{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:H656Q2DR5TGB5A33AQWTTBWEN4","short_pith_number":"pith:H656Q2DR","canonical_record":{"source":{"id":"1709.04082","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-12T23:13:38Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"785688b23e59d736f60d4641776953064f4b8cd6cc0013a55ec74398972065af","abstract_canon_sha256":"f9616d8dd86e736517d2deaf576bd793d02b0de2cfacf753ab28841cf15366bf"},"schema_version":"1.0"},"canonical_sha256":"3fbbe86871eccc1e837b042d3986c46f1abc6988a618ee9a6f26a84f4dfb1f47","source":{"kind":"arxiv","id":"1709.04082","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04082","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04082v2","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04082","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"pith_short_12","alias_value":"H656Q2DR5TGB","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H656Q2DR5TGB5A33","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H656Q2DR","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:H656Q2DR5TGB5A33AQWTTBWEN4","target":"record","payload":{"canonical_record":{"source":{"id":"1709.04082","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-12T23:13:38Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"785688b23e59d736f60d4641776953064f4b8cd6cc0013a55ec74398972065af","abstract_canon_sha256":"f9616d8dd86e736517d2deaf576bd793d02b0de2cfacf753ab28841cf15366bf"},"schema_version":"1.0"},"canonical_sha256":"3fbbe86871eccc1e837b042d3986c46f1abc6988a618ee9a6f26a84f4dfb1f47","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:31.076548Z","signature_b64":"CN4YTIiWD5UILN0PFgn8H8vrPFbTyMx99zP/HfTce1xs+ux4HhcxCXx4Mn4Jo+NocJRnJBGG+Zs94A/WiwV8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fbbe86871eccc1e837b042d3986c46f1abc6988a618ee9a6f26a84f4dfb1f47","last_reissued_at":"2026-05-17T23:42:31.075969Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:31.075969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.04082","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+ZcDqOFNy27TGF2s9ofAPuQTwAZoSaLfMdnI8WGqe8GTQZR/tMLPpACt/HOEiGbFJzRgLUdVcvw0Zb+UJwiWAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:41:49.654523Z"},"content_sha256":"b8c457fc8edc70165250d4c6c572681f382142825187a521a2bae4a0e4eb6306","schema_version":"1.0","event_id":"sha256:b8c457fc8edc70165250d4c6c572681f382142825187a521a2bae4a0e4eb6306"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:H656Q2DR5TGB5A33AQWTTBWEN4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An inhomogeneous Dirichlet theorem via shrinking targets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Dmitry Kleinbock, Nick Wadleigh","submitted_at":"2017-09-12T23:13:38Z","abstract_excerpt":"We give an integrability criterion on a real-valued non-increasing function $\\psi$ guaranteeing that for almost all (or almost no) pairs $(A, \\textbf{b})$, where $A$ is a real $m\\times n$ matrix and $\\textbf{b} \\in \\mathbb{R}^m$, the system $\\|A \\textbf{q}+\\textbf{b}-\\textbf{p}\\|^m< \\psi({T})$, $\\|\\textbf{q}\\|^n<{T}$ is solvable in $\\textbf{p} \\in \\mathbb{Z}^m$, $\\textbf{q} \\in \\mathbb{Z}^n$ for all sufficiently large $T$. The proof consists of a reduction to a shrinking target problem on the space of grids in $\\mathbb{R}^{m+n}$. We also comment on the homogeneous counterpart to this problem, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04082","kind":"arxiv","version":2},"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":"2026-05-17T23:42:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"csW4fnCHoFoa3zPvfM7CD4CBjdfMDbGZcbOTpp8kgxIOrqh54lsqm3uWgXVk7MVBMf9/itbzYhIYMgE+A7ddAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:41:49.655273Z"},"content_sha256":"164efe3e08666a47488db6c8f30bebaae6e763d5a9f2cb7e130502d82139f8f8","schema_version":"1.0","event_id":"sha256:164efe3e08666a47488db6c8f30bebaae6e763d5a9f2cb7e130502d82139f8f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H656Q2DR5TGB5A33AQWTTBWEN4/bundle.json","state_url":"https://pith.science/pith/H656Q2DR5TGB5A33AQWTTBWEN4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H656Q2DR5TGB5A33AQWTTBWEN4/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":"2026-05-31T10:41:49Z","links":{"resolver":"https://pith.science/pith/H656Q2DR5TGB5A33AQWTTBWEN4","bundle":"https://pith.science/pith/H656Q2DR5TGB5A33AQWTTBWEN4/bundle.json","state":"https://pith.science/pith/H656Q2DR5TGB5A33AQWTTBWEN4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H656Q2DR5TGB5A33AQWTTBWEN4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:H656Q2DR5TGB5A33AQWTTBWEN4","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":"f9616d8dd86e736517d2deaf576bd793d02b0de2cfacf753ab28841cf15366bf","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-12T23:13:38Z","title_canon_sha256":"785688b23e59d736f60d4641776953064f4b8cd6cc0013a55ec74398972065af"},"schema_version":"1.0","source":{"id":"1709.04082","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04082","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04082v2","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04082","created_at":"2026-05-17T23:42:31Z"},{"alias_kind":"pith_short_12","alias_value":"H656Q2DR5TGB","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"H656Q2DR5TGB5A33","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"H656Q2DR","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:164efe3e08666a47488db6c8f30bebaae6e763d5a9f2cb7e130502d82139f8f8","target":"graph","created_at":"2026-05-17T23:42:31Z","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 give an integrability criterion on a real-valued non-increasing function $\\psi$ guaranteeing that for almost all (or almost no) pairs $(A, \\textbf{b})$, where $A$ is a real $m\\times n$ matrix and $\\textbf{b} \\in \\mathbb{R}^m$, the system $\\|A \\textbf{q}+\\textbf{b}-\\textbf{p}\\|^m< \\psi({T})$, $\\|\\textbf{q}\\|^n<{T}$ is solvable in $\\textbf{p} \\in \\mathbb{Z}^m$, $\\textbf{q} \\in \\mathbb{Z}^n$ for all sufficiently large $T$. The proof consists of a reduction to a shrinking target problem on the space of grids in $\\mathbb{R}^{m+n}$. We also comment on the homogeneous counterpart to this problem, ","authors_text":"Dmitry Kleinbock, Nick Wadleigh","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-12T23:13:38Z","title":"An inhomogeneous Dirichlet theorem via shrinking targets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04082","kind":"arxiv","version":2},"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:b8c457fc8edc70165250d4c6c572681f382142825187a521a2bae4a0e4eb6306","target":"record","created_at":"2026-05-17T23:42:31Z","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":"f9616d8dd86e736517d2deaf576bd793d02b0de2cfacf753ab28841cf15366bf","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-12T23:13:38Z","title_canon_sha256":"785688b23e59d736f60d4641776953064f4b8cd6cc0013a55ec74398972065af"},"schema_version":"1.0","source":{"id":"1709.04082","kind":"arxiv","version":2}},"canonical_sha256":"3fbbe86871eccc1e837b042d3986c46f1abc6988a618ee9a6f26a84f4dfb1f47","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fbbe86871eccc1e837b042d3986c46f1abc6988a618ee9a6f26a84f4dfb1f47","first_computed_at":"2026-05-17T23:42:31.075969Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:31.075969Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CN4YTIiWD5UILN0PFgn8H8vrPFbTyMx99zP/HfTce1xs+ux4HhcxCXx4Mn4Jo+NocJRnJBGG+Zs94A/WiwV8Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:31.076548Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04082","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8c457fc8edc70165250d4c6c572681f382142825187a521a2bae4a0e4eb6306","sha256:164efe3e08666a47488db6c8f30bebaae6e763d5a9f2cb7e130502d82139f8f8"],"state_sha256":"2726a3d0e312f9f5f2fc385f439aabe128ecaf63818089981e4ff86f388567c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+vSgsb8ODbyTO+OFHiBRWNB/4AQ2zwoFxW9xAXftQ3kYUtJw59+A20VVxn6UpfOn+XUsWXsOxq6OYEv77nAhDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:41:49.659212Z","bundle_sha256":"73391d9a6afcae9739037b9a8b09f78aac901a59a5bd04201400d44225924d08"}}