{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Y2WA6374CMSVRS56JDBP4OTKHP","short_pith_number":"pith:Y2WA6374","canonical_record":{"source":{"id":"1310.2232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-08T19:30:49Z","cross_cats_sorted":[],"title_canon_sha256":"b94a97b1d8e51a743842072e53283964c6035a291837a27b9a42751e35987028","abstract_canon_sha256":"ce9621ff54c55e349c7ad5e94791bfae847523fe8568cb946d9b4ec38d0ae6b3"},"schema_version":"1.0"},"canonical_sha256":"c6ac0f6ffc132558cbbe48c2fe3a6a3bd3f0ba7df356fb54d48db88d2000ef7f","source":{"kind":"arxiv","id":"1310.2232","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2232","created_at":"2026-05-18T03:10:02Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2232v2","created_at":"2026-05-18T03:10:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2232","created_at":"2026-05-18T03:10:02Z"},{"alias_kind":"pith_short_12","alias_value":"Y2WA6374CMSV","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y2WA6374CMSVRS56","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y2WA6374","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Y2WA6374CMSVRS56JDBP4OTKHP","target":"record","payload":{"canonical_record":{"source":{"id":"1310.2232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-08T19:30:49Z","cross_cats_sorted":[],"title_canon_sha256":"b94a97b1d8e51a743842072e53283964c6035a291837a27b9a42751e35987028","abstract_canon_sha256":"ce9621ff54c55e349c7ad5e94791bfae847523fe8568cb946d9b4ec38d0ae6b3"},"schema_version":"1.0"},"canonical_sha256":"c6ac0f6ffc132558cbbe48c2fe3a6a3bd3f0ba7df356fb54d48db88d2000ef7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:02.987677Z","signature_b64":"DLOYH5fsFmDRKl8VpuFeq0mf8G8kmal8lHtH8TF6Fu4+ZxZliTHE/5WXdtLoOe8qYZnJbzxDmMgfmnzvitOBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6ac0f6ffc132558cbbe48c2fe3a6a3bd3f0ba7df356fb54d48db88d2000ef7f","last_reissued_at":"2026-05-18T03:10:02.987212Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:02.987212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.2232","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":"2026-05-18T03:10:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6na0Yre2kVIEP+WH1hVbNQx3jRwAFUSo2SZ8bUITjwfjTSaA6IU2gsQH5Yd+R25hB5c1kGSigSyCtIQEC4akCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:36:21.332872Z"},"content_sha256":"805d18cb128aad27726e5400426c0bf8ecbba31e0f5fdc717c8f75e807324e99","schema_version":"1.0","event_id":"sha256:805d18cb128aad27726e5400426c0bf8ecbba31e0f5fdc717c8f75e807324e99"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Y2WA6374CMSVRS56JDBP4OTKHP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Comparative Study of the Signal-to-Noise Ratios of Different Representations for Symbolic Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Changchuan Yin, Chuangyin Dang, Jiasong Wang","submitted_at":"2013-10-08T19:30:49Z","abstract_excerpt":"Based on the numerical representations by T basic vectors of a symbolic sequence consisting of T symbols, first, we prove mathematical that the total Fourier spectrum of the sequence is the square of the length of the sequence. In the meantime, we define the indicator sequences vector. Using the orthogonal or row orthogonal transformations of the indicator sequences vector, we construct some special numerical representations of the symbolic sequence and characterize the signal-to-noise ratios of the power spectrum of the numerical representations. After calculating the discrete Fourier transfo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2232","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":"2026-05-18T03:10:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"62zqr+90h/F8KIXrUR7bnoA7/TeiuRXTw+C/10ZktWU86z5kqC/doXj5Js2ZFc8tn6u8fQoy5DB4m4Z82yg/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:36:21.333279Z"},"content_sha256":"051fcf1111fe9f2d9a6dc7ea85ba7370a581adffdda50167851c844af2d084d3","schema_version":"1.0","event_id":"sha256:051fcf1111fe9f2d9a6dc7ea85ba7370a581adffdda50167851c844af2d084d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2WA6374CMSVRS56JDBP4OTKHP/bundle.json","state_url":"https://pith.science/pith