{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XS7T73YPXJAGIG4GFKWWIHH7HO","short_pith_number":"pith:XS7T73YP","canonical_record":{"source":{"id":"1808.10400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-30T17:08:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9280fbeb04e5b0c90512bc3e9960969684a5015051074c7a7978af12e16f7dc9","abstract_canon_sha256":"9a142293a533eb6d0cb5f01c914b4189dc965732d73728df1359c6ee7aaaf4ce"},"schema_version":"1.0"},"canonical_sha256":"bcbf3fef0fba40641b862aad641cff3b809ea5e8eddfdd07e2f61dc384648721","source":{"kind":"arxiv","id":"1808.10400","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10400","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10400v1","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10400","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"XS7T73YPXJAG","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XS7T73YPXJAGIG4G","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XS7T73YP","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XS7T73YPXJAGIG4GFKWWIHH7HO","target":"record","payload":{"canonical_record":{"source":{"id":"1808.10400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-30T17:08:53Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9280fbeb04e5b0c90512bc3e9960969684a5015051074c7a7978af12e16f7dc9","abstract_canon_sha256":"9a142293a533eb6d0cb5f01c914b4189dc965732d73728df1359c6ee7aaaf4ce"},"schema_version":"1.0"},"canonical_sha256":"bcbf3fef0fba40641b862aad641cff3b809ea5e8eddfdd07e2f61dc384648721","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:48.912430Z","signature_b64":"707fyoWbI/tTJsFlmHTRyawW1Xl1zsw7aN8SclOyT5uIveOMV7ZdhpTEDI2OwtXsoQx5lek6rLXO1vuQ0x0vDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcbf3fef0fba40641b862aad641cff3b809ea5e8eddfdd07e2f61dc384648721","last_reissued_at":"2026-05-18T00:06:48.911738Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:48.911738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.10400","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":"2026-05-18T00:06:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yIxYMRJoiBG+fGbjwGtS+Lp8Ly187JkxS0YJJ3j0Fn4TC19nNqG0Bsxwmmpb5TmxHPj0jWMeGjH4iqnz9B2/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:30:19.535501Z"},"content_sha256":"c520a2dd969eda2f0048039b9f340cab7d14367f78ceed7309ca5163bc27c071","schema_version":"1.0","event_id":"sha256:c520a2dd969eda2f0048039b9f340cab7d14367f78ceed7309ca5163bc27c071"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XS7T73YPXJAGIG4GFKWWIHH7HO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Radix-M Construction for Complementary Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Srdjan Z. Budisin","submitted_at":"2018-08-30T17:08:53Z","abstract_excerpt":"We extend the paraunitary (PU) theory for complementary pairs to comple- mentary sets and complete complementary codes (CCC) by proposing a new PU construction. A special, but very important case of complementary sets (and CC- C), based on standard delays, is analyzed in details and a new 'Radix-M generator' (RM-G) is presented. The RM-G can be viewed as a generalization of the Boolean generator for complementary pairs. An efficient correlator for standard complemen- tary sets and CCC is also presented. Finally, examples of polyphase, QAM and hexagonal PU sets of three sequences are given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10400","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":"2026-05-18T00:06:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"whKUjf8rP7Ad4s8BdAZj0rfzkSWQNKJLk+E1vY0Tc3GLc4PKBQVwm5g3gaV0yjQD9iyL2nYbo65XfVOq3A+YBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T10:30:19.535850Z"},"content_sha256":"8502f799e2a49d57bddf890ec94f6ac47c569ac4fff674fee565af602a3e77d1","schema_version":"1.0","event_id":"sha256:8502f799e2a49d57bddf890ec94f6ac47c569ac4fff674fee565af602a3e77d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XS7T73YPXJAGIG4GFKWWIHH7HO/bundle.json","state_url":"https://pith.science/pith/XS7T73YPXJAGIG4GFKWWIHH7HO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XS7T73YPXJAGIG4GFKWWIHH7HO/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":"2026-05-28T10:30:19Z","links":{"resolver":"https://pith.science/pith/XS7T73YPXJAGIG4GFKWWIHH7HO","bundle":"https://pith.science/pith/XS7T73YPXJAGIG4GFKWWIHH7HO/bundle.json","state":"https://pith.science/pith/XS7T73YPXJAGIG4GFKWWIHH7HO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XS7T73YPXJAGIG4GFKWWIHH7HO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XS7T73YPXJAGIG4GFKWWIHH7HO","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":"9a142293a533eb6d0cb5f01c914b4189dc965732d73728df1359c6ee7aaaf4ce","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-30T17:08:53Z","title_canon_sha256":"9280fbeb04e5b0c90512bc3e9960969684a5015051074c7a7978af12e16f7dc9"},"schema_version":"1.0","source":{"id":"1808.10400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.10400","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"arxiv_version","alias_value":"1808.10400v1","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.10400","created_at":"2026-05-18T00:06:48Z"},{"alias_kind":"pith_short_12","alias_value":"XS7T73YPXJAG","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XS7T73YPXJAGIG4G","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XS7T73YP","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:8502f799e2a49d57bddf890ec94f6ac47c569ac4fff674fee565af602a3e77d1","target":"graph","created_at":"2026-05-18T00:06:48Z","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 extend the paraunitary (PU) theory for complementary pairs to comple- mentary sets and complete complementary codes (CCC) by proposing a new PU construction. A special, but very important case of complementary sets (and CC- C), based on standard delays, is analyzed in details and a new 'Radix-M generator' (RM-G) is presented. The RM-G can be viewed as a generalization of the Boolean generator for complementary pairs. An efficient correlator for standard complemen- tary sets and CCC is also presented. Finally, examples of polyphase, QAM and hexagonal PU sets of three sequences are given.","authors_text":"Srdjan Z. Budisin","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-30T17:08:53Z","title":"A Radix-M Construction for Complementary Sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.10400","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:c520a2dd969eda2f0048039b9f340cab7d14367f78ceed7309ca5163bc27c071","target":"record","created_at":"2026-05-18T00:06:48Z","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":"9a142293a533eb6d0cb5f01c914b4189dc965732d73728df1359c6ee7aaaf4ce","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-30T17:08:53Z","title_canon_sha256":"9280fbeb04e5b0c90512bc3e9960969684a5015051074c7a7978af12e16f7dc9"},"schema_version":"1.0","source":{"id":"1808.10400","kind":"arxiv","version":1}},"canonical_sha256":"bcbf3fef0fba40641b862aad641cff3b809ea5e8eddfdd07e2f61dc384648721","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcbf3fef0fba40641b862aad641cff3b809ea5e8eddfdd07e2f61dc384648721","first_computed_at":"2026-05-18T00:06:48.911738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:48.911738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"707fyoWbI/tTJsFlmHTRyawW1Xl1zsw7aN8SclOyT5uIveOMV7ZdhpTEDI2OwtXsoQx5lek6rLXO1vuQ0x0vDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:48.912430Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.10400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c520a2dd969eda2f0048039b9f340cab7d14367f78ceed7309ca5163bc27c071","sha256:8502f799e2a49d57bddf890ec94f6ac47c569ac4fff674fee565af602a3e77d1"],"state_sha256":"d45b104a7a7e8123bfeb6bcc0217042a58e4045451a1dd07690d02fa0a124d2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ei3kyMlEL12h4tQ+LTbrdFLyLgOJfJk6PfhmabfDjrUGrUmyZRbCATwzBExCrL+21o6LDE8mXF4sgEkhDLmVDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T10:30:19.537830Z","bundle_sha256":"671b95dd843abcebcf46faea229ad8d5e587e5aac57308748d57c76baf0d6b10"}}