{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:V7D7YSK3VE3N5SLD5WRAAXBESV","short_pith_number":"pith:V7D7YSK3","canonical_record":{"source":{"id":"0812.3186","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-12-17T00:50:54Z","cross_cats_sorted":["cs.FL","math.NT"],"title_canon_sha256":"9683e68c818878eb71196a40755ab14aa1a38c75ec7f1d0f6c67f8e4e0d4e2a7","abstract_canon_sha256":"8e772a43aeafc55b5642ce674aaae87f6c4410e8b9f7eab90950445d06320d65"},"schema_version":"1.0"},"canonical_sha256":"afc7fc495ba936dec963eda2005c24957473b1189b9e6d35dd6ab4025e635b7b","source":{"kind":"arxiv","id":"0812.3186","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3186","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3186v3","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3186","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"V7D7YSK3VE3N","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"V7D7YSK3VE3N5SLD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"V7D7YSK3","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:V7D7YSK3VE3N5SLD5WRAAXBESV","target":"record","payload":{"canonical_record":{"source":{"id":"0812.3186","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-12-17T00:50:54Z","cross_cats_sorted":["cs.FL","math.NT"],"title_canon_sha256":"9683e68c818878eb71196a40755ab14aa1a38c75ec7f1d0f6c67f8e4e0d4e2a7","abstract_canon_sha256":"8e772a43aeafc55b5642ce674aaae87f6c4410e8b9f7eab90950445d06320d65"},"schema_version":"1.0"},"canonical_sha256":"afc7fc495ba936dec963eda2005c24957473b1189b9e6d35dd6ab4025e635b7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:04.604852Z","signature_b64":"NVTZGEvTf/FLvyBIo8vgrNAAMy0AXODtCVJPapoBDHvQQowrgmIdlY8rIn92geopcAH1iEvnb9IwJUwSoasTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"afc7fc495ba936dec963eda2005c24957473b1189b9e6d35dd6ab4025e635b7b","last_reissued_at":"2026-05-18T02:15:04.604437Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:04.604437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.3186","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:15:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N+cBQPwVkuNuA1fkSGTMCG+/NjD0PjVCQC/WeVMz1Mzk19jTS1EAcMRKOqIiWd9uHnG8IaUYBnoGFWSq0BviCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:07:12.166338Z"},"content_sha256":"e889549c5df5a8f67a111de72baab7c774b08fd9891b1e7efeb2be7cb8492314","schema_version":"1.0","event_id":"sha256:e889549c5df5a8f67a111de72baab7c774b08fd9891b1e7efeb2be7cb8492314"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:V7D7YSK3VE3N5SLD5WRAAXBESV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","math.NT"],"primary_cat":"math.CO","authors_text":"E. Grant, J. Shallit, T. Stoll","submitted_at":"2008-12-17T00:50:54Z","abstract_excerpt":"Motivated by the known autocorrelation properties of the Rudin-Shapiro sequence, we study the discrete correlation among infinite sequences over a finite alphabet, where we just take into account whether two symbols are identical. We show by combinatorial means that sequences cannot be \"too\" different, and by an explicit construction generalizing the Rudin-Shapiro sequence, we show that we can achieve the maximum possible difference."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3186","kind":"arxiv","version":3},"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":"2026-05-18T02:15:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lZTRsv8tnYtfXnwtK+iM+h7tcpb6E8z4IrhXhFSphajH08Q+oi8NpZGH6fuF7erDW/0VIlbJVfOtAbpSZx3TDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:07:12.166692Z"},"content_sha256":"7efae2387f82b806af5bcb794cd4c380f51fc3251c7158699bf1c3cf868cbe29","schema_version":"1.0","event_id":"sha256:7efae2387f82b806af5bcb794cd4c380f51fc3251c7158699bf1c3cf868cbe29"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V7D7YSK3VE3N5SLD5WRAAXBESV/bundle.json","state_url":"https://pith.science/pith/V7D7YSK3VE3N5SLD5WRAAXBESV