{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MH4O7D76TTCX6WWT6RMYS3T7ZI","short_pith_number":"pith:MH4O7D76","canonical_record":{"source":{"id":"1110.5467","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-25T11:24:44Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"397d24151eaf8099066f3c8868663d116b831aff3de7ad8d58b12be56a399dd8","abstract_canon_sha256":"722ee894bdb18831ddf49adbb21b76e617af43ddb6a190e0e94e6f82009c4ceb"},"schema_version":"1.0"},"canonical_sha256":"61f8ef8ffe9cc57f5ad3f459896e7fca0d9b46110719c7eade2500db26049ebc","source":{"kind":"arxiv","id":"1110.5467","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5467","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5467v1","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5467","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"MH4O7D76TTCX","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MH4O7D76TTCX6WWT","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MH4O7D76","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MH4O7D76TTCX6WWT6RMYS3T7ZI","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5467","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-25T11:24:44Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"397d24151eaf8099066f3c8868663d116b831aff3de7ad8d58b12be56a399dd8","abstract_canon_sha256":"722ee894bdb18831ddf49adbb21b76e617af43ddb6a190e0e94e6f82009c4ceb"},"schema_version":"1.0"},"canonical_sha256":"61f8ef8ffe9cc57f5ad3f459896e7fca0d9b46110719c7eade2500db26049ebc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:22.835902Z","signature_b64":"SED1Bf5z+gUPa7Nv3YwBL7VhEzl+nMvZo8g9gjgjqMehwSSpZNoOgkGjBplX1VdJkwTRIM/bx6IlYoztMxIGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61f8ef8ffe9cc57f5ad3f459896e7fca0d9b46110719c7eade2500db26049ebc","last_reissued_at":"2026-05-18T04:10:22.835286Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:22.835286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5467","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":"2026-05-18T04:10:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s/7OpKmvidxapB41T5jQqukNDPmulOdIJUfDyDprUYpDTZS7laDACmtBXYIqfajAVWoCDxYQAvPU81b4bjxuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:32:38.192393Z"},"content_sha256":"d5d5f4842480966fb8cff733de67c469b0986be4e8a33b260e0d517615d7edc5","schema_version":"1.0","event_id":"sha256:d5d5f4842480966fb8cff733de67c469b0986be4e8a33b260e0d517615d7edc5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MH4O7D76TTCX6WWT6RMYS3T7ZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inhomogeneous approximation with coprime integers and lattice orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Arnaldo Nogueira, Michel Laurent","submitted_at":"2011-10-25T11:24:44Z","abstract_excerpt":"We obtain variants of the classical Minkowski Theorem on inhomogeneous approximation where we require moreover that the solutions $p, q$ be coprime integers. We link the subject with density exponents of lattice orbits in the real plane."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5467","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":"2026-05-18T04:10:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6RcLFeU5Z+qtptP1awcQnLPAglmeyu7UmOjFkO/5QjIF7jK9PV/R1ECDH8nuxjoysPrNobbRDfayZrEw/AfABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T17:32:38.193032Z"},"content_sha256":"3a6e94f3142d13e35d805469bad9bad104661d6d9b7a81e44a4bdaa2c99a939f","schema_version":"1.0","event_id":"sha256:3a6e94f3142d13e35d805469bad9bad104661d6d9b7a81e44a4bdaa2c99a939f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MH4O7D76TTCX6WWT6RMYS3T7ZI/bundle.json","state_url":"https://pith.science/pith/MH4O7D76TTCX6WWT6RMYS3T7ZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MH4O7D76TTCX6WWT6RMYS3T7ZI/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":"2026-05-27T17:32:38Z","links":{"resolver":"https://pith.science/pith/MH4O7D76TTCX6WWT6RMYS3T7ZI","bundle":"https://pith.science/pith/MH4O7D76TTCX6WWT6RMYS3T7ZI/bundle.json","state":"https://pith.science/pith/MH4O7D76TTCX6WWT6RMYS3T7ZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MH4O7D76TTCX6WWT6RMYS3T7ZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MH4O7D76TTCX6WWT6RMYS3T7ZI","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":"722ee894bdb18831ddf49adbb21b76e617af43ddb6a190e0e94e6f82009c4ceb","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-25T11:24:44Z","title_canon_sha256":"397d24151eaf8099066f3c8868663d116b831aff3de7ad8d58b12be56a399dd8"},"schema_version":"1.0","source":{"id":"1110.5467","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5467","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5467v1","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5467","created_at":"2026-05-18T04:10:22Z"},{"alias_kind":"pith_short_12","alias_value":"MH4O7D76TTCX","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MH4O7D76TTCX6WWT","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MH4O7D76","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:3a6e94f3142d13e35d805469bad9bad104661d6d9b7a81e44a4bdaa2c99a939f","target":"graph","created_at":"2026-05-18T04:10:22Z","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 obtain variants of the classical Minkowski Theorem on inhomogeneous approximation where we require moreover that the solutions $p, q$ be coprime integers. We link the subject with density exponents of lattice orbits in the real plane.","authors_text":"Arnaldo Nogueira, Michel Laurent","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-25T11:24:44Z","title":"Inhomogeneous approximation with coprime integers and lattice orbits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5467","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:d5d5f4842480966fb8cff733de67c469b0986be4e8a33b260e0d517615d7edc5","target":"record","created_at":"2026-05-18T04:10:22Z","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":"722ee894bdb18831ddf49adbb21b76e617af43ddb6a190e0e94e6f82009c4ceb","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-10-25T11:24:44Z","title_canon_sha256":"397d24151eaf8099066f3c8868663d116b831aff3de7ad8d58b12be56a399dd8"},"schema_version":"1.0","source":{"id":"1110.5467","kind":"arxiv","version":1}},"canonical_sha256":"61f8ef8ffe9cc57f5ad3f459896e7fca0d9b46110719c7eade2500db26049ebc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61f8ef8ffe9cc57f5ad3f459896e7fca0d9b46110719c7eade2500db26049ebc","first_computed_at":"2026-05-18T04:10:22.835286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:22.835286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SED1Bf5z+gUPa7Nv3YwBL7VhEzl+nMvZo8g9gjgjqMehwSSpZNoOgkGjBplX1VdJkwTRIM/bx6IlYoztMxIGCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:22.835902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5467","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5d5f4842480966fb8cff733de67c469b0986be4e8a33b260e0d517615d7edc5","sha256:3a6e94f3142d13e35d805469bad9bad104661d6d9b7a81e44a4bdaa2c99a939f"],"state_sha256":"dc006af20705affc4127b5f5022bda8067526aba8a03f05d4b715326022c26cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LS6LjG+7mLvey9pAInzVm6Cnt/jAs6v/WskjD1RKzSPJ9CcpnG6MPD6HHIKy2FsPPzEPIrkZS5FVvfhFkitiDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T17:32:38.197203Z","bundle_sha256":"b79b7ee58281e58e86b765808b41db08526b9b4d707e7bf86fc7f36cc575f932"}}