{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PL5T56GMQK35DVENKHTZD457BI","short_pith_number":"pith:PL5T56GM","canonical_record":{"source":{"id":"1511.03582","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-11T17:35:50Z","cross_cats_sorted":[],"title_canon_sha256":"a9b16c00cae9df33de50e06ed2aa71baf6881d3e4f2db30acd9fd879ddf29d31","abstract_canon_sha256":"cc6af0b604b0a3e1a762acc10c3416b0d2f4280170faedd0db927e5b63125eb5"},"schema_version":"1.0"},"canonical_sha256":"7afb3ef8cc82b7d1d48d51e791f3bf0a270047fa6297d37c2ae0e06c6f6a9e7d","source":{"kind":"arxiv","id":"1511.03582","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03582","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03582v2","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03582","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"pith_short_12","alias_value":"PL5T56GMQK35","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PL5T56GMQK35DVEN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PL5T56GM","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PL5T56GMQK35DVENKHTZD457BI","target":"record","payload":{"canonical_record":{"source":{"id":"1511.03582","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-11T17:35:50Z","cross_cats_sorted":[],"title_canon_sha256":"a9b16c00cae9df33de50e06ed2aa71baf6881d3e4f2db30acd9fd879ddf29d31","abstract_canon_sha256":"cc6af0b604b0a3e1a762acc10c3416b0d2f4280170faedd0db927e5b63125eb5"},"schema_version":"1.0"},"canonical_sha256":"7afb3ef8cc82b7d1d48d51e791f3bf0a270047fa6297d37c2ae0e06c6f6a9e7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:41.665064Z","signature_b64":"CNtmU0JT4TrVER96AC2+MXgkTrEM5ckfFlvRMm54ZekVxielD0BclHr7x+9SB1Prh7y0Wyg8SNF1q3jSoIS8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7afb3ef8cc82b7d1d48d51e791f3bf0a270047fa6297d37c2ae0e06c6f6a9e7d","last_reissued_at":"2026-05-18T01:21:41.664616Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:41.664616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.03582","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":"2026-05-18T01:21:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"je3t3EL2Szqkf2OYyC7MDUb+6CLXzE/s8s8m2J4RO7w2H4Mqdj+Pj3GA6E0bTNHyWoLyXl7BJkuCi4dSGdTmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:41:22.623934Z"},"content_sha256":"fb72d3a78b0e4ebc24df15d624f7c64ec66c2e9cbd241efcf51b0d75505702f8","schema_version":"1.0","event_id":"sha256:fb72d3a78b0e4ebc24df15d624f7c64ec66c2e9cbd241efcf51b0d75505702f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PL5T56GMQK35DVENKHTZD457BI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computable Absolutely Normal Numbers and Discrepancies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Adrian-Maria Scheerer","submitted_at":"2015-11-11T17:35:50Z","abstract_excerpt":"We analyze algorithms that output absolutely normal numbers digit-by-digit with respect to quality of convergence to normality of the output, measured by the discrepancy. We consider explicit variants of algorithms by Sierpinski, by Turing and an adaption of constructive work on normal numbers by Schmidt. There seems to be a trade-off between the complexity of the algorithm and the speed of convergence to normality of the output."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03582","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":"2026-05-18T01:21:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tpZwGCy9aKd8whAJfYexo9jOprwXrmrjwIphnTEKfBJ3dG/Au1YzWuOUXa/S968GVo/BLgnwdq0lK4KdwARgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:41:22.624267Z"},"content_sha256":"9679735689a7fba3254482a6000dc7dee3f7cea15e0c82e41632f4658dc1c41e","schema_version":"1.0","event_id":"sha256:9679735689a7fba3254482a6000dc7dee3f7cea15e0c82e41632f4658dc1c41e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PL5T56GMQK35DVENKHTZD457BI/bundle.json","state_url":"https://pith.science/pith/PL5T56GMQK35DVENKHTZD457BI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PL5T56GMQK35DVENKHTZD457BI/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":"2026-06-20T07:41:22Z","links":{"resolver":"https://pith.science/pith/PL5T56GMQK35DVENKHTZD457BI","bundle":"https://pith.science/pith/PL5T56GMQK35DVENKHTZD457BI/bundle.json","state":"https://pith.science/pith/PL5T56GMQK35DVENKHTZD457BI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PL5T56GMQK35DVENKHTZD457BI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PL5T56GMQK35DVENKHTZD457BI","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":"cc6af0b604b0a3e1a762acc10c3416b0d2f4280170faedd0db927e5b63125eb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-11T17:35:50Z","title_canon_sha256":"a9b16c00cae9df33de50e06ed2aa71baf6881d3e4f2db30acd9fd879ddf29d31"},"schema_version":"1.0","source":{"id":"1511.03582","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03582","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03582v2","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03582","created_at":"2026-05-18T01:21:41Z"},{"alias_kind":"pith_short_12","alias_value":"PL5T56GMQK35","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PL5T56GMQK35DVEN","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PL5T56GM","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:9679735689a7fba3254482a6000dc7dee3f7cea15e0c82e41632f4658dc1c41e","target":"graph","created_at":"2026-05-18T01:21:41Z","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 analyze algorithms that output absolutely normal numbers digit-by-digit with respect to quality of convergence to normality of the output, measured by the discrepancy. We consider explicit variants of algorithms by Sierpinski, by Turing and an adaption of constructive work on normal numbers by Schmidt. There seems to be a trade-off between the complexity of the algorithm and the speed of convergence to normality of the output.","authors_text":"Adrian-Maria Scheerer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-11T17:35:50Z","title":"Computable Absolutely Normal Numbers and Discrepancies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03582","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:fb72d3a78b0e4ebc24df15d624f7c64ec66c2e9cbd241efcf51b0d75505702f8","target":"record","created_at":"2026-05-18T01:21:41Z","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":"cc6af0b604b0a3e1a762acc10c3416b0d2f4280170faedd0db927e5b63125eb5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-11-11T17:35:50Z","title_canon_sha256":"a9b16c00cae9df33de50e06ed2aa71baf6881d3e4f2db30acd9fd879ddf29d31"},"schema_version":"1.0","source":{"id":"1511.03582","kind":"arxiv","version":2}},"canonical_sha256":"7afb3ef8cc82b7d1d48d51e791f3bf0a270047fa6297d37c2ae0e06c6f6a9e7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7afb3ef8cc82b7d1d48d51e791f3bf0a270047fa6297d37c2ae0e06c6f6a9e7d","first_computed_at":"2026-05-18T01:21:41.664616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:41.664616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CNtmU0JT4TrVER96AC2+MXgkTrEM5ckfFlvRMm54ZekVxielD0BclHr7x+9SB1Prh7y0Wyg8SNF1q3jSoIS8Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:41.665064Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03582","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb72d3a78b0e4ebc24df15d624f7c64ec66c2e9cbd241efcf51b0d75505702f8","sha256:9679735689a7fba3254482a6000dc7dee3f7cea15e0c82e41632f4658dc1c41e"],"state_sha256":"cfb68b4c3143156f05bdd04763f3d366ce33c916cd3807c75a73a344e11bc5f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uAHGZ015SFitG5q4r2riGT5nmCsoSiNzoGLJXUKihFDN/pYbBn5o8/mRvxHJrX3NFulixSeX8jRZXkCOOu1rBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:41:22.626235Z","bundle_sha256":"1e26463a6153c46eb86fd5c4a77361145154c1708839ca04cf4eefcedf259cf9"}}