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V7D7YSK3VE3N5SLD5WRAAXBESV/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":"2026-06-25T20:07:12Z","links":{"resolver":"https://pith.science/pith/V7D7YSK3VE3N5SLD5WRAAXBESV","bundle":"https://pith.science/pith/V7D7YSK3VE3N5SLD5WRAAXBESV/bundle.json","state":"https://pith.science/pith/V7D7YSK3VE3N5SLD5WRAAXBESV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V7D7YSK3VE3N5SLD5WRAAXBESV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:V7D7YSK3VE3N5SLD5WRAAXBESV","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":"8e772a43aeafc55b5642ce674aaae87f6c4410e8b9f7eab90950445d06320d65","cross_cats_sorted":["cs.FL","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-12-17T00:50:54Z","title_canon_sha256":"9683e68c818878eb71196a40755ab14aa1a38c75ec7f1d0f6c67f8e4e0d4e2a7"},"schema_version":"1.0","source":{"id":"0812.3186","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.3186","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"0812.3186v3","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.3186","created_at":"2026-05-18T02:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"V7D7YSK3VE3N","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"V7D7YSK3VE3N5SLD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"V7D7YSK3","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:7efae2387f82b806af5bcb794cd4c380f51fc3251c7158699bf1c3cf868cbe29","target":"graph","created_at":"2026-05-18T02:15:04Z","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":"Motivated by the known autocorrelation properties of the Rudin-Shapiro sequence, we study the discrete correlation among infinite sequences over a finite alphabet, where we just take into account whether two symbols are identical. We show by combinatorial means that sequences cannot be \"too\" different, and by an explicit construction generalizing the Rudin-Shapiro sequence, we show that we can achieve the maximum possible difference.","authors_text":"E. Grant, J. Shallit, T. Stoll","cross_cats":["cs.FL","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-12-17T00:50:54Z","title":"Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.3186","kind":"arxiv","version":3},"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:e889549c5df5a8f67a111de72baab7c774b08fd9891b1e7efeb2be7cb8492314","target":"record","created_at":"2026-05-18T02:15:04Z","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":"8e772a43aeafc55b5642ce674aaae87f6c4410e8b9f7eab90950445d06320d65","cross_cats_sorted":["cs.FL","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-12-17T00:50:54Z","title_canon_sha256":"9683e68c818878eb71196a40755ab14aa1a38c75ec7f1d0f6c67f8e4e0d4e2a7"},"schema_version":"1.0","source":{"id":"0812.3186","kind":"arxiv","version":3}},"canonical_sha256":"afc7fc495ba936dec963eda2005c24957473b1189b9e6d35dd6ab4025e635b7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"afc7fc495ba936dec963eda2005c24957473b1189b9e6d35dd6ab4025e635b7b","first_computed_at":"2026-05-18T02:15:04.604437Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:04.604437Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NVTZGEvTf/FLvyBIo8vgrNAAMy0AXODtCVJPapoBDHvQQowrgmIdlY8rIn92geopcAH1iEvnb9IwJUwSoasTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:04.604852Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.3186","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e889549c5df5a8f67a111de72baab7c774b08fd9891b1e7efeb2be7cb8492314","sha256:7efae2387f82b806af5bcb794cd4c380f51fc3251c7158699bf1c3cf868cbe29"],"state_sha256":"6f0d84fb8a94602263b114e34292663636dae316a44f557ba9a7d82caf332f51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3A6u0Fa8PvooDUIpQNZ8GxqPQOrfanuuO3oo1Wb6Dbxn3hdEM8r4pLDIIpmitdtrPxTM+GZc1cqpOKVv2aFeCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:07:12.168658Z","bundle_sha256":"cf33352793a5becec048689a545f8f90f751b6f24c87837c97caf48d220c6220"}}