/Y2WA6374CMSVRS56JDBP4OTKHP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2WA6374CMSVRS56JDBP4OTKHP/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":"2026-06-03T12:36:21Z","links":{"resolver":"https://pith.science/pith/Y2WA6374CMSVRS56JDBP4OTKHP","bundle":"https://pith.science/pith/Y2WA6374CMSVRS56JDBP4OTKHP/bundle.json","state":"https://pith.science/pith/Y2WA6374CMSVRS56JDBP4OTKHP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2WA6374CMSVRS56JDBP4OTKHP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Y2WA6374CMSVRS56JDBP4OTKHP","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":"ce9621ff54c55e349c7ad5e94791bfae847523fe8568cb946d9b4ec38d0ae6b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-08T19:30:49Z","title_canon_sha256":"b94a97b1d8e51a743842072e53283964c6035a291837a27b9a42751e35987028"},"schema_version":"1.0","source":{"id":"1310.2232","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.2232","created_at":"2026-05-18T03:10:02Z"},{"alias_kind":"arxiv_version","alias_value":"1310.2232v2","created_at":"2026-05-18T03:10:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2232","created_at":"2026-05-18T03:10:02Z"},{"alias_kind":"pith_short_12","alias_value":"Y2WA6374CMSV","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y2WA6374CMSVRS56","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y2WA6374","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:051fcf1111fe9f2d9a6dc7ea85ba7370a581adffdda50167851c844af2d084d3","target":"graph","created_at":"2026-05-18T03:10:02Z","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":"Based on the numerical representations by T basic vectors of a symbolic sequence consisting of T symbols, first, we prove mathematical that the total Fourier spectrum of the sequence is the square of the length of the sequence. In the meantime, we define the indicator sequences vector. Using the orthogonal or row orthogonal transformations of the indicator sequences vector, we construct some special numerical representations of the symbolic sequence and characterize the signal-to-noise ratios of the power spectrum of the numerical representations. After calculating the discrete Fourier transfo","authors_text":"Changchuan Yin, Chuangyin Dang, Jiasong Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-08T19:30:49Z","title":"A Comparative Study of the Signal-to-Noise Ratios of Different Representations for Symbolic Sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2232","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":"sha256:805d18cb128aad27726e5400426c0bf8ecbba31e0f5fdc717c8f75e807324e99","target":"record","created_at":"2026-05-18T03:10:02Z","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":"ce9621ff54c55e349c7ad5e94791bfae847523fe8568cb946d9b4ec38d0ae6b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-10-08T19:30:49Z","title_canon_sha256":"b94a97b1d8e51a743842072e53283964c6035a291837a27b9a42751e35987028"},"schema_version":"1.0","source":{"id":"1310.2232","kind":"arxiv","version":2}},"canonical_sha256":"c6ac0f6ffc132558cbbe48c2fe3a6a3bd3f0ba7df356fb54d48db88d2000ef7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6ac0f6ffc132558cbbe48c2fe3a6a3bd3f0ba7df356fb54d48db88d2000ef7f","first_computed_at":"2026-05-18T03:10:02.987212Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:02.987212Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DLOYH5fsFmDRKl8VpuFeq0mf8G8kmal8lHtH8TF6Fu4+ZxZliTHE/5WXdtLoOe8qYZnJbzxDmMgfmnzvitOBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:02.987677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.2232","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:805d18cb128aad27726e5400426c0bf8ecbba31e0f5fdc717c8f75e807324e99","sha256:051fcf1111fe9f2d9a6dc7ea85ba7370a581adffdda50167851c844af2d084d3"],"state_sha256":"73b3e7e9867ddbd6c1f3f9b745c7f9b76996883cb5c08c37c9ae1c2fb2eaa3b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pgEZDsyf4Ulo9KwGb3sVU/EYBJfXwuh1AForlKblJEhWDz9bgkK/Qdk8XdSDKb4SGuwiOGfb0NwvoWQSldIuBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T12:36:21.335366Z","bundle_sha256":"3738d85c00fcbb64adc61bf7eb31f216824317cc3c96836b991e26cfb238f608"}}