{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:SAKVGP4VPOZ435TRLG3OD2WBDT","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":"42b21be1c3d066770546774aec7c49e15f99b315a693f8c0960cc509518a3853","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-11-28T13:08:24Z","title_canon_sha256":"3117690e8311c61bec74189183568f885e4bf530bf17af0a1e4f92b671b41a92"},"schema_version":"1.0","source":{"id":"math/0511678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0511678","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"arxiv_version","alias_value":"math/0511678v1","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0511678","created_at":"2026-05-18T03:56:23Z"},{"alias_kind":"pith_short_12","alias_value":"SAKVGP4VPOZ4","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"SAKVGP4VPOZ435TR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"SAKVGP4V","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:dc8b1361feb8b239f6b27e2d61873d44fb8b55979a1807fb5709240191aa817f","target":"graph","created_at":"2026-05-18T03:56:23Z","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":"For any given real number $\\alpha$ with bounded partial quotients, we construct explicitly continuum many real numbers $\\beta$ with bounded partial quotients for which the pair $(\\alpha, \\beta)$ satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.","authors_text":"Boris Adamczewski (ICJ), Yann Bugeaud (IRMA)","cross_cats":[],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2005-11-28T13:08:24Z","title":"On the Littlewood conjecture in simultaneous Diophantine approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511678","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":"sha256:21f397bfe5e6af21d2952fb524e468970dcb524a5a988a1dfa7f553f013856db","target":"record","created_at":"2026-05-18T03:56:23Z","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":"42b21be1c3d066770546774aec7c49e15f99b315a693f8c0960cc509518a3853","cross_cats_sorted":[],"license":"","primary_cat":"math.NT","submitted_at":"2005-11-28T13:08:24Z","title_canon_sha256":"3117690e8311c61bec74189183568f885e4bf530bf17af0a1e4f92b671b41a92"},"schema_version":"1.0","source":{"id":"math/0511678","kind":"arxiv","version":1}},"canonical_sha256":"9015533f957bb3cdf67159b6e1eac11cc79db6f196d0b07ce034a653d6c35d4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9015533f957bb3cdf67159b6e1eac11cc79db6f196d0b07ce034a653d6c35d4a","first_computed_at":"2026-05-18T03:56:23.244561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:23.244561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DsDAwXJgvPiv714Od2ju1aLpnN1Z0wddbSk5ki/rqm9PIWGvwZHE1UJk0p6EeiiuDj1nox0uZX36pxA2wjsyAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:23.245192Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0511678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21f397bfe5e6af21d2952fb524e468970dcb524a5a988a1dfa7f553f013856db","sha256:dc8b1361feb8b239f6b27e2d61873d44fb8b55979a1807fb5709240191aa817f"],"state_sha256":"fad892af8e625a09038f3967b95350bedba937175210f6aec256eec102c5c3ce"}