{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5PR33TTZUIUGNVIYIEKMXKPXQC","short_pith_number":"pith:5PR33TTZ","canonical_record":{"source":{"id":"1504.05121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-20T16:56:40Z","cross_cats_sorted":[],"title_canon_sha256":"11ce2f2aa2d872faa8e3b7c464393e9f8f6fd015aad286cadbd18ed7f02e1b15","abstract_canon_sha256":"e13c2439f6b36a6480ae1d232af242e94d9c1574116cf403120eaa11a92cfef0"},"schema_version":"1.0"},"canonical_sha256":"ebe3bdce79a22866d5184114cba9f780a018fa95bb2df5bf02d352ba8f44f9b3","source":{"kind":"arxiv","id":"1504.05121","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05121","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05121v1","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05121","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"5PR33TTZUIUG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5PR33TTZUIUGNVIY","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5PR33TTZ","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5PR33TTZUIUGNVIYIEKMXKPXQC","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-20T16:56:40Z","cross_cats_sorted":[],"title_canon_sha256":"11ce2f2aa2d872faa8e3b7c464393e9f8f6fd015aad286cadbd18ed7f02e1b15","abstract_canon_sha256":"e13c2439f6b36a6480ae1d232af242e94d9c1574116cf403120eaa11a92cfef0"},"schema_version":"1.0"},"canonical_sha256":"ebe3bdce79a22866d5184114cba9f780a018fa95bb2df5bf02d352ba8f44f9b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:34.550306Z","signature_b64":"R1DPkZmbDL8C5h3xjKv1ilKjN/5c98J+4s+odzzDpzyGTfaJSm6yKL7WJFde5yyriv1Ywl/m2UPbfQXNt1+8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebe3bdce79a22866d5184114cba9f780a018fa95bb2df5bf02d352ba8f44f9b3","last_reissued_at":"2026-05-17T23:53:34.549521Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:34.549521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05121","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":"2026-05-17T23:53:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2UcjKBQEdCf6u+ry9w3orVWgfb/uTATec8io40hvoyoc8FbmBjuypHHKTdQTYbwvMQLrpS3ySymhEqCebwXdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:13:04.636106Z"},"content_sha256":"de18b597b546689355e32ba0018b9ba3955eea85bf53874e0949264bc978c8c5","schema_version":"1.0","event_id":"sha256:de18b597b546689355e32ba0018b9ba3955eea85bf53874e0949264bc978c8c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5PR33TTZUIUGNVIYIEKMXKPXQC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-trivial matrix actions preserve normality for continued fractions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Joseph Vandehey","submitted_at":"2015-04-20T16:56:40Z","abstract_excerpt":"A seminal result due to Wall states that if $x$ is normal to a given base $b$ then so is $rx+s$ for any rational numbers $r,s$ with $r\\neq 0$. We show that a stronger result is true for normality with respect to the continued fraction expansion. In particular, suppose $a,b,c,d\\in \\mathbb{Z}$ with $ad-bc\\neq 0$. Then if $x$ is continued fraction normal, so is $(ax+b)/(cx+d)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05121","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":"2026-05-17T23:53:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"snUQzxtXFR9ysTp+DmBV5mOLABFyEMeUbMg9MQWxQyS/12ePNqkYnp7jPqTX+84qeVVjGCs64GCpOvSxnpNFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T07:13:04.636802Z"},"content_sha256":"899f1c1dc5a0f1eaf8b3f0c080a87251f14d7265191a07e671371feedce38b0a","schema_version":"1.0","event_id":"sha256:899f1c1dc5a0f1eaf8b3f0c080a87251f14d7265191a07e671371feedce38b0a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5PR33TTZUIUGNVIYIEKMXKPXQC/bundle.json","state_url":"https://pith.science/pith/5PR33TTZUIUGNVIYIEKMXKPXQC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5PR33TTZUIUGNVIYIEKMXKPXQC/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":"2026-05-31T07:13:04Z","links":{"resolver":"https://pith.science/pith/5PR33TTZUIUGNVIYIEKMXKPXQC","bundle":"https://pith.science/pith/5PR33TTZUIUGNVIYIEKMXKPXQC/bundle.json","state":"https://pith.science/pith/5PR33TTZUIUGNVIYIEKMXKPXQC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5PR33TTZUIUGNVIYIEKMXKPXQC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5PR33TTZUIUGNVIYIEKMXKPXQC","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":"e13c2439f6b36a6480ae1d232af242e94d9c1574116cf403120eaa11a92cfef0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-20T16:56:40Z","title_canon_sha256":"11ce2f2aa2d872faa8e3b7c464393e9f8f6fd015aad286cadbd18ed7f02e1b15"},"schema_version":"1.0","source":{"id":"1504.05121","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05121","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05121v1","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05121","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"5PR33TTZUIUG","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5PR33TTZUIUGNVIY","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5PR33TTZ","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:899f1c1dc5a0f1eaf8b3f0c080a87251f14d7265191a07e671371feedce38b0a","target":"graph","created_at":"2026-05-17T23:53:34Z","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":"A seminal result due to Wall states that if $x$ is normal to a given base $b$ then so is $rx+s$ for any rational numbers $r,s$ with $r\\neq 0$. We show that a stronger result is true for normality with respect to the continued fraction expansion. In particular, suppose $a,b,c,d\\in \\mathbb{Z}$ with $ad-bc\\neq 0$. Then if $x$ is continued fraction normal, so is $(ax+b)/(cx+d)$.","authors_text":"Joseph Vandehey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-20T16:56:40Z","title":"Non-trivial matrix actions preserve normality for continued fractions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05121","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:de18b597b546689355e32ba0018b9ba3955eea85bf53874e0949264bc978c8c5","target":"record","created_at":"2026-05-17T23:53:34Z","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":"e13c2439f6b36a6480ae1d232af242e94d9c1574116cf403120eaa11a92cfef0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-20T16:56:40Z","title_canon_sha256":"11ce2f2aa2d872faa8e3b7c464393e9f8f6fd015aad286cadbd18ed7f02e1b15"},"schema_version":"1.0","source":{"id":"1504.05121","kind":"arxiv","version":1}},"canonical_sha256":"ebe3bdce79a22866d5184114cba9f780a018fa95bb2df5bf02d352ba8f44f9b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebe3bdce79a22866d5184114cba9f780a018fa95bb2df5bf02d352ba8f44f9b3","first_computed_at":"2026-05-17T23:53:34.549521Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:34.549521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R1DPkZmbDL8C5h3xjKv1ilKjN/5c98J+4s+odzzDpzyGTfaJSm6yKL7WJFde5yyriv1Ywl/m2UPbfQXNt1+8Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:34.550306Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05121","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de18b597b546689355e32ba0018b9ba3955eea85bf53874e0949264bc978c8c5","sha256:899f1c1dc5a0f1eaf8b3f0c080a87251f14d7265191a07e671371feedce38b0a"],"state_sha256":"f916d69d90c4c9d4a22d4fd0a44f60f44cc333ae9522e79d8e978cb59f8a38cf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sn/fB3LMPoFQSSZnZx3T1O2Ai7ECqar54nmlGdqROylqKb7gsC2u1/HuOjAzG+k+9GJMpMvqBZaPhWdzHvdCBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T07:13:04.640437Z","bundle_sha256":"f799c8a3dd06c825beb97800052068fcfd266007d688a68f62fce5c865d5712b"}}