{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6EZV5UZJG6RRLM7JL6EFU2JZPT","short_pith_number":"pith:6EZV5UZJ","canonical_record":{"source":{"id":"1205.6433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-29T17:42:15Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"389820f418ce78b989ff94b9c191710a16ee49d481521b2bbef21a4dc24bc955","abstract_canon_sha256":"f69090c197670efba72cb3a36fd24e40c8afc3ee38ce3e60ee428b2fbc91c350"},"schema_version":"1.0"},"canonical_sha256":"f1335ed32937a315b3e95f885a69397cc94632e6d0beb9f1375ab894743c9848","source":{"kind":"arxiv","id":"1205.6433","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6433","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6433v1","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6433","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"6EZV5UZJG6RR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6EZV5UZJG6RRLM7J","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6EZV5UZJ","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6EZV5UZJG6RRLM7JL6EFU2JZPT","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-29T17:42:15Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"389820f418ce78b989ff94b9c191710a16ee49d481521b2bbef21a4dc24bc955","abstract_canon_sha256":"f69090c197670efba72cb3a36fd24e40c8afc3ee38ce3e60ee428b2fbc91c350"},"schema_version":"1.0"},"canonical_sha256":"f1335ed32937a315b3e95f885a69397cc94632e6d0beb9f1375ab894743c9848","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:51.633127Z","signature_b64":"ZoDBX8TFDdlt86B+YHKe/y/Lhbu0Ld/7aPkBeYA9lIpuuTqkuQ45IXlOSV5LZjRj7h8CnBb61mj3V7erWfECCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1335ed32937a315b3e95f885a69397cc94632e6d0beb9f1375ab894743c9848","last_reissued_at":"2026-05-18T03:39:51.632743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:51.632743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6433","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":"2026-05-18T03:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NkgvV13+U2enUzuR1BC3hbOTkuHb8WwU6sUVE/IiuMsKErGN+xCvLKoiOtSlNF+wfpMgEVyj0hOuAY5XXBSHCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:48:15.745371Z"},"content_sha256":"31854ca920fa800664f50e336d5c4e5d5869e73be23947dbaf3b0a3e0d2a1322","schema_version":"1.0","event_id":"sha256:31854ca920fa800664f50e336d5c4e5d5869e73be23947dbaf3b0a3e0d2a1322"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6EZV5UZJG6RRLM7JL6EFU2JZPT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Algebraic symmetries of generic $(m+1)$ dimensional periodic Costas arrays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Andrew Z. Tirkel, Jos\\'e Ortiz-Ubarri, Oscar Moreno, Rafael Arce-Nazario, Solomon W. Golomb","submitted_at":"2012-05-29T17:42:15Z","abstract_excerpt":"In this work we present two generators for the group of symmetries of the generic $(m+1)$ dimensional periodic Costas arrays over elementary abelian $(\\mathbb{Z}_p)^m$ groups: one that is defined by multiplication on $m$ dimensions and the other by shear (addition) on $m$ dimensions. Through exhaustive search we observe that these two generators characterize the group of symmetries for the examples we were able to compute. Following the results, we conjecture that these generators characterize the group of symmetries of the generic $(m+1)$ dimensional periodic Costas arrays over elementary abe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6433","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":"2026-05-18T03:39:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ByPKUcE4rNWyI5QcHEZ9hM/LKPplWWc/ouNb4TYc2AKcXj+/xziAc9t8Oe/g8VlJWtRG6ussTdR40KSVlAGIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:48:15.746029Z"},"content_sha256":"176712531b56c60da4ec9f547d037cc56762383e56e9ff1a08f38130ff81c681","schema_version":"1.0","event_id":"sha256:176712531b56c60da4ec9f547d037cc56762383e56e9ff1a08f38130ff81c681"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6EZV5UZJG6RRLM7JL6EFU2JZPT/bundle.json","state_url":"https://pith.science