{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:F3SUKKM2YAU4Q3U4CAT776FAFZ","short_pith_number":"pith:F3SUKKM2","canonical_record":{"source":{"id":"1310.3772","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-14T18:32:43Z","cross_cats_sorted":[],"title_canon_sha256":"02c33866ef73de64698ddfe165d2507143eb65ffd1f5d4c1972441100fb2ec5d","abstract_canon_sha256":"da99e1db90fa57a164dae04e2ab4fa7bdda499b6e38cd056153a69b572f63655"},"schema_version":"1.0"},"canonical_sha256":"2ee545299ac029c86e9c1027fff8a02e742db608b69049799be0230b6ae34247","source":{"kind":"arxiv","id":"1310.3772","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3772","created_at":"2026-05-18T02:38:37Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3772v4","created_at":"2026-05-18T02:38:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3772","created_at":"2026-05-18T02:38:37Z"},{"alias_kind":"pith_short_12","alias_value":"F3SUKKM2YAU4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"F3SUKKM2YAU4Q3U4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"F3SUKKM2","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:F3SUKKM2YAU4Q3U4CAT776FAFZ","target":"record","payload":{"canonical_record":{"source":{"id":"1310.3772","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-14T18:32:43Z","cross_cats_sorted":[],"title_canon_sha256":"02c33866ef73de64698ddfe165d2507143eb65ffd1f5d4c1972441100fb2ec5d","abstract_canon_sha256":"da99e1db90fa57a164dae04e2ab4fa7bdda499b6e38cd056153a69b572f63655"},"schema_version":"1.0"},"canonical_sha256":"2ee545299ac029c86e9c1027fff8a02e742db608b69049799be0230b6ae34247","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:38:37.379720Z","signature_b64":"n0tCYsKJc2f9++TTKdd3qVm+nu7EIQ1uB9LG2HkLADKozcvOjeUqbiUoCb8uYAwWRzShfRFweDCwK5FpF406CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ee545299ac029c86e9c1027fff8a02e742db608b69049799be0230b6ae34247","last_reissued_at":"2026-05-18T02:38:37.379213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:38:37.379213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.3772","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:38:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YgjvUeXtahV5/okZcZwvt/jOvfayyXdmmCQ0kvkvi7Baiu6V8OV7COaDASOT8p4t/09/NMub9wUm0EL+XYMCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:33:54.640344Z"},"content_sha256":"8bf1b465cd29ee415141a77ab1cc96b995b2fadd23a21dc59723eccec81cc3cd","schema_version":"1.0","event_id":"sha256:8bf1b465cd29ee415141a77ab1cc96b995b2fadd23a21dc59723eccec81cc3cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:F3SUKKM2YAU4Q3U4CAT776FAFZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Improvement To Zaremba's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"ShinnYih Huang","submitted_at":"2013-10-14T18:32:43Z","abstract_excerpt":"We prove there exists a density one subset $\\dd \\subset \\N$ such that each $n \\in \\dd$ is the denominator of a finite continued fraction with partial quotients bounded by 5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3772","kind":"arxiv","version":4},"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":"2026-05-18T02:38:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u0DYl5tcdU77X+J+5wfIo2HtRWti2dc0f1z9OSWvDfaHSzfuEhc9IJATnvseeNj1GKwexwqstcE9zGZgGh7ODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:33:54.640739Z"},"content_sha256":"76c29a8a9fb59105607ffc7f4365efe8c0bf310ecb33846ce866b4f241270c23","schema_version":"1.0","event_id":"sha256:76c29a8a9fb59105607ffc7f4365efe8c0bf310ecb33846ce866b4f241270c23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3SUKKM2YAU4Q3U4CAT776FAFZ/bundle.json","state_url":"https://pith.science/pith/F3SUKKM2YAU4Q3U4CAT776FAFZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3SUKKM2YAU4Q3U4CAT776FAFZ/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":"2026-06-05T18:33:54Z","links":{"resolver":"https://pith.science/pith/F3SUKKM2YAU4Q3U4CAT776FAFZ","bundle":"https://pith.science/pith/F3SUKKM2YAU4Q3U4CAT776FAFZ/bundle.json","state":"https://pith.science/pith/F3SUKKM2YAU4Q3U4CAT776FAFZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3SUKKM2YAU4Q3U4CAT776FAFZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:F3SUKKM2YAU4Q3U4CAT776FAFZ","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":"da99e1db90fa57a164dae04e2ab4fa7bdda499b6e38cd056153a69b572f63655","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-14T18:32:43Z","title_canon_sha256":"02c33866ef73de64698ddfe165d2507143eb65ffd1f5d4c1972441100fb2ec5d"},"schema_version":"1.0","source":{"id":"1310.3772","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3772","created_at":"2026-05-18T02:38:37Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3772v4","created_at":"2026-05-18T02:38:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3772","created_at":"2026-05-18T02:38:37Z"},{"alias_kind":"pith_short_12","alias_value":"F3SUKKM2YAU4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"F3SUKKM2YAU4Q3U4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"F3SUKKM2","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:76c29a8a9fb59105607ffc7f4365efe8c0bf310ecb33846ce866b4f241270c23","target":"graph","created_at":"2026-05-18T02:38:37Z","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 prove there exists a density one subset $\\dd \\subset \\N$ such that each $n \\in \\dd$ is the denominator of a finite continued fraction with partial quotients bounded by 5.","authors_text":"ShinnYih Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-14T18:32:43Z","title":"An Improvement To Zaremba's Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3772","kind":"arxiv","version":4},"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":"sha256:8bf1b465cd29ee415141a77ab1cc96b995b2fadd23a21dc59723eccec81cc3cd","target":"record","created_at":"2026-05-18T02:38:37Z","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":"da99e1db90fa57a164dae04e2ab4fa7bdda499b6e38cd056153a69b572f63655","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-10-14T18:32:43Z","title_canon_sha256":"02c33866ef73de64698ddfe165d2507143eb65ffd1f5d4c1972441100fb2ec5d"},"schema_version":"1.0","source":{"id":"1310.3772","kind":"arxiv","version":4}},"canonical_sha256":"2ee545299ac029c86e9c1027fff8a02e742db608b69049799be0230b6ae34247","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ee545299ac029c86e9c1027fff8a02e742db608b69049799be0230b6ae34247","first_computed_at":"2026-05-18T02:38:37.379213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:37.379213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n0tCYsKJc2f9++TTKdd3qVm+nu7EIQ1uB9LG2HkLADKozcvOjeUqbiUoCb8uYAwWRzShfRFweDCwK5FpF406CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:37.379720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3772","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8bf1b465cd29ee415141a77ab1cc96b995b2fadd23a21dc59723eccec81cc3cd","sha256:76c29a8a9fb59105607ffc7f4365efe8c0bf310ecb33846ce866b4f241270c23"],"state_sha256":"4343467f7ec83da5c9c5dae20d4eae14c8cacee749d1b4e1e9161b205138b6c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QmnsAeSBDa8b3jAtvacXKCl4OWyAszL+WZb86uWVfYMK9r0AoWcKl80Wy9NopIcSYeTzAQJOQKV+6tfjLKZsBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:33:54.642775Z","bundle_sha256":"11594e278d5e1816b8bf52931f0998e1727949ffb26e9b02963f1e161468cdbe"}}