SEPV2B7U","canonical_record":{"source":{"id":"1609.03038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-10T12:14:52Z","cross_cats_sorted":[],"title_canon_sha256":"8f4565e9395eedaad3ef674ad5eaec543abdf672d512c08c172735c51b8f3b12","abstract_canon_sha256":"0edb3313de61a3e59649feead26efcb762cb02b47329312dec5b372666c787ca"},"schema_version":"1.0"},"canonical_sha256":"911f5d07f487633f1b1f8441d8d6dc62612bf618073f704e861d42a1b21e5c42","source":{"kind":"arxiv","id":"1609.03038","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03038","created_at":"2026-05-18T01:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03038v2","created_at":"2026-05-18T01:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03038","created_at":"2026-05-18T01:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"SEPV2B7UQ5RT","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SEPV2B7UQ5RT6GY7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SEPV2B7U","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SEPV2B7UQ5RT6GY7QRA5RVW4MJ","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03038","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-10T12:14:52Z","cross_cats_sorted":[],"title_canon_sha256":"8f4565e9395eedaad3ef674ad5eaec543abdf672d512c08c172735c51b8f3b12","abstract_canon_sha256":"0edb3313de61a3e59649feead26efcb762cb02b47329312dec5b372666c787ca"},"schema_version":"1.0"},"canonical_sha256":"911f5d07f487633f1b1f8441d8d6dc62612bf618073f704e861d42a1b21e5c42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:56.427648Z","signature_b64":"mPQMt1JyBfjjsgRH+MYeZwOmnj2KdAB5avtaLTeojvvV5faR8bS9nRgh7oE1rO6piB0scA5heDmKwarr/CAMBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"911f5d07f487633f1b1f8441d8d6dc62612bf618073f704e861d42a1b21e5c42","last_reissued_at":"2026-05-18T01:03:56.426945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:56.426945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03038","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":"2026-05-18T01:03:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9xqgn1hh+cQD70MaRkDUyeB3CG3v7EmifxTXjviVUWDVA4BYReFJVfeHeuF7Hyh+jJbwbeCuOrMVE+gU1ROLCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:15:49.985529Z"},"content_sha256":"3d9f9cd4f6b7f18f8b4ae3afa2cf4baf9eb42ef53e00009d19135a22fda6197a","schema_version":"1.0","event_id":"sha256:3d9f9cd4f6b7f18f8b4ae3afa2cf4baf9eb42ef53e00009d19135a22fda6197a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SEPV2B7UQ5RT6GY7QRA5RVW4MJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Self-Dual Abelian Codes in some Non-Principal Ideal Group Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Parinyawat Choosuwan, Patanee Udomkavanich, Somphong Jitman","submitted_at":"2016-09-10T12:14:52Z","abstract_excerpt":"The main focus of this paper is the complete enumeration of self-dual abelian codes in non-principal ideal group algebras $\\mathbb{F}_{2^k}[A\\times \\mathbb{Z}_2\\times \\mathbb{Z}_{2^s}]$ with respect to both the Euclidean and Hermitian inner products, where $k$ and $s$ are positive integers and $A$ is an abelian group of odd order. Based on the well-know characterization of Euclidean and Hermitian self-dual abelian codes, we show that such enumeration can be obtained in terms of a suitable product of the number of cyclic codes, the number of Euclidean self-dual cyclic codes, and the number of H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03038","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":"2026-05-18T01:03:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vok+yhAvnUELafk45GszJUG3KJMrr7trhkBOa+bBISXdjJv1I42bQpmIiQQLKOjIoVNQcQWDvqz/mUF4HcX9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:15:49.985884Z"},"content_sha256":"8d4214c4205e4675f4f1693caee209d931a697250a076b95ad263fafead5281d","schema_version":"1.0","event_id":"sha256:8d4214c4205e4675f4f1693caee209d931a697250a076b95ad263fafead5281d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SEPV2B7UQ5RT6GY7QRA5RVW4MJ/bundle.json","state_url":"https://pith.science/pith/SEPV2B7UQ5RT6GY7QRA5RVW4MJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