{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EKJSDSCHWAE36WHWIODQ35WOTM","short_pith_number":"pith:EKJSDSCH","canonical_record":{"source":{"id":"1311.0455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-03T10:42:41Z","cross_cats_sorted":[],"title_canon_sha256":"aa2a620091299eb3108441ddcd982d85cf588d0fee0179c9b74b5bded9df3252","abstract_canon_sha256":"5c4774e955850d153474d5a2c7541e7f38d02937a6e5d4161427ad65c68bb9a7"},"schema_version":"1.0"},"canonical_sha256":"229321c847b009bf58f643870df6ce9b3c3d046a435d84e7388350b35830b72e","source":{"kind":"arxiv","id":"1311.0455","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0455","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0455v1","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0455","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"EKJSDSCHWAE3","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EKJSDSCHWAE36WHW","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EKJSDSCH","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EKJSDSCHWAE36WHWIODQ35WOTM","target":"record","payload":{"canonical_record":{"source":{"id":"1311.0455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-03T10:42:41Z","cross_cats_sorted":[],"title_canon_sha256":"aa2a620091299eb3108441ddcd982d85cf588d0fee0179c9b74b5bded9df3252","abstract_canon_sha256":"5c4774e955850d153474d5a2c7541e7f38d02937a6e5d4161427ad65c68bb9a7"},"schema_version":"1.0"},"canonical_sha256":"229321c847b009bf58f643870df6ce9b3c3d046a435d84e7388350b35830b72e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:47.253768Z","signature_b64":"HWdhZllLxExlpTbxwFoJpDM8JpURj1gdibcELR6pLUtFAzDBVJ6LfmBMGphVpJxuDVGCYIAcZuM1/1Egd5unAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"229321c847b009bf58f643870df6ce9b3c3d046a435d84e7388350b35830b72e","last_reissued_at":"2026-05-18T00:18:47.253130Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:47.253130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.0455","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":"2026-05-18T00:18:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z5mUgSGGnvDKZx6Aip/wg93CUY2tf2/RbTryICOJKQCbVe5iAbNlDnMMHzN3yc9Lc+tR5yWkiUomy1L53pTOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:33:43.292549Z"},"content_sha256":"b9b6401182c1e7d94841627f38befcbb7357b941d00c145fb8d169091d4b845a","schema_version":"1.0","event_id":"sha256:b9b6401182c1e7d94841627f38befcbb7357b941d00c145fb8d169091d4b845a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EKJSDSCHWAE36WHWIODQ35WOTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geodesic continued fractions and LLL","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Frits Beukers","submitted_at":"2013-11-03T10:42:41Z","abstract_excerpt":"We discuss a proposal for a continued fraction-like algorithm to determine simultaneous rational approximations to $d$ real numbers $\\alpha_1,\\ldots,\\alpha_d$. It combines an algorithm of Hermite and Lagarias with ideas from LLL-reduction. We dynamically LLL-reduce a quadratic form with parameter $t$ as $t\\downarrow0$. The new idea in this paper is that checking the LLL-conditions consists of solving linear equations in $t$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0455","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":"2026-05-18T00:18:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4lQfV+Txz1ehobDh+bBAqRueij6A5tzdMneF5ravjG5sZpemWj5FwBCbF/6OelpiesserwUBwOUmBAhLMhJnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T12:33:43.292900Z"},"content_sha256":"773be23ce6633a3fbc9bd31930b57cfa3599432aba4cce37d2b9f066cecbe05f","schema_version":"1.0","event_id":"sha256:773be23ce6633a3fbc9bd31930b57cfa3599432aba4cce37d2b9f066cecbe05f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKJSDSCHWAE36WHWIODQ35WOTM/bundle.json","state_url":"https://pith.science/pith/EKJSDSCHWAE36WHWIODQ35WOTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKJSDSCHWAE36WHWIODQ35WOTM/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":"2026-07-02T12:33:43Z","links":{"resolver":"https://pith.science/pith/EKJSDSCHWAE36WHWIODQ35WOTM","bundle":"https://pith.science/pith/EKJSDSCHWAE36WHWIODQ35WOTM/bundle.json","state":"https://pith.science/pith/EKJSDSCHWAE36WHWIODQ35WOTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKJSDSCHWAE36WHWIODQ35WOTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EKJSDSCHWAE36WHWIODQ35WOTM","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":"5c4774e955850d153474d5a2c7541e7f38d02937a6e5d4161427ad65c68bb9a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-03T10:42:41Z","title_canon_sha256":"aa2a620091299eb3108441ddcd982d85cf588d0fee0179c9b74b5bded9df3252"},"schema_version":"1.0","source":{"id":"1311.0455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0455","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0455v1","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0455","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"EKJSDSCHWAE3","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EKJSDSCHWAE36WHW","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EKJSDSCH","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:773be23ce6633a3fbc9bd31930b57cfa3599432aba4cce37d2b9f066cecbe05f","target":"graph","created_at":"2026-05-18T00:18:47Z","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 discuss a proposal for a continued fraction-like algorithm to determine simultaneous rational approximations to $d$ real numbers $\\alpha_1,\\ldots,\\alpha_d$. It combines an algorithm of Hermite and Lagarias with ideas from LLL-reduction. We dynamically LLL-reduce a quadratic form with parameter $t$ as $t\\downarrow0$. The new idea in this paper is that checking the LLL-conditions consists of solving linear equations in $t$.","authors_text":"Frits Beukers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-03T10:42:41Z","title":"Geodesic continued fractions and LLL"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0455","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:b9b6401182c1e7d94841627f38befcbb7357b941d00c145fb8d169091d4b845a","target":"record","created_at":"2026-05-18T00:18:47Z","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":"5c4774e955850d153474d5a2c7541e7f38d02937a6e5d4161427ad65c68bb9a7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-11-03T10:42:41Z","title_canon_sha256":"aa2a620091299eb3108441ddcd982d85cf588d0fee0179c9b74b5bded9df3252"},"schema_version":"1.0","source":{"id":"1311.0455","kind":"arxiv","version":1}},"canonical_sha256":"229321c847b009bf58f643870df6ce9b3c3d046a435d84e7388350b35830b72e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"229321c847b009bf58f643870df6ce9b3c3d046a435d84e7388350b35830b72e","first_computed_at":"2026-05-18T00:18:47.253130Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:47.253130Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HWdhZllLxExlpTbxwFoJpDM8JpURj1gdibcELR6pLUtFAzDBVJ6LfmBMGphVpJxuDVGCYIAcZuM1/1Egd5unAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:47.253768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9b6401182c1e7d94841627f38befcbb7357b941d00c145fb8d169091d4b845a","sha256:773be23ce6633a3fbc9bd31930b57cfa3599432aba4cce37d2b9f066cecbe05f"],"state_sha256":"f87a8f1a10e52aa56814a20a6bd0e79cfcae7a6c31cfaa4734a3da6fe17cb9cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"87tdrBnpriXvlbmgINQHDLr4gDmNt4EX2WvfigvnKgXt3EnledEfidzHdRk0ZiPWiU6zR7aUBMXGJ7VXk8gdAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T12:33:43.294863Z","bundle_sha256":"71cccc0fd6c9d35584afbdc96ff9d4ebb56f5b0c177426774d44c4c0696fb9bd"}}