{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZDNEBBYWMKZYXVOQG5B2XNDJEN","short_pith_number":"pith:ZDNEBBYW","canonical_record":{"source":{"id":"1603.04055","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-13T18:00:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"fec838ab84ecbb0ccf4620b91a8b545d0e4856414d78d8b97814e9dcea974bab","abstract_canon_sha256":"454598f3160953bc7d74c8c4c7b68373fa3f04112bd753f68a9353ebcb9e8023"},"schema_version":"1.0"},"canonical_sha256":"c8da40871662b38bd5d03743abb469236dae206eea11b5da2ab958227fc32f15","source":{"kind":"arxiv","id":"1603.04055","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04055","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04055v1","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04055","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZDNEBBYWMKZY","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZDNEBBYWMKZYXVOQ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZDNEBBYW","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZDNEBBYWMKZYXVOQG5B2XNDJEN","target":"record","payload":{"canonical_record":{"source":{"id":"1603.04055","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-13T18:00:34Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"fec838ab84ecbb0ccf4620b91a8b545d0e4856414d78d8b97814e9dcea974bab","abstract_canon_sha256":"454598f3160953bc7d74c8c4c7b68373fa3f04112bd753f68a9353ebcb9e8023"},"schema_version":"1.0"},"canonical_sha256":"c8da40871662b38bd5d03743abb469236dae206eea11b5da2ab958227fc32f15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:09.542177Z","signature_b64":"sPMXMVVRPGoQ2RsPPCHoG3CNQn7Hm34aalCMuGWeO4siWuhDTl8I8YTCFeKo1SDFsbQdzBdu0iVi4J4F4tusDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8da40871662b38bd5d03743abb469236dae206eea11b5da2ab958227fc32f15","last_reissued_at":"2026-05-18T01:19:09.541220Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:09.541220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.04055","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DH1Kk86WI0QPpK6C/URWp7OeQDZ4C0jnx0c79xRb5Cpq1XTUZfJiqknabIV89qstvoK5izTKmeYzGnO71WijDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:07:19.217339Z"},"content_sha256":"1d720ab541e6a16a4aea5fdda74737379a3f668057331a305ad1f5c16c2e15db","schema_version":"1.0","event_id":"sha256:1d720ab541e6a16a4aea5fdda74737379a3f668057331a305ad1f5c16c2e15db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZDNEBBYWMKZYXVOQG5B2XNDJEN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of cyclic DNA codes over the Ring $\\Z_4[u]/\\langle u^2-1 \\rangle $ Based on the deletion distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Abhay Kumar Singh, Sukhamoy Pattanayak","submitted_at":"2016-03-13T18:00:34Z","abstract_excerpt":"In this paper, we develop the theory for constructing DNA cyclic codes of odd length over $R=\\Z_4[u]/\\langle u^2-1 \\rangle$ based on the deletion distance. Firstly, we relate DNA pairs with a special 16 elements of ring $R$. Cyclic codes of odd length over $R$ satisfy the reverse constraint and the reverse-complement constraint are discussed in this paper. We also study the $GC$-content of these codes and their deletion distance. The paper concludes with some examples of cyclic DNA codes with $GC$-content and their respective deletion distance."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04055","kind":"arxiv","version":1},"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":"2026-05-18T01:19:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PJvEa3LDp2mvNc8G+PUOzQ+FV1ltSvmKGe3F0HG7+/hpJFSlLMhpQsULphEJyr/0Pm4nbsABabb+AKUgPK3YBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:07:19.217833Z"},"content_sha256":"91d689a6ba5b822d3408f9d26d6cec025d87de3b47d28c74ebe08038c080e372","schema_version":"1.0","event_id":"sha256:91d689a6ba5b822d3408f9d26d6cec025d87de3b47d28c74ebe08038c080e372"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZDNEBBYWMKZYXVOQG5B2XNDJEN/bundle.json","state_url":"https://pith.science/pith/ZDNEBBYWMKZYXVOQG5B2XNDJEN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZDNEBBYWMKZYXVOQG5B2XNDJEN/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":"2026-06-24T21:07:19Z","links":{"resolver":"https://pith.science/pith/ZDNEBBYWMKZYXVOQG5B2XNDJEN","bundle":"https://pith.science/pith/ZDNEBBYWMKZYXVOQG5B2XNDJEN/bundle.json","state":"https://pith.science/pith/ZDNEBBYWMKZYXVOQG5B2XNDJEN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZDNEBBYWMKZYXVOQG5B2XNDJEN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZDNEBBYWMKZYXVOQG5B2XNDJEN","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":"454598f3160953bc7d74c8c4c7b68373fa3f04112bd753f68a9353ebcb9e8023","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-13T18:00:34Z","title_canon_sha256":"fec838ab84ecbb0ccf4620b91a8b545d0e4856414d78d8b97814e9dcea974bab"},"schema_version":"1.0","source":{"id":"1603.04055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04055","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04055v1","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04055","created_at":"2026-05-18T01:19:09Z"},{"alias_kind":"pith_short_12","alias_value":"ZDNEBBYWMKZY","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZDNEBBYWMKZYXVOQ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZDNEBBYW","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:91d689a6ba5b822d3408f9d26d6cec025d87de3b47d28c74ebe08038c080e372","target":"graph","created_at":"2026-05-18T01:19:09Z","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 paper, we develop the theory for constructing DNA cyclic codes of odd length over $R=\\Z_4[u]/\\langle u^2-1 \\rangle$ based on the deletion distance. Firstly, we relate DNA pairs with a special 16 elements of ring $R$. Cyclic codes of odd length over $R$ satisfy the reverse constraint and the reverse-complement constraint are discussed in this paper. We also study the $GC$-content of these codes and their deletion distance. The paper concludes with some examples of cyclic DNA codes with $GC$-content and their respective deletion distance.","authors_text":"Abhay Kumar Singh, Sukhamoy Pattanayak","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-13T18:00:34Z","title":"Construction of cyclic DNA codes over the Ring $\\Z_4[u]/\\langle u^2-1 \\rangle $ Based on the deletion distance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04055","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":"sha256:1d720ab541e6a16a4aea5fdda74737379a3f668057331a305ad1f5c16c2e15db","target":"record","created_at":"2026-05-18T01:19:09Z","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":"454598f3160953bc7d74c8c4c7b68373fa3f04112bd753f68a9353ebcb9e8023","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-03-13T18:00:34Z","title_canon_sha256":"fec838ab84ecbb0ccf4620b91a8b545d0e4856414d78d8b97814e9dcea974bab"},"schema_version":"1.0","source":{"id":"1603.04055","kind":"arxiv","version":1}},"canonical_sha256":"c8da40871662b38bd5d03743abb469236dae206eea11b5da2ab958227fc32f15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c8da40871662b38bd5d03743abb469236dae206eea11b5da2ab958227fc32f15","first_computed_at":"2026-05-18T01:19:09.541220Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:09.541220Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sPMXMVVRPGoQ2RsPPCHoG3CNQn7Hm34aalCMuGWeO4siWuhDTl8I8YTCFeKo1SDFsbQdzBdu0iVi4J4F4tusDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:09.542177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d720ab541e6a16a4aea5fdda74737379a3f668057331a305ad1f5c16c2e15db","sha256:91d689a6ba5b822d3408f9d26d6cec025d87de3b47d28c74ebe08038c080e372"],"state_sha256":"440bf11226f85808ad394a11e0dd72cd3445b6e47fc20bebc372ba4660258ed2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H/ASL+zm5LzLipqqhFIqKbN4+rWoP7mCkQbWNgq5VBMFNnjwnUCcCSN3SX2+KFak0BXVEolmsJ0Ntjx5sQEgAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:07:19.220402Z","bundle_sha256":"9621385f961eab9a71bbf76c624d193fd6f4a4bf58adaaa8ee801b78c1149e57"}}