/pith/6EZV5UZJG6RRLM7JL6EFU2JZPT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6EZV5UZJG6RRLM7JL6EFU2JZPT/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":"2026-06-07T21:48:15Z","links":{"resolver":"https://pith.science/pith/6EZV5UZJG6RRLM7JL6EFU2JZPT","bundle":"https://pith.science/pith/6EZV5UZJG6RRLM7JL6EFU2JZPT/bundle.json","state":"https://pith.science/pith/6EZV5UZJG6RRLM7JL6EFU2JZPT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6EZV5UZJG6RRLM7JL6EFU2JZPT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6EZV5UZJG6RRLM7JL6EFU2JZPT","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":"f69090c197670efba72cb3a36fd24e40c8afc3ee38ce3e60ee428b2fbc91c350","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-29T17:42:15Z","title_canon_sha256":"389820f418ce78b989ff94b9c191710a16ee49d481521b2bbef21a4dc24bc955"},"schema_version":"1.0","source":{"id":"1205.6433","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6433","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6433v1","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6433","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"6EZV5UZJG6RR","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6EZV5UZJG6RRLM7J","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6EZV5UZJ","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:176712531b56c60da4ec9f547d037cc56762383e56e9ff1a08f38130ff81c681","target":"graph","created_at":"2026-05-18T03:39:51Z","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 present two generators for the group of symmetries of the generic $(m+1)$ dimensional periodic Costas arrays over elementary abelian $(\\mathbb{Z}_p)^m$ groups: one that is defined by multiplication on $m$ dimensions and the other by shear (addition) on $m$ dimensions. Through exhaustive search we observe that these two generators characterize the group of symmetries for the examples we were able to compute. Following the results, we conjecture that these generators characterize the group of symmetries of the generic $(m+1)$ dimensional periodic Costas arrays over elementary abe","authors_text":"Andrew Z. Tirkel, Jos\\'e Ortiz-Ubarri, Oscar Moreno, Rafael Arce-Nazario, Solomon W. Golomb","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-29T17:42:15Z","title":"Algebraic symmetries of generic $(m+1)$ dimensional periodic Costas arrays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6433","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":"sha256:31854ca920fa800664f50e336d5c4e5d5869e73be23947dbaf3b0a3e0d2a1322","target":"record","created_at":"2026-05-18T03:39:51Z","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":"f69090c197670efba72cb3a36fd24e40c8afc3ee38ce3e60ee428b2fbc91c350","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-05-29T17:42:15Z","title_canon_sha256":"389820f418ce78b989ff94b9c191710a16ee49d481521b2bbef21a4dc24bc955"},"schema_version":"1.0","source":{"id":"1205.6433","kind":"arxiv","version":1}},"canonical_sha256":"f1335ed32937a315b3e95f885a69397cc94632e6d0beb9f1375ab894743c9848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1335ed32937a315b3e95f885a69397cc94632e6d0beb9f1375ab894743c9848","first_computed_at":"2026-05-18T03:39:51.632743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:51.632743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZoDBX8TFDdlt86B+YHKe/y/Lhbu0Ld/7aPkBeYA9lIpuuTqkuQ45IXlOSV5LZjRj7h8CnBb61mj3V7erWfECCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:51.633127Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31854ca920fa800664f50e336d5c4e5d5869e73be23947dbaf3b0a3e0d2a1322","sha256:176712531b56c60da4ec9f547d037cc56762383e56e9ff1a08f38130ff81c681"],"state_sha256":"eea47441d86ae6ba7cc456be153e17b43364699ea415fff4f96f3bcc95f56a07"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6HWewckZkoeW3ghLOxAzwWnUIHTov1K32vgdS9b9+LOjsyNHpoAEMvjhj2J141BMJvgYPEQcrvqrMZVSBq0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:48:15.749720Z","bundle_sha256":"c5d14127c8fc78c2b7577d7083b037dabfef793b833d0f034ce4d2de198d06ee"}}