SEPV2B7UQ5RT6GY7QRA5RVW4MJ/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":"2026-06-01T09:15:49Z","links":{"resolver":"https://pith.science/pith/SEPV2B7UQ5RT6GY7QRA5RVW4MJ","bundle":"https://pith.science/pith/SEPV2B7UQ5RT6GY7QRA5RVW4MJ/bundle.json","state":"https://pith.science/pith/SEPV2B7UQ5RT6GY7QRA5RVW4MJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SEPV2B7UQ5RT6GY7QRA5RVW4MJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SEPV2B7UQ5RT6GY7QRA5RVW4MJ","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":"0edb3313de61a3e59649feead26efcb762cb02b47329312dec5b372666c787ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-10T12:14:52Z","title_canon_sha256":"8f4565e9395eedaad3ef674ad5eaec543abdf672d512c08c172735c51b8f3b12"},"schema_version":"1.0","source":{"id":"1609.03038","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03038","created_at":"2026-05-18T01:03:56Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03038v2","created_at":"2026-05-18T01:03:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03038","created_at":"2026-05-18T01:03:56Z"},{"alias_kind":"pith_short_12","alias_value":"SEPV2B7UQ5RT","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SEPV2B7UQ5RT6GY7","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SEPV2B7U","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:8d4214c4205e4675f4f1693caee209d931a697250a076b95ad263fafead5281d","target":"graph","created_at":"2026-05-18T01:03:56Z","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":"The main focus of this paper is the complete enumeration of self-dual abelian codes in non-principal ideal group algebras $\\mathbb{F}_{2^k}[A\\times \\mathbb{Z}_2\\times \\mathbb{Z}_{2^s}]$ with respect to both the Euclidean and Hermitian inner products, where $k$ and $s$ are positive integers and $A$ is an abelian group of odd order. Based on the well-know characterization of Euclidean and Hermitian self-dual abelian codes, we show that such enumeration can be obtained in terms of a suitable product of the number of cyclic codes, the number of Euclidean self-dual cyclic codes, and the number of H","authors_text":"Parinyawat Choosuwan, Patanee Udomkavanich, Somphong Jitman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-10T12:14:52Z","title":"Self-Dual Abelian Codes in some Non-Principal Ideal Group Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03038","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":"sha256:3d9f9cd4f6b7f18f8b4ae3afa2cf4baf9eb42ef53e00009d19135a22fda6197a","target":"record","created_at":"2026-05-18T01:03:56Z","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":"0edb3313de61a3e59649feead26efcb762cb02b47329312dec5b372666c787ca","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-09-10T12:14:52Z","title_canon_sha256":"8f4565e9395eedaad3ef674ad5eaec543abdf672d512c08c172735c51b8f3b12"},"schema_version":"1.0","source":{"id":"1609.03038","kind":"arxiv","version":2}},"canonical_sha256":"911f5d07f487633f1b1f8441d8d6dc62612bf618073f704e861d42a1b21e5c42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"911f5d07f487633f1b1f8441d8d6dc62612bf618073f704e861d42a1b21e5c42","first_computed_at":"2026-05-18T01:03:56.426945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:56.426945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mPQMt1JyBfjjsgRH+MYeZwOmnj2KdAB5avtaLTeojvvV5faR8bS9nRgh7oE1rO6piB0scA5heDmKwarr/CAMBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:56.427648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03038","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d9f9cd4f6b7f18f8b4ae3afa2cf4baf9eb42ef53e00009d19135a22fda6197a","sha256:8d4214c4205e4675f4f1693caee209d931a697250a076b95ad263fafead5281d"],"state_sha256":"4541a68076492c3b1de9b9949779778a4c0b47cd60d285bb3a27932d73fcf249"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xcprQuxjtFLTrVMVExOKbkdqo2kGJVFzH0EhybTgxwglghsRLhFn8pI4efdAYQlzK8IqZzelvtfa7yAAv7udAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:15:49.987948Z","bundle_sha256":"4848007482498d262235e0cc81cbfba66769572e5e974f3b94150a17633f8322"}}